Major changes are underway for this site:

• Some content has been or will be migrated to my new site, likelyso.com. The theme of the new site is "Your Health, Your Money. Worthy questions. Likely answers."
• All new posts appear at likelyso.com/blog.  A few of the posts listed below may be updated and migrated to the new site, but most will be archived.
• Some pages, calculators, and historical posts have been or soon will be deleted permanently.

NOTE: For better, more current information about rotated portfolios, go to: likelyso.com/money.

My posts since June have used historical data to introduce rotation as way to manage a diversified portfolio of stocks and bonds. Today's post launches an ongoing series of updates that will review how rotation works in real time, month by month, on a sample set of portfolios. Initially, the updates will be posted here. In time, they will move to a subscription newletter.

Sample Portfolios
Some of the portfolios use low-fee Exchange-Traded Funds (ETFs) available in any brokerage account; others use low-fee mutual funds similar to those typically available in 401(k) and 403(b) retirement plans. The funds and ETFs track well-defined indexes or, in exceptional cases, use quantitative methods that limit the discretion of the fund's manager. Some of the portfolios use a short three-month window to decide which ETFs or funds to hold; others use a longer 12-month window.

The portfolios were constructed from simulations that used at least 25 years of monthly historical data. Going forward, actual performance will be updated once a month. A strict rule for all the portfolios is that any change in a portfolio's composition is held at least until the next monthly update.

The sample portfolios are organized in four groups, corresponding to four types of investment goals or risk tolerances. Today's updates provide one example in each group. Other examples will be added in coming weeks.

All-Max Portfolios
The dominant goal of an all-max portfolio is to maximize total return in the long run. It aims to hold equities rather than bonds, except when bonds are demonstrably performing better than equities. The guiding principle is to rotate out of stocks and into bonds when the total return of stocks, relative to that of bonds, has weakened, or vice versa. The portfolio may be 100% in stocks or 100% in bonds. However, if the portfolio has more than one equity ETF or fund, such as one for domestic U.S. companies and another for international ones, then it may sometimes hold a mixture of stocks and bonds. That may happen, for example, if U.S. equities are stronger than bonds, but international equities are not.

Today's example for this group, shown in the chart above, is All-Max Global Markets 100-to-0 ETFs. It is contructed from four ETFs that track broad indexes of domestic and international stocks and U.S. Treasury bonds. At a given time, each ETF is 0%, approximately 25%, or approximately 50% of the portfolio, with a 5% variance that triggers rebalancing. The ETFs and their current allocations are:
​

• Vanguard Total Stock Market ETF (VTI). Now at 0%, its target level had been 25% in July.
• Vanguard FTSE Developed Markets ETF (VEA): Its current level is 0%, as it has been since June 1.
• Vanguard Long-Term Treasury ETF (VGLT): Its target level is 50% now, as it was in July.
• Vanguard Intermediate-Term Bond Index ETF (BIV): Now at 50%, it received the proceeds from selling VTI on August 1.

A forthcoming post will provide details on a 25-year simulation of this portfolio. In markets without a steady trend, including most of the past year, the portfolio's three-month window for evaluating ETF performance may generate choppy results. However, over the past decade or longer, it has outperformed benchmarks such as Vanguard's LifeStrategy Growth Fund or the composite of global equities, as the chart demonstrates.

Mostly-Max Portfolios
In this group, the blended goals are, primarily, to maximize total returns and, secondarily, to minimize drawdowns. For partial protection against sudden drawdowns, a mostly-max portfolio always holds a minority of its assests in a bond fund or ETF. It aims to hold a substantial majority in equities when they are strong relative to bonds, rotating to 100% in bonds only when stocks have weakened.

For this group, today's example is Mostly-Max Low Volatility 80-to-0 ETFs. See my recent post for a 25-year simulation of this portfolio. It is composed of the following ETFs, whose target levels remain unchanged from last month:
​

• iShares Edge MSCI Minimum Volatility USA (USMV). Currently 60%.
• iShares Edge MSCI Minimum Volatility EAFE (EFAV). Currently 0%.
• Vanguard Total World Bond ETF (BNDW). Currently 20%. It may rotate to 0% or to as much as 80%. BNDW holds equal portions of Vanguard's broad indexes for U.S. and international bonds.
• Vanguard Long-Term Bond ETF (BLV). Always 20%, as a hedge against sudden drawdowns.

This portfolio compares ETFs on a 12-month window and therefore tends to hold a postion for many months. In a forthcoming post, a similar portfolio using mutual funds will highlight the performance of Vanguard's excellent Global Minimum Volatility Fund (VMVFX).

Mostly-Min Portfolios
The blended goals of this group are, with high priority, to minimize drawdowns and, with less weight, to boost total returns. Today's example for this group is Mostly-Min US Balanced 60-or-0 Fund. As the chart above illustrates, the total return of this portfolio over the past 25 years has modestly exceeded a standard 60-40 mix of U.S. stocks and bonds. In doing so, the mostly-min portfolio avoided major drawdowns and matched the low volatility of 10-year Treasuries. The very simple strategy of this portfolios is always to invest entirely in one of three indexed mutual funds:
​

• Vanguard Balanced Index Fund (VBIAX), which targets 60% in U.S. equities and 40% in U.S. bonds.
• Vanguard Intermediate-Term Bond Index (VBILX), which invests 100% in diversified U.S. bonds. This fund has held 100% of the portfolio's assets since June 1.
• Vanguard Short-Term Bond Index (VBIRX), which the portfolio occasionally uses for temporary holdings.

Normally, the portfolio rotates between the 60-40 balanced fund and the intermediate bond  fund. However, to limit flip-flops and to honor the restrictions on frequent trading that investment firms and retirement plans typically impose, the portfolio will, on rare occasions, hold all its assets in the short-term bond fund. A detailed post later this month will explain the mechanics and long-term performance of this portfolio, including details about when and why to hold the short-term bond fund.

All-Min Portfolios
Here the overarching goal is to minimize drawdowns in a portfolio that never has more than a minority exposure to equities. The example today is All-Min Global Income 30-or-0 Fund. It has a simple strategy of investing all its assets in one of three indexed mutual funds:
​​

• Vanguard Target Retirement Income Fund (VTINX), which targets 30% in global equities and 70% in worldwide bonds, including some that are indexed to U.S. inflation.
• Vanguard Intermediate-Term Treasury Index (VSIGX). All the portfolio's assets have been invested here since January, and remain so this month.
• Vanguard Short-Term Bond Index (VBIRX). 

Normally, the portfolio holds either the 30-70 income fund or the intermediate Treasury fund for many consecutive months. However, to limit churn and honor restrictions on frequent trading, it may sometimes hold the short-term bond fund for a month or two. As will be documented in a forthcoming post, the rotation strategy of this all-min portfolio has, historically, achieved higher total returns with smaller drawdowns than investing exclusively and continously in either of its two main alternatives, the 30-70 fund or intermediate Treasuries.

Disclosures
These portfolios are presented for information only, not as investment advice. They are based on simulations that may not capture or reproduce every aspect of actual investing. Historical results are no guarantee of future performance. All investments are subject to risks. You may lose money, and your assets may be vulnerable to inflation. You are responsible for your own investment decisions.

Able to Pay LLC does not own, sell, or manage any of these portfolios. Alex Wilkinson may own similar portfolios in personal accounts.

On June 3, 2019, my post What Now: Sell, Rebalance, or Rotate? launched an on-going series comparing rebalanced portfolios with a new strategy of rotation. On that date, a simple version of the rotation strategy caused a portfolio invested entirely in stocks to convert all its assets to U.S. Treasuries. On the date of this post, July 1, 2019, another instance of that strategy caused a traditional portfolio of 60% stocks and 40% bonds to switch to 100% bonds. This post describes how the rotation strategy works, using these two portfolios as examples.

Different Portfolios for Different Goals
The two portfolios are alike in some ways and very different in others. Neither portfolio is always invested in stocks or always in bonds. Both do both. Neither portfolio holds a static mix of stocks and bonds. Both vary their mixture over time. One of the two holds Exchange Traded Funds (ETFs) and may switch them several times a year. The other holds traditional mutual funds and imposes controls to limit turnover. Yet both portfolios use rotation to achieve better returns and substantially lower drawdowns than traditional alternatives.

The two portfolios are suited to investors with different goals.

Suppose your primary goal were maximize long-term gains, even at the risk of some turbulence. Then you might find the chart above to be compelling. It shows that, over various 25-year time-periods from 1919 to 2019, spanning a variety of countries and currencies, the strongest returns, adjusted for local inflation, came from rotating between a high ceiling of 100% invested in stocks and a low floor of 0% in stocks. Call it a max-gain strategy of 100-or-0 rotation. Historically, this strategy has managed to sidestep most of the damage of prolonged drawdowns in stock markets, such as happened most recently in 2008-2009. However, it is vulnerable to sudden one-month downturns, such as the October crashes that exceeded 20% in 1929 and 1987, and numerous months with losses approaching 10%, including the recent demise in December 2018.

If one-month losses of that magniture seems a bridge too far, then the goal of your journey as an investor might be a compromise between maximizing gains and minimizing losses. Your preference would be a minimax strategy, as illustrated in the next chart. Taking a different prespective on the same extensive data as the previous chart, this one shows that the best compromise imposes a ceiling of 50% to 60% in stocks and a floor of 0% in stocks. That's a minimax stategy of 60-or-0 rotation. (50-or-0 performs virtually the same.)

Two risk-controls are at work here. With a ceiling of 60% invested in stocks, your exposure during a sudden 20% downturn is reduced to 12%. Furthermore, with a floor of 0%, you have no exposure to the bulk of a long decline in the stock market, provided that you rotate from stocks to bonds early in the decline. ​

To map out the routes of these financial journeys, let's examine the two specific portfolios that used rotation to switch from stocks to bonds on June 1 and July 1 this year.

Max-Gain Rotate 100-or-0
​This portfolio aims to maximize gains by moving its assets across three basic index funds. The moves occur, on average, about four times per year, possibly with tax consequences if executed in a taxable account. Since 1996, the portfolio has never held the same assets for a full year, though it occasionally came close. At a given time, it is invested entirely in one of three indexed ETFs:

• The entire U.S. stock market, via Vanguard Total Stock Market ETF (VTI) or a similar low-cost fund such as iShared ITOT.
• Non-U.S. stock markets as represented by Vanguard Total International Stock ETF (VXUS) or a similar low-cost ETF such as State Street SPDW.
• Long-term U.S. Treasuries with average durations close to 20 years, as represented by Vanguard VGLT or alternatives such as iShares TLT or TLH.

The portfolio's strategy is to review these index ETFs at the end of every month, and invest entirely in the one whose three-month total return is the highest. On June 30, 2019, using the Vanguard ETFs, long-term Treasuries ranked first at 5.71%; U.S. stocks were next at 4.08%; and international stocks were last at 2.80%. Because the portfolio had previously moved all its assets to Treasuries on June 1, 2019, no change was indicated for July.

Historical results for this portfolio can be closely approximated by Vanguard mutual funds whose indexes match the firm's current ETFs. For the 23-year period from July 1, 1996, to June 30, 2019, the hytpothetical performance of the three mutual funds, had it been possible to trade them like ETFs, would have been as shown in the chart below. One line in the chart shows the rotation strategy for Max-Gain Rotate 100-or-0. A second line compares the results of investing equally in the same three funds, 33.3% each, and rebalancing them at the end of the month if the allocation's total drift exceeds 5% (as when a fund in this portfolio went above 38.3% or below 28.3% of the portfolio's total value).

The rotated portfolio was superior to the rebalanced alternative in measurable ways. It had a bigger nominal return (14.7% vs. 7.6%) and a superior risk-adjusted return (7.5% vs. 0.5%). To reap these substantial benefits, however, one had to endure a maximum drawdown that was large (-18.8%). Painful as it might have been, that drawdown was mild compared to the rebalanced portfolio (-36.4%). 

Minimax Rotate 60-or-0
To place stronger limits on drawdowns, Minimax Rotate 60-or-0 accepts returns that are less stellar, though still very good. This strategy may be suitable both for taxable accounts and for IRA and 401k savings. On average, the portfolio has had one change per year since 1995, although it had a few of them in some years and occasionally went without a change for two years or longer. At a given time, the portfolio is invested entirely in one of two ways:

• A mutual fund that holds 60% U.S. stocks and 40% U.S. bonds, such as Vanguard Balanced Index Admiral Shares (VBIAX) or equivalent all-U.S. funds.
• A broad mix of 5-to-10 year U.S. corporate and Treasury bonds, such as Vanguard Intermediate-Term Bond Index Admiral (VBILX) or the equivalent. 

The portfolio's strategy is to review the performance of these two funds bimonthly (at the end of even-numbered months) and invest in the one whose total return is better over the previous 12 months. The bimonthly schedule reduces the portfolio's churn and honors the one-month limit that investment firms typically place on selling and repurchasing the same mutual fund. On June 30, 2019, the 12-month total return was better for the bond fund (VBILX, 9.99%) than for the balanced fund (VBIAX, 8.91%). A month earlier, the opposite was true. Hence the portfolio moved all its assets to the bond fund on July 1, 2019, to be left there for at least two months.

The chart above shows results based on the longest available history of the two Vanguard mutual funds (VBIAX and VBILX) from March 1, 1995, to June 30, 2019. The rotation strategy successfully side-stepped long declines during the dot-com collapse of 2000-2003 and the severe recession of 2008-2009. The traditional 60-40 index fund did not. Consequently, the biggest drawdown of the Minimax Rotate 60-or-0 portfolio was much smaller (-13.0%) than that of Vanguard's 60-40 fund (-32.6%). And recall that the max-gain strategy had a drawdown of -18.8% for the same period.

Yet, as the chart shows, the minimax strategy also met its other objective of generating decent returns. Though less amazing than the max-gain portfolio, minimax rotation did somewhat better than traditional 60-40 rebalancing (8.5% vs. 8.2% in nominal returns). In short, when compared to other alternatives, minimax rotation did indeed produce commendable gains at a notably lower cost in drawdowns and churn.

Some Technical Details
To understand the measurements and data underlying the charts and analysis in this post, see my posts last month, especially Best Options to Minimize Drawdowns and Floors and Ceilings, Part 2.

My previous post examined ways to minimize drawdowns in a portfolio. This one turns the table to study how best to maximize returns.

Admittedly, it's not a clean dichotomy. When analyzing drawdowns but confronted with portfolios that impose similar limits on them, the urge is strong to see how the portfolios compare on returns. The same urge will sneak into the storyline here. Focusing primarily on portfolio returns, I'll admit some consideration of drawdowns if the returns are not decisive. 

100 Years of Large-Cap Stocks in the U.S.
Shown in the chart above are key findings for large-cap stocks in the U.S. between April 1919 and March 2019. As I've noted previously, different 25-year segments of this period exhibited dramatically different results for investors. Yet across all the historical variations of that century, the trends captured in the chart were consistent. Looking closely, you can see three of them.

1. The pair of bars on the left show that holding a high percentage of the portfolio in large-cap stocks paid sizable real returns in the long-run. These returns are annualized and adjusted for inflation. The two portfolios represented by the bars on the left were 100% invested in stocks all or most of the time.
2. On the other hand, the pair of bars on the right show that if you adjust for the risk of drawdowns, then the relative returns of these portfolios were modest. A relative return is the portfolio's surplus over investing 100% in 10-year Treasuries, after compensating for the portfolio's incremental risk of drawdowns. The risk-adjusted bars on the right show that the same stock-heavy portfolios were barely a percentage point or two better than 10-year Treasuries. For the additional risk taken, the reward was limited. (An earlier post explains how I calculate relative returns.)
3. Finally, the color-contrast in the chart compares two methods of portfolio management. The blue bars show the average outcome of buying and holding large-cap stocks for a full 25-year cycle. The red bars average the same 25-year periods, but within a period, the portfolio's holdings rotate between being completely in large-cap stocks or wholly in 10-year Treasuries. The criterion for deciding whether to hold equities or Treasuries is the total return of those two assets in recent months (as explained in What Now: Sell, Rebalance, or Rotate? and in Best Options to Minimize Drawdowns). The message of the color-contrast in the chart is that rotation delivered better outcomes than buy-and-hold, because it more effectively controlled the risk of drawdowns.

"What about rebalancing?" you might ask. Was there a portfolio that rebalanced large-cap stocks and 10-year Treasury bonds to achieve best-in-class returns? The answer for the U.S. was, "No, not with any consistency." In three of the four 25-year periods since 1919, no rebalanced portfolio outperformed one that bought and held large-caps for the duration. In one case alone, 1919 to 1944, it was a close call. Then, rebalancing 90% in stocks against 10% in Treasuries ended in a dead-heat with 100% in stocks, as both methods had real returns of 7.3% and relative returns at 4.4%.

25 Years of Large-Cap Stocks in Germany, Japan & Australia
The results in other countries, however, were sometimes different from the U.S. In a post titled Does Rotatation Work in Global Markets?, I showed recent 25-year returns in three other countries, with local large-cap stocks and local 10-year Treasuries, invested in local currencies, adjusted for local inflation. In two of the countries, Germany and Japan, Treasuries outperformed the relevant large-cap index, and in the third, Australia, they almost did.

If you believe an oft-cited legend that stocks always beat bonds for holding periods longer than 20 years, this is not supposed to happen. But it did there, implying that it could here. In the unlikely event that you might foresee this outcome in advance, you could elect to rebalance a portfolio to target levels of 25% in stocks and 75% in Treasuries. As shown in the chart, doing so for Germany, Japan, and Australia between 1994 and 2019 yielded better real returns than any other rebalanced portfolio and, on average, also bested an all-stocks portfolio in those countries.

Even better results would have accrued by using the rotation strategy, placing 100% in large-caps when their recent total returns were temporarily better than local 10-year Treasuries and otherwise investing all the portfolio's assets in those Treasuries. Happily, for this strategy, you don't have to guess whether stocks or bonds will be stronger in the future. You simply adapt to whichever has been stronger in recent months.

A cautionary note, however, is that all the foregoing comments are limited to real returns. For relative returns, which adjust for the risk of drawdowns, the results were, to be blunt, pathetic. Considering the risks taken, no strategy that invested in stocks in these countries was much better, in the last quarter-century, than one that bought and held 10-year local Treasury bonds.

25 Years of Low-Volatility Stocks Worldwide
For completeness, should low-volatility stocks be considered when the goal is to maximize returns? It makes sense to consider them when trying to limit drawdowns, because by design, stocks chosen for their low volatility should, theoretically, fall less than the average equity when the stock market takes a tumble. On the upside, however, an advantage for low-volatility stocks is not obvious.

Empirically, academic research implies that such an advantage may exist (as reviewed, for example, in Andrew Ang's textbook on asset management). In the research, when equities were selected for a portfolio because their price-fluctuations were low or because they were weakly correlated with market averages, the studies reported that the portfolio's returns approximated or modestly exceeded those of the full stock market, even when it was rising.

​Accordingly, the next chart summarizes results averaged across three indexes of low-volatility stocks from April 1994 to March 2019. The indexes are tracked by iShares ETFs for the U.S., for developed countries outside the U.S., and for stock-markets globally. The trading histories of the ETFs were too short for this analysis, which was based instead on the index histories in U.S. dollars and on U.S. 10-year Treasuries.

On close inspection, several aspects of this chart are noteworthy.

1. ​​First, as in the academic research, a 6.8% real return for these low-volatility indexes over the last 25 years compared favorably to the 7.2% real return of large-cap U.S. stocks over a much longer history, which was shown in the first chart in this post.
2. Once again, the rotation strategy outperformed buy-and-hold.
3. Perhaps surprisingly, the relative returns for these low-volatility indexes were quite good on the upside. They did double-duty, in effect, generating stock-like returns while handily limiting the risk of drawdowns.
4. Rebalancing low-volatility stocks would not have been the method of choice for maximizing returns. At its best settings, rebalancing yielded just 4.6%, well below the levels attained for buy-and-hold and rotation. Furthermore, when adjusted for risk, it was unremarkable, like its counterpart in the analysis of Germany, Japan, and Australia. That said, if one's goal were to limit drawdowns with minimal effort, rebalancing 25% in low-volatility stocks against 75% in intermediate Treasuries would be attractive.

Key Takeaways

1. If you aim to maximize returns, ask whether you are willing to exert the discipline and monthly effort to apply the strategy of rotation. If so, rotating well diversified, low-volatility ETFs may generate the best risk-adjusted returns. Rotating broad-market averages should also reward you for the risks taken, scoring slightly higher than low-volatility ETFs on real returns but slightly lower on risk-adjusted ones.
2. Buying and holding stocks may often deliver better returns than buying and holding Treasury bonds, provided that the holding period is very long. Often. But not always! Even at 25 years, there are historical cases where long-held Treasuries have beaten long-held equities.
3. Rebalancing is not optimal for maximizing returns. As a strategy, its best application may be for goals that aim to reduce drawdowns.
4. A big caveat: For a goal that seeks a compromise between maximizing returns and minimizing drawdowns, the analysis in this post offers no guidance. That's coming in my next post in this series.

For these purposes, where the spending dates are indefinite or a few years away, an ideal portfolio would generate minimal drawdowns while offering a reasonable potential for  assets to grow. What are the best ways to construct such a portfolio? The historical results of some good options are summarized in the chart above. It compares large-cap stocks to the average of several low-drawdown portfolios. The data for the chart cover various countries, time periods, and methods of asset-management. All the methods that are averaged together in the chart drastically reduced drawdowns. Some of them achieved returns rivaling those of large-cap stocks. The effort they might require from you to manage your funds would range from virtually none to a modest, once-monthly review. This post reveals the details behind the average results in the chart, explaining how low-drawdown portfolios can be built and how they have performed historically.

Portfolio Options
To analyze the historical data, I designed portfolios to simulate risk-averse investors who chose to do one of the following:

• Invest entirely in Treasuries. As in my other posts, constant maturity,10-year Treasuries were used for this purpose. They correspond closely to mutual funds and ETF's that hold intermediate-term government securities. Except for periods when government policies or unusual financial conditions force interest rates to fall below the current inflation rate, 10-year Treasuries should be quite safe. Investing in them is the default choice, the benchmark against which all other low-drawdown portfolios are measured.
• Combine 10-year Treasuries with large-cap stocks. The rationale for this option was that diversifying a portfolio to include a small to moderate portion of equities should strengthen it. Treasuries and stocks tend to have a slightly negative correlation. In times when Treasuries fall in value, stocks may rise, on average. The key question is how much to invest in stocks to get just the right amount of compensation for the occasional weakness of Treasuries.
• Combine 10-year Treasuries with low-volatility stocks. When one's goal is to limit the drawdowns in a portfolio containing some equities, it would seem reasonable to favor the stocks that are least inclined to fall when the overall market plunges. This option is new, as mutual funds and ETFs for low-volatility stocks have become available only very recently. For most such funds, the available history is meager. Fortunately, one excellent set of data has worldwide low-volatility indexes with 25 years of history, just enough to match the 25-year periods analyzed throughout the series of posts that began here on June 3, 2019. (For specifics, see the section below titled "Some Technical Details.")

Given portfolios containing both Treasuries and stocks, the historical analysis examined two ways in which one might manage the portfolio's assets:

• Rebalancing. Set a target for the percentage of stocks to be held. Monitor the portfolio monthly, and, if it has drifted 5% or more from the target, exchange assets to restore the balance. For example, if the target is 15% but the current level has risen to 20% or fallen to 10%, restore the portfolio's funds to the 15% target. 
• Rotation. Set a ceiling for the percentage of stocks held in the portfolio during times when, compared to Treasuries, stocks have been performing well. Also set a floor for the percentage of stocks to be held when stocks have been performing worse than Treasuries. Once a month, compare the total return of stocks and that of Treasuries, over a window of a few months, and respond accordingly. For example, suppose that the ceiling were 80% and the floor 20%; that this month's review showed Treasuries to be doing better than stocks; and that last month's review showed the opposite. Then you would exchange funds to move from last month's ceiling of 80% stocks to this month's floor of 20%. In general, each monthly review would dictate one of three actions:
  1. Exchange funds to match the desired floor or ceiling value, if the recent total returns of stocks and Treasuries indicate a switch, or ...
  2. Rebalance to maintain the current allocations, give or take 5%, or ...
  3. Do nothing if this month's better-performing asset is the same as last month's, and the portfolio's allocations are within 5% of the intended values.

Best Options
The chart below shows drawdown metrics for multiple portfolios, across a variety of countries and time-periods. Although the data and results are multi-faceted, the main message is quite simple. Compared to an all-stocks portfolio, several excellent portfolios reduced drawdowns significantly, all of them by nearly the same amount, over the historical spans of this analysis.

The left half of the chart aggregates the same data-sets as in my other recent posts: large-cap stocks and 10-year Treasuries across four 25-year periods for the U.S. since 1919, in dollars, and the most recent 25-year period for Germany, Japan, and Australia, in their local currencies. The right half adds the most recent 25-year period for a global stock index (in dollars); the same period for US 10-year Treasuries; and the average over that time of three low-volatility indexes, one for the U.S., another for developed countries outside the U.S., and the last for worldwide stocks including the U.S. (See "Some Technical Details" below.)

Both sides of the chart show drawdowns measured three ways: the maximum cumulative decline within a 25-year period, the worst single month in that period, and the average accumulated loss for all months when the portfolio's value was falling.

As would be expected, portfolios invested 100% in stocks had big drawdowns, despite achieving good cumulative returns in the long run.  Their maximum drawdowns in 25 years averaged -55%. Their worst-month drawdowns and their average on-going drawdowns  were between -15% and -20%.

On all these measures, the low-drawdown portfolios excelled. Their maximum cumulative loss during a 25-year period was consistently better than -10%; the worst-month drawdown was, on average, between -4% to -6%; and the average on-going loss during periods of decline was -2% to -3%.

The next chart shows additional measurements for the best portfolios:

• ​Drawdown Reduction: This value is the percentage by which a portfolio avoided the losses of an all-stocks portfolio for the same country or region and the same 25-year period.
• Real Return: This metric for a portfolio's performance included reinvestment of dividends and interest, and was adjusted for local inflation over the relevant time-period.

 Let's examine these portfolios one by one:

• 10YTreas Local. Results summarized in the two left-most bars in the chart came from investing 100% in 10-year Treasuries, both from 1919 to 2019 in the U.S. and from 1994 to 2019 in Germany, Japan, and Australia, always in local curriences. The maximum, worst-month, and average drawdowns of these all-bond portfolios were, on average, 81% better than investing locally in large-cap stocks. The total returns were 3.2% above local inflation.  A comparable all-stocks portfolio, with its large drawdowns, would have had better returns, but not hugely so (4.9%, not shown in the chart).
• Rebalance LC 10%. Portfolios under this heading rebalanced 10% in local large-cap stocks and 90% in local 10-year Treasuries, over the same countries and time-periods. The reduction of drawdowns was slightly better than all-Treasuries (83% vs. 81%), as was the real return (3.6% vs. 3.2%). Results nearly as good would have accrued if the rebalanced allocation to stocks had been 15%. In short, with rebalancing as the strategy, a modest allocation to local large-cap stocks had slightly less risk and better returns than investing entirely in local 10-year Treasuries.
• Rotate LC 30-or-10. Across a comprehensive set of rotation strategies, the best performance for the same countries and 25-year periods resulted from swapping between a ceiling of 30% and a floor of 0% in local large-cap stocks. Over time, this strategy averaged about 19% in stocks and 81% in local Treasuries (with the time in stocks occurring only when they had done better than Treasuries over a recent three-month window). This portfolio, too, outperformed the all-Treasuries benchmark, reducing drawdowns comparably (82% vs. 81%) and achieving better real-returns by a good margin (4.7% vs. 3.2%).
• 10YTreas US$. To evaluate low-volatility ETFs from 1994 to 2019, the analysis emulated the behavior of an investor in the U.S. In effect, the analysis used dollars to purchase U.S. and international low-volatility ETFs, and compared the results to investing dollars either in U.S. Treasury bonds or in a worldwide index of stocks in all developed countries including the U.S. As shown in the chart above, a portfolio of 10-year U.S. Treasuries held for 25 years, starting in 1994, reduced drawdowns by 77%, compared to investing entirely in worldwide stocks for the same period. While the return of the all-equity index exceeded U.S. inflation (5.2%, not shown in the chart), the U.S. Treasury benchmark also did well (3.5% above U.S. inflation). 
• Rebalance MV 25%. When applied to minimum-volatility indexes for large-cap and mid-cap stocks, the rebalancing strategy that generated the smallest drawdowns had an allocation of 25%. That's notably higher than the allocation of 10% that best reduced drawdowns for all large-cap stocks. Rebalancing to 25% for minimum volatility reduced drawdowns more than investing in benchmark U.S. Treasuries (82% vs. 77%). It also generated better real returns (4.6% vs. 3.5%).
• Rotate MV 40-or-15. For the rotation strategy, the combination of floor and ceiling values that best limited drawdowns was 40% at the ceiling and 15% at the floor. Over the most recent 25 years, drawdowns were reduced 84% by the strategy of swapping between 40% and 15% in minimum volatility indexes while investing the remainder in U.S. Treasuries. Real returns were the best of all methods (5.3%), much better than the benchmark for Treasuries (3.5%) and on par with buying and holding all stocks in the worldwide index (5.2%, not shown in the chart).

Key Takeaways
If your primary goal is to limit drawdowns on investments to be spent more than a year or two in the future, several good options are available. The choice between them may depend on how much effort you are willing to put into monitoring and managing your portfolio.

1. As a hands-off, low-effort method, investing entirely in local, intermediate-term government securities, comparable to 10-year Treasuries, is certainly a good choice. It is likely to generate better returns than bank deposits or money-market funds, to stay ahead of inflation in most periods, and to suffer drawdowns only temporarily and modestly. That said, this strategy is not completely risk-free. The cautionary counterexample is 1944 to 1969 in the U.S., when 10-year Treasuries fell behind inflation by -0.7% per year, resulting in a cumulative 16% loss in buying power over the 25-year period.
2. Rebalancing requires a bit of work. If done with a low allocation to stocks, around 10% to 15%, it can be safer than the all-Treasuries method, and it may generate modestly better returns. It certainly seems worth the effort (and possibly worth the expense, if you get your investment firm to do the work).
3. Rotation, like rebalancing, will require you to monitor your portfolio every month. The necessary effort is probably not much more than doing your own rebalancing. To limit drawdowns, the best settings for the rotation strategy were competitive with Treasuries and with rebalancing. Significantly, rotation bested all other strategies on real returns. (For more examples, see Rotating Out of Harm's Way and Does Rotation Work in Global Markets.)
4. Low-volatility funds seem particularly well-suited for portfolios whose goal is to minimize drawdowns. Had you opted for rebalancing, you would have had better returns at no additional risk by targeting 25% in minimum-volatilty stocks than by maintaining 10% or 15% in large-cap stocks. A similar advantage for minimum volatility stocks also held, over the most recent quarter century, for the rotation strategy.

Some Technical Details
Information about technical details in an earlier post in this series apply to the findings reported here. Additional details follow.

1. Only monthly data was available for some of the countries and time-periods in this analysis. For monthly rebalancing, a threshhold of 5% works well. Had weekly data been available, the preferred method would have been to check weekly and rebalance if the drift surpasses 3%. See my article on rebalancing for a comprehensive analysis.
2. In the results reported here, the window for rotation was three months, unless specifically stated otherwise. However, in findings not displayed here, windows from two to six months often performed similarly in the long run. For some purposes, longer windows up to one year may be advisable for some investors, e.g., to limit churn that might have tax-consequences.
3. The low-volatility indexes were from MSCI, for the period from April 1994 to March 2019. These indexes underlie three ETF's offered by iShares: USMV for medium-to-large U.S. companies, EFAV for medium-to-large companies in developed countries outside the U.S., and ACWV for companies in both developed and developing nations worldwide. Although the underlying indexes have a quarter-century of data, the ETF's have traded publicly for far less time. Were you to consider only the shorter trading history of the ETFs, you might conclude that buying and holding low-volatility ETFs at a high percentage of your portfolio would be a very safe strategy, even better than holding all-Treasuries. However, the trading history includes no major collapse in stock prices, such as the dot-com bust of 2000-2003 and the deep recession of 2008-2009. During those periods, the indexes had substantial drawdowns, averaging -40%. Using the 25-year index history, instead of the shorter ETF history, captured drawdown risks of this magnitude.
4. Drawdown metrics were calculated as follows:

• Maximum Drawdown: For each month in a 25-year period when the portfolio's value is lower than it's previous peak in the period, calculate the percentage loss. Over the entire 25 years, calculate the maximum of this monthly value.
• Worst 1-Month Drawdown: For each month in a 25-year period, calculate the percentage change in the portfolio's value compared to the previous month. Find the minimum of these values.
• Average Drawdown: For each month in a 25-year period, calculate the percentage change in the portfolio's value compared to the previous month. For all months in which this value is negative, calculate the average.
• Drawdown Reduction: For a 25-year period, find the Maximum Drawdown, Worst 1-Month Drawdown, and Average Drawdown values for a portfolio invested entirely in a reference set of stocks, designated as m(s), w(s), and a(s), respectively. Find the same values for a comparison portfolio, designated as m(c), w(s), and a(c), respectively. Then calculate the average of 1 - m(c)/m(s), 1 - w(c)/w(s), and 1-a(c)/a(s).

Yesterday's post showed how four investment strategies handled two consecutive 25-year periods between 1944 and 1994, for stocks and bonds in the U.S. Today I'll examine the same strategies over two additional 25-year periods, bookending the previous ones and thus spanning a full century. The first period, 1919 to 1944, had the Great Depression; the second, 1994 to 2019, had the dot-com crash and the Great Recession. Truly, those were stress-tests for any portfolio.

The two charts below capture the main points of interest. (Or, to follow the story-line from the beginning, go back to my June 3 post, What Now: Sell, Rebalance, or Rotate?)

Had you held the S&P 500 (or something similar) throughout the bull market of the 1920's, the dreadful 1930's, and much of World War II, you would have suffered two big drawdowns. The killer, exceeding -80%, took three excruciating years from 1929 to 1932. Another, in 1937, was swifter and, at -41%, must have felt almost as frightful. Look, too, at 60-40 rebalancing! It offered no shelter, hugging the all-stocks portfolio as if in numbed desperation.

Treasury bonds, by comparison, gave an astoundingly smooth ride, perhaps because the bond-market was less mature than it is now or, more likely, because the U.S. Treasury controlled interest rates in a much different manner than the Federal Reserve has done since the 1950's. Yet, as good as the all-Treasury portfolio might have been, it was easily surpassed by 100-or-0 Rotation, a strategy that went all-in on stocks when their recent trend was better than 10-year Treasuries, and all-in on those same Treasuries when they had lately been the better of the two options. In this analysis, "lately" means, very simply, not last month, but the last several.

A half-century later, remarkably similar patterns began to emerge, like old music found in tattered manuscripts and replayed on new instruments. From 1994 to 2009, stocks had a bull market whose brassy boasting was soon silenced by a da capo of drawdowns. For its part, a 60-40 rebalanced porfolio held close to the rhythm of stocks. Treasuries made steady progress, while moving to a subdued drumbeat. Once again, a portfolio of 100-or-0 Rotation avoided firm commitments and, charmingly fickle, danced with each month's better partner. Doing so, it largely side-stepped the worst moments and outdid all others.

Taken together, the four 25-year periods shown in today's and yesterday's posts constitute a statistical sample. Averaging measurements across the four intervals generates an estimate of the outcomes one might expect in future quarter-centuries. For example, an average of the four maximum drawdowns will estimate the expected maximum drawdown in any future 25-year period.

Estimating in this way is more useful than simply calculating the maximum drawdown over the past 100 years. You and I won't be investing for 100 years.  The expectation for any 25-years, based on an admittedly small sample of four, is statistically more reliable and pragmatically more relevant than an expectation for 100 years, based on an even smaller sample of one.

Accordingly, the summary chart below shows several expected outcomes for future quarter-centuries. It also compares expectations across the four investment strategies.

Were you to invest entirely in the S&P 500 over the next 25 years, you should brace for a drawdown of about -48% at some point, plus a bad month with a paper loss of -19%, as you march toward an eventual inflation-adjusted annual return of 7%. In short: nice gains, big pains. Investing entirely in 10-year Treasuries would likely have much smaller drawdowns  of -9% at the low point and -5% in the worst month, but your gains would be correspondingly reduced to about 2% or 3% more than inflation. A typical plan of 60-40 Rebalancing would reduce the pain of drawdowns, compared to the S&P 500, while also sacrificing some gains. Best of all, however, would be 10-or-0 Rotation, which could be expected to generate better gains than the S&P 500 and smaller drawdowns.

My next post will apply the same four portfolios to countries outside the U.S., for the most recent 25-year period.

Historically, you would have gotten good returns by simply holding a target percentage of your portfolio in stocks over many years, keeping the rest in 10-year bonds, and rebalancing periodically if the percentages drifted from your target. However, you would have suffered many drawdowns, sometimes extreme, lasting months or years. A week ago, I gave some examples as part of a series that started with my June 3 post for current U.S. markets, What Now: Sell, Rebalance, or Rotate? 

This week's posts will introduce rotation as an an altenative to rebalancing. Today's examples are for U.S. stock and bond markets dating back to 1919. Four investment strategies are applied to this 100-year period:

• 100% in the S&P 500, with dividends reinvested.
• 100% in 10-year Treasury bonds with interest reinvested.
• 60% in the S&P 500 and 40% in 10-year Treasuries. At the end of each month, either reinvest the income in its source or, if the percentage in stocks has drifted to 55% or 65%, then rebalance stocks and bonds to their respective targets.
• Either 100% in the S&P 500 or 100% in 10-year Treasuries, according to their recent performance, checked at the end of each month.

Comparing the strategies over the 100-year period from April 1919 to March 2019, 60-40 rebalancing and 100-or-0 rotation were virtually identical in one key way: over the long term, their equity exposures were virtually the same, 60.9% for rebalancing and 60.6% for rotation. In both cases, the portfolio tended to drift more toward stocks than toward bonds. For rebalancing, the long-term exposure to stocks was therefore slightly above the target of 60%. For rotation, the similar outcome over the full 100 years is an interesting coincidence. However, over shorter 25-year intervals, the stock-exposure of 100-or-0 rotation was variable.

Between 1944 and 1969 (depicted above), 100-or-0 rotation was 69% in stocks, on average. That happened because during these years, stocks strongly outperformed bonds. (See this earlier post for some possible reasons.) Then, continuously holding 100% in the S&P 500 would have been the best strategy; rotation often avoided bonds and thus out-performed rebalancing; and Treasuries were exceptionally weak, actually falling behind the inflation rate.

The next 25 years told a different story, as illustrated below. A sharp recession in the mid-1970's, followed by high inflation and high interest rates, then by prolonged rate cuts, combined overall to make the total return of bonds competitive with stock-returns. The strategy of 100-or-0 rotation responded in kind, allocating even-handedly, with an average stock-exposure of 53%. For the full 25 years, rotation beat all the other strategies, not by putting all its eggs in one basket, or by juggling two baskets at all times, but by opting periodically for the basket that better suited the changing financial environment.

The four 25-year periods since 1919 exhibited a variety of environments, including the two described above; the bull market of the 1920's and Great Depression of the 1930's; and the dot-com bubble, Great Recession, and recent bull market of the 21st century. Across it all, if given 25 years, a strategy of 100-or-0 Rotation ...

• Beat 60-40 Rebalancing, every time
• Beat 100% invested in the S&P 500, three of four times
• Beat 100% placed in 10-year Treasuries, every time
• Beat inflation handily, for every 25-year period

In forthcoming posts, I'll continue this introduction to rotation as an investment strategy, examining questions like these:

• Using both raw returns and risk-adjusted metrics, how did rotation fare across 25-year periods and across countries?
• What about drawdowns, as in "flash-crashes" and major recessions? Did rotation handle them better than rebalancing?
• Is 100-or-0 the best way to do rotation, at all times and for all investors? Or would less drastic exchanges be better, depending on circumstances?

Finally, regarding how, exactly, to implement a rotation strategy, I will get there in due course. The main idea is pretty simple: check monthly and pick the better of two investments, stocks or bonds. I'll save the specifics until more of the details and nuances have been explained.

Suppose from 1944 to 1969, you held and rebalanced a portfolio matching the S&P 500 index and 10-year U.S. Treasury bonds. Would that have been the optimal investment strategy for those 25 years? This post answers the question, using data similar to posts earlier this week on recent 25-year periods for the Nikkei 225 in Japan and the Dax 30 in Germany. It's all part of a series that follows up my June 3 post about current U.S. markets, What Now: Sell, Rebalance, or Rotate? 

Comparing this chart to the previous ones for Japan and Germany, one difference stands out. Stocks were indisputably the superior investment. The worst drawdown in the total return of the S&P 500 from April 1944 through March 1969 was -22.3%. In the usual parlance, that's merely a "correction," not a "crash." In the worst single month, had you held all your money in stocks, your loss on paper would have been -14.4%. Those drawdowns, admittedly not small enough to match Treasury bonds, were far less painful than the maximums exceeding -65% and the monthly values around -25% for stock-portfolios in Japan and Germany from 1994 to 2019.

Remarkably, the cumulative real return of an all-stocks portfolio in the U.S., from 1944 to 1969, was 10.4% per year. After inflation! Incredible. The real buying power of your dollars would have grown 11-fold in 25 years. Of course, you had to be there. You had to be alive  then with money to invest. And you had to be smart enough or lucky enough to place all your chips on stocks, at a time when the world war was not yet over, the G.I. Bill not yet conceived, the baby-boom not begun, interstate highways unknown, air-travel restricted to the wealthy, and rationing of necessities the norm. Maybe you would have foreseen that there was nowhere to go but up.

Or maybe the habits of rationing food and buying war-bonds would have inclined you toward the perceived safety of Treasuries. What a mistake that would have been! Over the next 25 years, your real returns would have gone negative. Treasury bonds, in that period, were anything but safe. Cumulatively, they suffered a -16% loss in buying power, as their -0.7% real rate of return compounded. No single month announced this loss. The worst one was merely -2.4%. Japan's and Germany's more recent government bonds had monthly drawdowns twice that amount, but they also had more numerous months of positive, inflation-adjusted returns that generated real gains in the long run.

​The quarter-century from 1944 to 1969 was, coincidentally, when the Bretton Woods Agreement governed global currencies. It made the dollar dominant, governing world markets, for better or worse, by the force of U.S. ownership of the majority of the world's gold. Interest rates in the U.S. were capped for many years early in that period, for fear of post-war deflation, when the reality was an inflationary spike in prices. Then, when interest rates were belatedly allowed to rise, they did so slowly but inexorably for the rest of the period, causing bond prices to fall, also slowly and inexorably. Perhaps misguided monetary governance like this will never happen again. Or maybe not this pattern in particular, but another one crafted in a future time of uncertainty, with similar unforeseen and unhappy consequences. We won't know until, if, and after it may happen.

In the final analysis, the U.S. experience from 1944 to 1969 conveys the same lesson as did the German and Japanese results for 1994-2019. Had a post-war investor in the U.S. opted for the compromise of investing half in stocks and half in Treasuries, rebalancing them monthly to 50-50, if needed, when they drifted to 45-55, then the outcome after 25 years would have been quite satisfactory. In round numbers, the maximum drawdown would have been a tolerable -10%; the worst month, only -8%; and the annualized real return, a handsome 5%.

Summing up the three cases, we have one (Japan, recently) where going all-in on bonds was best; another (the U.S., a half-century earlier) where that would have been a disaster; and two where stocks were best, once by a small amount (Germany, recently) and once by a huge margin (the post-war U.S. again). A rebalancing strategy was never best nor worst, yet all three times it beat inflation. The rub, however, is that rebalancing only partly managed the problem of severe drawdowns.

Next week, posts in this series will continue with a fresh look at a different strategy, rotation, to examine whether it can succeed when rebalancing comes up short.

On June 1, 2019, a new method I've been analyzing recommended rotating out of stocks and into bonds, in both tax-sheltered and taxable accounts, except for low-volatility stocks. The method was developed from 100 years of historical data for US stocks, treasury bonds, and inflation; 25 years of data for international stocks, bonds, and inflation; and 25 years of indexes for minimum volatility stocks worldwide. Here's a chart that illustrates how the method would have performed since 1919 in the US. ... To see the chart and read the rest of this post, go to my new website: https://likelyso.com/why-rotate

Accurately measuring whether stocks are over- or under-valued is hard enough. Yet even if that problem were solved, others would remain. An indicator that predicts a big change in stock prices over the near term is likely to have a wild margin of error. Longer term, the error-rate may decline, leading to a safer, more confident prediction, but the price-change will also fade to a smaller size. Is there any way to have it all: calculate a credible benefit, capture it safely, and bank it soon?

Earlier posts on this topic proposed how best to measure whether stocks are over- or under-valued. To recap, three ideas are key.

• According to solid academic studies, Shiller's ten-year CAPE is a good starting point. Andrew Ang's Asset Management (chapter 8, section 5.2 ) explains CAPE's uniquely reliable, if somewhat modest, power as a predictor
• The standard measurement of CAPE can be improved by computing it over a longer period than ten years with a method that gradually reduces the weight of older data, and by applying logarithms to ensure that high and low readings are judged evenly.
• Some credence should be given to the possibility that CAPE has its own long-term trend. Predictions can be improve by filtering out this trend, at least partially.

"Corrected CAPE" is the term used here to designate a metric that applies all these ideas. To learn more, follow the links above.

As of early 2016, the corrected CAPE is rather high, approximately +0.4. A corrected CAPE this much above a neutral value of zero implies over-valued stocks, hence a risk that future returns from stocks will be less than normal. Given this reading, how much weakness in stock prices might one expect? Is a swift decline likely, or an extended period of lackluster gains, or what? The answer, it turns out, depends on whether the goal is to predict changes for next year, the next decade, or even farther into the future.

In the chart above, the CAPE Effect is a multiplier that tells how much to adjust the future returns of U.S. stocks, given a value of the corrected CAPE. The blue dots are actual data points from a comprehensive study covering the period from 1896 through 2015. The red line is a statistically fitted model used in our calculators.*

Given corrected CAPE's early 2016 value of +0.4, a one-year forecast is an effect of roughly 0.4 * 0.14 = 0.056 on a log scale. The spreadsheet function EXP(0.056) converts back to a percentage, 5.8%, which is the predicted reduction in real (inflation-adjusted) stock-returns over the next year, because of the current over-valuation. For the 1896-2015 period of the study, compound real returns were about 6.6% per year, so the year-ahead prediction is a return of 6.6% - 5.8%, or a meager 0.8% better than inflation, including reinvested dividends. With economists currently predicting an inflation rate of about 2%, the nominal return would be 2.8%. That's less than the historical return of ten-year Treasury bonds.

​If U.S. stocks were held longer, for the next 20 years, the chart predicts the effect would still be negative but less drastic, roughly half as large. The compound, inflation-adjusted return would be reduced about 2.6%. Instead of enjoying average real returns of 6.6% annually for two decades, one's portfolio of U.S. stocks would grow 6.5% - 2.6% = 4.0% per year, above inflation. That's not shabby. It's better than bonds, but below average for the long-term performance of stocks.

​What the chart says, in short, is that buying stocks today is like paying a premium price for a house when real-estate is hot. Even after holding the investment for many years, one's annualized profits may be tepid.

There's a problem, however, in making decisions like these. The next chart shows why. It presents the same data points (the blue dots), bracketed by their margins of error.** Statistically, most of the historical data falls between the upper and lower margins of error (the orange lines). A big gap between the lines implies great uncertainty; a narrow gap means the prediction is more trustworthy.

For stock investments held one year, the margin of error is extreme. While the average one-year effect might be alluring, actual one-year results have often been very different, in both directions. Evidently, a short-term forecast is both big and wild. It's like predicting tomorrow's weather to be a 90% chance of rain, maybe a steady downpour, maybe a brief drizzle.

At the other extreme, for a holding period of 30 to 40 years, the prediction is much more precise, thanks to a tiny margin of error. It's a safe forecast, but the effect has become small. Now the weather forecast is for a certainty of rain this season, totaling 5 to 6 inches, but there's no telling which days will be wet.

The ideal case would be to find the points on the chart where the range of uncertainty excludes a zero effect, which appears to happen after about three or four years, yet the effect-size remains large enough to matter, which seems possible up to the mid-twenties.

Our calculators quantify these ideas by giving a weight to the corrected CAPE.*** As the margin of error decreases, the weight goes up. At the same time, as the effect-size declines, the weight goes down. The statistical model finds an optimal way to calculate the weights, and, it so happens, the weight steadily increases from one to 24 years, then very gradually declines.  

For a concrete example, start with the chart below. It shows how our calculators simulate the portfolio of a hypothetical investor who matches this description:

• She has moderate preferences. Her goal is a compromise between maximizing gains and minimizing losses, and she is somewhat able to tolerate ups and downs in her investments.
• She plans to start spending her savings in two years, when she will retire. Given her health status and current age, she expects to continue spending for a total of 25 years.
• If she had children, she might add another five or ten years of spending, to allow her heirs to spend-down any residual savings after she dies. But she has no children and prefers to maximize her retirement budget by spending all her investments. Her home equity provides a safety net.

The calculator's statistical model, shown by the red line, sets the investor's exposure to stocks, given her preferences and the time remaining until invested funds will be spent.^ The blue bars are slices or portions of her portfolio, one for each year of anticipated spending.

Because this particular investor's preferences are moderate, the calculator assigns 65% as her maximum exposure to stocks, for investments held 20 years or longer. Anything not invested in stocks goes to bonds, at durations that depend on how soon the funds will be spent.

More than half the portfolio will be held 12 years or longer, and is therefor invested near the maximum level of 65% stocks and 35% bonds. The other half is invested with increasing caution, depending on proximity to the retirement date. As the investor ages and begins to spend her savings, the blue bars will, in effect, march to the left in the chart while staying under the model's red line, thus causing her portfolio to become more conservative over time. Right now, with retirement still two years away and many years of longevity on the horizon, her investments are, overall, about 60% in stocks.

That's without any adjustment for stocks being over- or under-valued. The next chart shows how much this investor's profile would have changed, when adjusted by the corrected CAPE, had the current date been any year between 1920 and 2015. Over those 96 years, 80% of the data fell between the lines shown as High CAPE and Low CAPE (10% were even higher, 10% even lower).

​As it happens, the corrected CAPE in early 2016 is approaching the value marked by the blue line, where High CAPE means that stocks are over-valued. In times like these, the hypothetical investor's profile gets shifted to the blue line, where the maximum invested in stocks is adjusted down to about 50%. On the other hand, if today's corrected CAPE were like the green line in the chart, with stocks a real bargain (Low CAPE), then more than 75% would be invested in stocks to be held for a decade or more. Notice, however, what happens for near-term holdings that will be spent in two or three years. Here, the calculator makes hardly any adjustment for CAPE.

If the holding period were extended well beyond 30 years, the adjustment would diminish somewhat because the effect of CAPE would very gradually fade. But it would not vanish completely in any normal lifetime. To give a specific example, if you had bought stocks near the top of the dot-com bubble in late 1999, when over-valuation of stocks peaked, your returns, even if you held the stocks for many decades, would likely be poorer than if you had purchased at a more normal price.

One final note is important. Some time in the next decade or two, stocks could take a tumble. If they do, the corrected CAPE may fall to a level that recommends a higher-than-normal exposure to stocks. If you adjust your stock allocation periodically, perhaps every quarter or year, according to the calculator's then-current recommendations, the result will be to move some of your holdings in and out of stocks as they become cheap or expensive, taking into account your evolving plans to spend your savings. In that sense, today's relatively expensive stocks are not a permanent penalty for your portfolio. They are a reason for caution that will last only until more optimism is warranted.

* The data for the study were monthly prices of the S&P 500, or a reasonable surrogate, and corresponding estimates of consumer inflation, from 1871 to 2015, as compiled by Robert Shiller. The period from 1871 to 1895 was used to initialize the values of the corrected CAPE. The plotted points in the chart are slopes from regressing LN(r) on LN(c), where r is the annualized real return on stocks, with dividends reinvested, and LN(c) is the corrected CAPE as described in an earlier post. The fitted line is a power function of the form s = -b * POWER( m, y ) where s is the slope; b and m are fitted constants; and y is the holding period in years.

** Statistically, the margin of error is the standard error of the least-squares estimated slope, on a natural-log scale.

*** The weight is k * s / e, where s is the slope; e, the standard error of the slope; and k, a fitted constant. All are on a natural-log scale. The weight is fitted to optimize the natural-log of the annualized real return.

^ The calculator's model for stock-allocations is an exponential function of the form:
p = q + u * ( 1 - EXP( - (y-1)/v) ),
where p is the portion allocated to stocks; q is a minimum allocation when there is one year left before spending starts; q + u is the upper limit or asymptote of the stock allocation; y is the holding period or "slice"; and v is a factor that controls the rate of rising from the minimum to the asymptote. As described here, this model worked better than other growth functions as a method of optimizing returns.

​

Measured by CAPE, stocks in the U.S. seem expensive now. But CAPE has an historical bias. In the early 20th century, it drifted to consistently low values; in recent decades, to persistently high ones. These trends occurred whether the stock market was booming or busting. After removing CAPE's apparent bias, stocks in 2016 seem nearly normal. Which of these opposing views is more credible?

As noted in an earlier post, CAPE is a uniquely reliable predictor of future stock prices. It tends to correctly forecast the long-term direction, up or down, although it does better for the distant future than for next month or even the next year or two. A refined version of CAPE, called LogrCAPE0.33%, is shown below for the years from 1896 through 2015.* 

Right now, the computed value of this version of CAPE is above 0.5, as indicate by the last plotted value at the right end of the blue line. That's higher than the market peaks in 1929 and the late 1960's, which were excellent times to cut back on stock-ownership. However, the long-term trend of CAPE, plotted with the red line, suggests that CAPE was depressed in value throughout the early 20th century, then rose to higher levels in recent decades. A majority of the below-zero observations occurred before 1950, yet virtually every value since the late 1980's has been above zero. An extension of the trend-line suggests that CAPE may continue to have high relative values for another decade or more.

It's reasonable to ask whether CAPE would be a better predictor if its long trend were taken into consideration. Accordingly, the next chart adjusts the LogrCAPE0.33% metric by removing the trend.** The picture is more balanced, with values above and below zero occurring in every quarter-century. And the new trend-line is flat (a statistical necessity). Looking at recent values, the selloff in 2008 and early 2009 now looks like a good buying opportunity, with the de-trended CAPE hitting a low of -0.5. The current, near-normal value raises no alarm to avoid stocks.

One reason to be skeptical of the de-trended CAPE is that many other indicators say stocks are over-valued and are thus likely to weaken in the future. But what if all the indicators, including CAPE, share the same historical bias? Perhaps something about global economies or contemporary finance has changed fundamentally since late in the last century and will persist for decades to come. Maybe investors have more confidence in long-term payoffs from owning stocks because they see value in more global trade, or in better management of national economies, or in reduced fear of world wars and pandemics. Who knows? Lending credence to this speculation is a telling statistic. In a comprehensive analysis of U.S. markets since 1896 for periods of owning stocks from 1 to 40 years, the de-trended CAPE explained more variance (26%) in real returns than did LogrCAPE0.33% (20%).***

A rational person could take either side of the argument. Our calculators strike a compromise. They report value-adjusted allocations to stocks and bonds by first averaging LogrCAPE0.33% and the de-trended CAPE, then estimating allocations and returns from that average. Additional details about the statistical machinery of the calculators are posted here.

* For improved statistical results, the refined version computes a very long-term 0.33% exponential average of companies' earnings, instead of the classical 10-year ordinary average. It then takes the natural logarithm this ratio: current, inflation-adjusted prices divided by the exponentially averaged earnings. In a slight improvement on the standard method, the current month's price adds in the inflation-adjusted value of one month of dividends.

** The trend-line is a log-linear cubic polynomial. The de-trended CAPE is simply LogrCAPE0.33% minus the value predicted by the least square fit of the cubic model.

*** The to-be-predicted variable in the analysis was the actual, inflation-adjusted, compound annual return of U.S. stocks, with dividends reinvested. The returns were computed for all holding periods from one to 20 years, plus all even-numbered holding periods from 22 to 40 years, from January 1896 through December 2015. In a least-squares regression, the observed returns were predicted from a combination of CAPE and the holding period, using a function of the form r = b * c * POWER( m, y ) + a, where r is the log-real-return; c is the de-trended CAPE or LogrCAPE0.33%; a, b, and m are fitted constants; and y is the holding period.

Shiller's CAPE is a sensible measure of whether U.S. stocks are over- or under-valued. But for statistical analysis, it has some weaknesses. Correcting them can improve the insights that CAPE may offer about future returns from stock investments.

Robert Shiller's CAPE is a well established, highly respected metric of the extent to which U.S. stocks are over- or under-valued, rooted in historical data that spans more than a century. Among its good points: CAPE is based on an idea which, on its face, makes a lot of sense. And it does a better job of predicting future stock prices than many other contenders (albeit, with some caveats). So, what's not to like?

First, consider the good points.

Essentially, CAPE compares a one-time snapshot to an historical trend. The snapshot is the price of stocks for large U.S. companies at a given time (the Standard and Poor's 500 or a reasonable surrogate). The trend is the average earnings of those companies for the preceding decade. Why use a 10-year average? Shiller's insight was that doing so smooths out the peaks and dips in earnings that companies experience during the normal boom and bust of economic cycles. Of course, over periods as long as a decade, inflation has to be considered, so CAPE adjusts all stock prices and earnings to express them in current dollars. In short, CAPE estimates whether, after making sensible adjustment for inflation, the current price of stocks is cheap or dear compared to companies' demonstrated ability to generate earnings. For a stock-buyer who wants to capture future earnings, it makes perfect sense.

​What's more, CAPE is a decent predictor, according to standard statistical tests. In Asset Management, Andrew Ang evaluated 14 possible predictors of future stock returns, over periods from 90 days to five years. CAPE was one of only two that gave statistically reliable predictions, and, of those two, only CAPE can be calculated contemporaneously. If you want to make a decent prediction, without waiting for future data, CAPE is the metric of choice.

Now, the weak points:

• Balance. When calculated as a simple ratio and used in that form to conduct statistical analysis, CAPE is imbalanced. It gives too much weight to very high values (extreme over-valuation) and too little weight to very low ones (extreme under-valuation).
• Persistence. Counting current earnings for exactly ten years, equally weighted throughout that period, is not optimal. The persistent effects of extreme conditions are better captured by averaging earnings in a different manner.
• Trend. CAPE's message may be clouded by its own long-term trends. The CAPE value that is purportedly normal today may differ from what was normal decades ago.

​For each of these problems, fortunately, there is a plausible correction.

To see how CAPE over-weights high values and under-weights low ones, consider the chart below. It shows historical values of CAPE, from January 1896 to December 2015, assigned to bins in what statisticians call a "histogram."

In this chart, the values are reasonably well balanced, although a slight elongation to the left has replaced PE10Y's extreme elongation to the right. Accordingly, the statistical skew for LogrPE10Y is -0.17, which is close to the ideal value of zero, though slightly negative. By using the median for the calculation, LogrPE10Y has exactly half its values below zero, and half above. Furthermore, a doubling of stock-prices would raise the metric from zero to about 0.7, while a halving would lower it by the same amount, to -0.7.

Notice that, in the chart for LogrPE10Y, halving of normal valuations has occurred a bit more often since 1896 than doubling of valuations. That's evident because the bars below -0.75 are somewhat higher than the ones above +0.75. From looking at the original, badly skewed chart for the ordinary PE10Y, you would never have seen that. In fact, you might have concluded just the opposite, because of PE10Y's long tail to the right. This observation is one way to appreciate the misleading nature CAPE's classical computation. 

In PE10Y, today's price is compared to ten years of annualized, inflation-adjusted earnings, with the earnings estimated each month. Every month's estimate gets the same weight. But why should ten-year-old earnings get the same weight as current earnings, while those from eleven years ago get no weight at all?

​Shiller's original idea was that a decade-long average filters out the business cycle. While it may do so ordinarily, there are exceptions. For example, a period without a recession, but slightly longer than ten years, occurred from February 1991 to April 2001. Furthermore, the impact of earnings on stock-prices may be more than economic. There may be a behavioral component, as well. Investors' memory of extreme events like the bull market from 1982 to 2000 or the crash from 1929 to 1932 may influence their perception of stock-values. Would a twenty-year CAPE, for example, be a better filter of very long bull markets? Would an extended series of weights that decline ever so gradually for a very long time resemble investors' lingering memory of fearsome crashes?

The following chart addresses these questions by depicting three different ways to compute the average earnings in CAPE.

Since 1896, CAPE has not varied randomly. Over periods of 20 years or so, it has tended to hover at negative, neutral, or positive levels, not wandering freely across the full range of potential values. The chart below demonstrates the non-random behavior, using LogrPE0.3% for CAPE. The plotted line is a fitted (cubic) polynomial. If CAPE were truly random, the line would be flat or nearly so.

The trend shown in the chart poses some ambiguity about the proper interpretation of CAPE. For example, the dot-com peak in 2000 was double the size of any previous peak, when measured on raw values of LogrPE0.3%. However, when measured by the excess above trend, the extremity of 2000 was about the same as the 1929 peak. Making the interpretation even more difficult, the trend as of 2016 could look different when the fitted line is recomputed a decade or two in the future. If the fitted line were projected into the future, it would forecast a leveling-off, with today's CAPE becoming the "new normal." But, as Mark Twain famously observed, forecasting is hazardous, especially when you are trying to predict the future. It's just not clear whether current stock-prices are almost normal (compared to the trend line) or extremely over-valued  (assuming zero to be normal).

Speculatively, one might view the long trend as a behavioral indicator. Perhaps investors get accustomed to high or low stock-valuations, causing the "normal" level of CAPE to rise during long-term bull markets and to fall during periods of prolonged economic distress.

Whatever the reason, the long trend suggests why the explained variance, reported in an earlier chart, is low. It's just 20% because the statistical model made no adjustment for the long trend. Realistically, invoking CAPE to predict future stock-returns or to design a portfolio is a rough approximation. Using it is better than ignoring it. And, although LogrPE0.3% is a "better CAPE," it offers modest improvements, not guarantees.

Follow-up posts examine how the "better CAPE" can be used judiciously to fine-tune an investment portfolio and to adjust realistic expectations of future returns. In doing so, the follow-ups give a deep-dive into the merits of de-trending CAPE and the inner workings of our calculators.

* In data of the sort used here, with overlapping time-periods, traditional statistical tests may be biased. Ang's book, in chapter 8, section 5.2, explains why. Thus, the absolute level of explained variance (R-Squared) should be taken with caution. That said, different methods of measuring CAPE were all subject to the same biases. Comparing the explained variance of the methods is probably correct directionally, if not in magnitude.
​
** Two sets of regression analyses were performed. In both sets, real (inflation adjusted) stock-returns were predicted from CAPE values, using monthly data from January 1896 to December 2015. For exponential averages, PE10Y in December 1880 was the starting value. Annualized stock-returns, with dividends reinvested, were computed for all annual holding periods from one to 20 years, and for all biennial holding periods from 22 to 40 years. In one set of analyses (reported here), the regression slopes and intercepts were forced to be constant across all holding periods. In a second set (to be covered in a future post), the regression parameters were allowed to vary for each holding period.

Does your adviser put your interests first? Are your adviser's recommendations colored by sales commissions he or she may get or by fees extracted from your account? Historically, the federal agencies responsible for overseeing the financial industry have imposed minimal requirements on investment advisers and financial professionals. Advisers were required to recommend reasonable products, not necessarily the ones that would be lowest in cost or otherwise best suited to your financial goals.

Then, early in 2015, the U.S. Department of Labor (DoL) announced a plan to tighten the requirements by imposing new regulations. The DoL drafted regulations whose objectives were to:

• Strengthen the responsibility of retirement plans and retirement advisers to act in their clients' best interest, and
• Extend fiduciary requirements to IRA providers and to rollovers between IRA and 401(k) or 403(b) plans.

The DoL solicited public comments and, after receiving nearly 400,000 of them, published the official new regulations on April 6, 2016.

Note that the DoL's jurisdiction extends only to retirement accounts. It does not cover ordinary brokerage and after-tax savings accounts. That, in itself, is an important limitation. Furthermore, the final regulations, while arguably an improvement, are weaker than the original proposal on several counts. Among the many commentaries appearing in the financial media, two articles that aptly describe the limitations of the new DoL regulations are here and here. Rather than reprise the skepticism evident in those articles, my aim in this post is to suggest how you can evaluate your own adviser, taking into consideration what the new regulations do and don't require.

Ask your adviser the following questions. Or review the website of the adviser's firm to see whether the answers are available there. A genuine fiduciary (one who puts your interests first) would answer "Yes" to all, or very nearly all, of these questions. Some of them are based on ideas in the original DoL proposal that were weakened, regrettably, after some investment firms objected.

1. Will you sign a written fiduciary oath, as recommended by National Association of Personal Financial Advisers and the Committee for the Fiduciary Standard? (Note: If the answer is, "I support the oath but my legal department won't let me sign it," that counts as a "No.")
2. Will you charge a flat fee or hourly rate for work delivered or a fixed percentage of the assets that you manage in my accounts, and not charge a sales commission of any kind? (Note: You should pay your financial adviser as you would pay your attorney or accountant.)
3. If your employer gets revenue or fees from any of the products you recommend to me, will you provide a detailed accounting of those charges, even if you personally get no commission? 
4. When you recommend products to me, will you provide a detailed list of all fees and charges I will pay for purchasing and owning those products, including total annual dollar amounts for current and future years?
5. When you recommend products to me, will you show me multiple firms that offer such products, comparing the merits of each firm?
6. When you provide financial advice about investments or savings, will you show me the potential future performance of my account, including a most-likely estimate and a worst-case estimate?
7. Will your advice show how the future performance of my investments or savings might be impacted if either inflation or deflation occurs?
8. If my financial goals or preferences change for any reason, will you be available to help me understand the impact of making the changes?

The point of asking these questions is that the federal regulations simply are not strong enough to guarantee that your adviser will put your interests first, even if he or she professes to be a fiduciary under current guidelines. To download a pdf copy of the questions, click below:

The best and most popular news-posts at able2pay.com are being updated and moved. To see what's available, click on Retirement or on the Goals, Investing, or Portfolios menus at the top of this page. Included under Portfolios is an article on Basic Portfolios that amplifies the post immediately below.

Do you want  guidance on funds to buy in your 401(k), 403(b) or IRA, college-savings, or investment account? Here's an easy method from able2pay.com.

• Answer two questions to set targets for stocks and bonds, suitable for your goals and preferences.
• Allocate to three basic funds, which any firm will offer.

Step 1. Set a target percentage for stock funds.
When do you expect to spend most or all of the investments in this account?

• All in the next year or two: Set final target = 0% and stop (skip the next question).
• Most or all within five years: Set preliminary target = 30% and continue.
• Six or more years from now: Set preliminary target = 60% and continue.

What is more important to you, maximizing gains or minimizing losses?

• Maximize gains: Add 15% to your target.
• Minimize losses: Subtract 15% from your target.
• Do both: Keep your preliminary target (no change).

You now have a target of 0%, 15%, 30%, 45%, 60% or 75%. This is the amount you will allocate to stock funds. The rest will go to bond funds. (If you want more finely tuned values, you can get them with our Best-Invest calculator.)

Step 2. Allocate to suitable stock and bond funds.
Use your target to find the matching row in the table below. Then use the percentages in your row to invest in the funds shown by the column headings. Most 401(k), 403(b), IRA, college-savings, and investment accounts will offer these funds or equivalents. Below the table are descriptions that will help you find the right ones for your account.

• U.S. Stocks: Use an index fund that invests in the total U.S. stock market. If not available, use an index fund of large-cap U.S. stocks or the S&P 500. Avoid anything that's not indexed or that's more specific.
• International Stocks: Use an index fund that invests in all non-U.S. stock markets. If not available, use an index fund of EAFE stocks (developed countries outside the U.S.). Avoid anything that's not indexed or that's more specific.
• Intermediate Bonds: Use a bond fund that invests primarily in a broad mix of U.S. treasury and corporate bonds. Avoid funds with a limited focus on TIPS or on inflation-linked, international, high-yield, or short-term bonds. In a 401(k), 403(b), or IRA account, you should also avoid municipal bonds.
• Short-Term Bonds: Use a fund of U.S. treasury bonds with maturities less than five years. If not available, use instead a short-term bond index fund or a money-market fund.

Optional Step for IRA and Taxable Accounts
The following options are good improvements for an IRA or taxable account, but are unlikely to be available for your 401(k), 403(b), or college-savings plan:

• Invest at Betterment, and simply use the target from Step 1. Betterment's automated service will invest in a well-designed set of U.S. and international stocks and bonds.
• Invest  at Vanguard, using the alternate table below and these funds: Global Minimum Volatility; either Mid-Cap Value Index or Strategic Equity; Intermediate-Term Bond Index; and Short-Term Treasury.
• Invest in a low-fee brokerage account such as Fidelity or TD Ameritrade, using the alternate table below and these Exchange-Traded Funds (ETFs): iShares MSCI All-Country World Minimum Volatility (ACWV), Vanguard Mid-Cap Value (VOE) or equivalent; Vanguard Intermediate-Term Bond (BIV) or equivalent; Vanguard Short-Term Government Bond (VGSH) or equivalent.

To learn more about global low-volatility stocks, mid-to-small value-stocks, and Betterment's portfolio, see the article Diversify! on the Portfolios menu.

To get a rough budget, you'll need to estimate your overall expenses, your sources of income, and how long you need your income to last. The method outlined here is meant to be a first step, an approximation. It will help you judge whether your income may enable you to reach your main goals. It won't answer every question, down to the last dollar. But it's a good start.

Here's an overview of the method, step-by-step. It has five "round numbers" that are close enough for a rough budget.

1. Find Life+6, your life expectancy plus an extra cushion of six years.
2. Use tax returns and account statements from last year, plus the inflation rate for the past 12 months, to estimate your annual expenses this year. This number is what you actually spent last year, including tax payments, but excluding income you saved, all adjusted for current inflation.
3. Find your stable income from Social Security, pensions, income annuities, and reliable work, also adjusted for current inflation. Life+6 plays a part in calculating this number.
4. If your stable income won't cover your annual expenses, find your spending balance. This is the amount available to extract from your spending account. As detailed in Enable Your Accounts, a spending account is a temporary reserve where you manage one or two years of living expenses.
5. If your annual expenses are still not met, calculate the safe payout you can take from your retirement accounts and taxable savings. With Life+6, there's a simple, reasonable way to do this calculation. (Our Safe-Payout calculator does it for you, and offers other options, as well.)

Should you be over 70 years and 6 months of age, and required by the IRS to take minimum distributions from your retirement accounts, these would go to your spending account in step 4, if needed, and next to your safe payout or taxable savings in step 5.

For worked examples of each step, click here to read the full article.

This post was part of a series on building a portfolio of mutual funds or Exchange Traded Funds. Much of the series has been moved to articles on the Portfolios menu:

• Basic Portfolios: Some simple ideas that work remarkably well.
• Diversify: Effective ways to diversify with bonds and stocks, globally.
• Factor Investing: Specialized portfolios that employ techniques from academic research.
• Respond to Inflation: Realistic options for inflation-protection, near-term and long-term. (Not yet moved, this topic is covered below, in this post.

On the topic of inflation, Andrew Ang's fine textbook, Asset Management, offers many good insights, to which I am much indebted (see his chapter 11). I've superimposed my own analysis, however, and sometimes relied on additional sources.

It's helpful, I think, to focus on inflation with three sets of questions:

• Near-term: At a given time and for the next year or two, how should an investor's portfolio adapt to inflation or, equally important, to deflation? This question matters if, and only if, you plan to spend some of your investments in the next year or two.
• Long-term: What investments, if held a long time, will best protect against inflation? Do the same investments protect against deflation? And how long is long enough?
• Correlates: Both near-term and long-term, what investments (if any) are correlated with inflation (or deflation)? If one applies diversification criteria, do any of the popular candidates, such as TIPS, commodities, and real estate, truly add value?

An important conclusion will be that sensible protection against inflation and deflation is possible, but by different methods for the near-term than for the long-term. Furthermore, the popular candidates may not be the best or the only methods you should consider.

Here's an interesting test. You come to me in December, asking "What will inflation be next year?" I caution that nobody knows the perfect answer, but one indicator is quite good and amazingly simple. "It has correlated 0.64 with next year's inflation for the past 100 years," I proclaim. Then I show you data for the past century, using the chart below. Can you guess what my indicator is?

No, it's not the price of oil or gold. It's not the return on inflation-indexed bonds, or the median price of homes, or any exotic financial product. And it's a lot simpler than the economic model favored by this year's hot economist. It's last year's inflation. Yup. Next year's inflation is pretty well predicted by inflation over the most recent 12 months. That's because inflation (or lack of it) tends to persist. *

Despite the dire tone of some articles and commentary, inflation is not like a thief in the night who steals your heirloom jewelry, sets your home ablaze, and swiftly vanishes before dawn, leaving your wealth devastated. He's more like the unwelcome guest, your financially reckless cousin, who emails you one day and shows up on your couch the next, feasts from your pantry, maxes all your credit accounts, totals your car, and requires strenuous measures to be evicted, leaving you poor, thin, weary, and forgiveably ungracious after a prolonged ordeal.

The point is that you'll know when inflation is becoming a problem. One of the more obvious clues will be that interest rates are rising. That clue, as it happens, also defines your best defense.

T-Bills
As Ang and others before him have pointed out, the asset most strongly correlated with inflation and the best single hedge against it is a 3-month Treasury Bill. As inflation rises or falls, the interest rate on T-Bills tends to follow. Because T-Bills can be redeemed and reinvested at the newest rate every three months, the response to inflation, although lagging somewhat, is timely. 

Even so, it's not a perfect hedge, mainly because policies of the Federal Reserve sometimes (not always!) hold T-Bill rates below the inflation rate. That happened for nearly two decades during the Great Depression and World War II, and again, more recently, for six years and still counting since the financial panic of 2008-2009.

These limitations notwithstanding, a T-Bill offers good protection against inflation for expenses you know you will have to pay within the next year or so. Here's a concrete example:

• A hypothetical saver needs $1000 per month to pay expenses that are not covered by her other sources of income, such as work, Social Security, or an annuity.
• In late December, she has $3000 in a bank account (earning next to nothing) to cover her expenses through March. She withdraws $12,000 from her investment or retirement account, and buys a 3-month T-Bill. (She can do so easily and with no fees whatsoever at www.treasurydirect.gov.)
• In April, she redeems the T-Bill and puts enough in her bank account to cover the next three months' expenses. If her expenses have risen (or fallen) a bit in the past three months, she sensibly increases (or decreases) the amount set aside in her bank account, thus maintaining a smooth standard of living. (To simulate these adjustments, I exactly matched them to the change in consumer prices, up or down, for the previous quarter.) The remainder gets reinvested in a new 3-month T-Bill.
• She does the same in July and October.
• At the end of December, she looks at the amount she will get by redeeming the most recent T-Bill, to see if it will cover the first three months of the coming year. She wants it to cover her real expenses, which may have risen above $1000 per month because of inflation over the past year.

Had this strategy been followed every year from 1934 to 2014, the results would have been as shown in the chart below. The value depicted in the chart is the surplus (or deficit) over the amount needed for the first quarter of the coming year, adjusted for inflation.

Before 1952, when interest rates were restrained by the federal government, the results were weak. On average, the amount available after a year was nearly 9% less than the amount needed for the next three months. These were desperate times, financially, and it is not clear that any one-year savings plan could have done better.

From 1952 through 2014, the results were good. On average, there was a real 1% surplus, and surpluses occurred much more often than deficits. On the assumption that future federal policies may resemble those enforced since the early 1950's, the T-Bill strategy looks attractive.

Short-Term Treasuries
What if you were willing to take a bit of a chance on longer-term bonds? For example, how about a short-term Treasury fund whose bonds have average maturities around 2 years? One might expect such a fund to respond to inflation less quickly than T-Bills, but to pay a higher rate of interest and to be penalized somewhat less when federal policies suppress the interest on T-Bills. The next chart shows the results from using 2-year Treasuries instead of 3-month T-Bills.

Clearly, there is much more variation from year to year, which is not good for budgeting. On the other hand, the average surplus for the period 1952-2014 was higher, around 2%. In several years, the surplus was a full month's expenses. Here's an idea: What if the surpluses were carried over, to offset subsequent deficits?

A variant of that idea turns out to be highly effective, perhaps the best strategy of all. It works like this:

• In the first year, save two years' expenses ($24,000 for our hypothetical saver) instead of one ($12,000).
• Use a fund of 2-year Treasuries instead of T-Bills.
• Don't spend any surplus. Don't try to replenish any deficit. Simply add next year's expenses at the end of each year, adjusted according to the past year's inflation, exactly as in the T-Bill strategy.

The extra deposit at the outset serves as a cushion, creating, in effect, a reserve fund.

This strategy accumulates unspent surpluses over time, even in difficult periods. The chart above illustrates how the strategy would have worked in three very different 26-year periods. The first period, 1934-1959, saw a toxic mix of occasional high inflation, recessions with steep deflation, and persistent suppression of Treasury rates. During this time, the strategy lost some of its reserves but never went to ground. Bear in mind that the values in the chart are real dollars (inflation adjusted). Thus, the $3000 of buying power that remained on reserve at the end of 1959 would have seemed much larger in nominal dollars. The second period, 1961-1986, spanned multiple recessions and successive years of high inflation. Yet it maintained good reserves throughout. The final period, 1988-2013, benefited from a bull market in Treasuries and ended with enough surplus to cover more than two years of inflation-adjusted expenses.

Short-Term TIPS
Originally, they were called Treasury Inflation-Protected Securities, or TIPS. But they never truly guaranteed protection from inflation, and the Treasury Department now calls them Treasury Inflation Indexed Notes or TIINs, if their maturity is five years. The new name is apt because in recent times, their value as an inflation hedge has been about as good as, well, TIIN.

Surprised? Consider this example. In October 2010, you could have bought TIPS from the Treasury Department that would mature four years and eight months later, in April 2015. Those TIPS would have paid a measly interest rate of 0.5%, which would have seemed reasonable because T-Bills paid even less. At the time, the big institutions that bid at Treasury auctions expected inflation to start rising. So they bid up the price of the TIPS, thereby forcing buyers to pay, on average, $1055 for a bond that could be redeemed in nearly five years for $1000 plus inflation. They were counting on inflation to recoup the extra $55 and then some. As it all worked out, the cumulative inflation between October 2010 and April 2015 was 8.2% (equivalent to 1.7% per year). The buyer was therefore paid about $1082 in April 2015, plus those flimsy interest payments twice a year. For the initial investment of $1055, the buyer got a real (inflation adjusted) total return of about 1% per year. The five-year bet on inflation paid off, in this case.

But what if the original buyers' expectations were wrong? It can happen. In July 2014, no one anticipated that inflation for the next 12 months would be virtually zero, but that's what it was (0.2%). If you had bid on TIPS in early 2014 expecting a 1% real return, you would be holding a loss after the first year. Because mutual funds and ETFs buy, sell, and redeem TIPS continuously, they are vulnerable to such miscalculations. They can lose money when their inflation bets are too high. 

For some evidence, consider the chart below. It shows the real (inflation-adjusted) returns since late 2009 for two funds: STPZ, the PIMCO ETF for short-term TIPS; and VSGBX, a Vanguard fund for short-term bonds from the Treasury Department and other federal agencies. The PIMCO fund holds TIPS exclusively; the Vanguard fund holds no TIPS at all. Over the six-year period, both funds virtually matched inflation, with a terminal value near $1.00 for every dollar originally invested. But the TIPS fund was more volatile, rising or falling as its inflation bets came out winners or losers.

It would be nice to know if the long-term trend will resemble the short history shown in this chart. Alas, six years is the longest history available for a short-term TIPS fund as of September 2015. Pending additional evidence, a rational investor could use a short-term TIPS fund, instead of short-term Treasuries, but the outcome might not be any better, and the ride may be less smooth. An educated guess is that short-term TIPS may do better when inflation is rising, while short-term Treasuries might excel when deflation and recession are lurking.

Academic studies and historical data imply that near-term protection against inflation (and deflation) can be secured by either of these strategies:

• Hold a year's worth of anticipated expenses in 3-month T-Bills, redeeming and re-investing every three months. Virtually as good, use a savings or money-market fund if it is safe, very liquid, and pays interest at or above the rate of T-Bills.
• Or, hold two years of anticipated expenses in a fund of short-term U.S. government bonds. Withdraw expenses for a year, and replenish with anticipated expenses for the next year, keeping any surplus on reserve. A fund of short-term TIPS may be reasonable, but other U.S. government bonds are likely to offer more consistent performance.

In the next and final post in this series, we'll look at long-run inflation and the best strategies to mitigate its effects on your portfolio.

* In the chart, an outlier that goes against the trend is the solitary point in the lower right quadrant. It's for 1921 when, after World War I brought inflation that exceeded 15% annually, the economy sank sharply into recession. Within the year, high inflation switched to extreme deflation. It's the only such whipsaw in the past century. In fact, it's an exception that proves the rule because the preceding inflationary trend persisted for four years, and the subsequent deflation lasted for two, followed by several years of low inflation and the booming economy of the Roaring Twenties.

Disclaimer: Historical data cannot guarantee future results. Although a mixture of bonds and stocks may be safer than investing exclusively in one class of assets, diversification cannot guarantee a positive return. Losses are always possible with any investment strategy. Nothing here is intended as an endorsement, offer, or solicitation for any particular investment, security, or type of insurance.

This post is part of a series on building a portfolio of mutual funds or Exchange Traded Funds. The topics of the series, listed below, have been expanded into a downloadable handbook at Enable!, our online bookstore. The download includes new content on account types, sample portfolios, technical methods, and more.

• Start with Basics: Some simple ideas that work remarkably well.
• Diversify Smartly: Effective ways to diversify with bonds and stocks, globally.
• Focus on Factors: Specialized portfolios that employ techniques from academic research.
• Respond to Inflation: Realistic options for inflation-protection, near-term and long-term.

Bonds may seem simple. But they aren’t. To explain how they might diversify a portfolio, I’ll start with a common-sense overview, then give some basic recommendations for U.S. bonds. After that, if you want details and justifications, you can optionally read to the end of this post. International bonds are covered in a separate post.

You buy bonds, they pay interest until they mature, then you get your original deposit back. Almost like CDs, right?

Well, not exactly. With bonds, the price goes up or down as the prevailing interest rates go down or up. It’s backwards. Rising interest rates mean falling values for the bonds in your portfolio, and vice versa.

Plus this. With bonds, unlike CDs, you have to worry whether the bond-issuer will default, stop paying the interest you are due, and maybe return less than your original purchase amount. Treasury bonds, issued by the U.S. government, are the least likely to default, hence the safest. Corporate bonds have a higher risk of default, particularly from low-rated companies.

Foreign bonds, anyone? If they are issued by, say, the United Kingdom or Japan, the risk of default is probably very low. But there’s a catch. You have to buy the bonds in British pounds or Japanese yen and convert the interest-payments to dollars.  You have become a currency gambler.

Then there’s inflation. If it goes up (or down), interest rates will tend to rise (or fall), but not immediately, and your bond values go the other way (eventually). What’s more, there’s presumed inflation, the rise or fall that bond-investors expect to occur. This expectation affects bond-prices, too. And guess what? The expectations may be wrong (because inflation is hard to predict). Even if the expectation is right, and inflation perks up as forecasted, long-term interest rates are likely to respond later and less than short-term ones. All of which makes bond-pricing and inflation-watching a real puzzler.

Try to figure this one out: You thought inflation rates would rise, followed in a few months by rising interest rates, after which the U.S. economy would slow down to what economists once called a “soft landing,” and a mild recession would then grip the globe. As events unfolded, interest rates did rise, but inflation failed to follow, and every economy worldwide tanked more than forecasted, causing some indebted companies and weak governments to default. What happened to your bond portfolio?

Give up? Some investment firms do essentially that, opting for the easy recommendation to buy a portfolio that covers the “total bond market.” Examples: VBMFX plus VTIBX from Vanguard; or AGG plus IGOV from iShares; or ETF combinations weighted to mimic the world’s bond markets, as done at Betterment, Schwab, and others. (Actually, these are “near-total” funds as they rightly exclude junk-bonds from low-rated companies and tax-advantaged bonds from city and state government.)

The following recommendations are based on academic research as reviewed in a fine textbook by Andrew Ang, and on my own detailed analysis of U.S. Treasury and corporate bonds from 1953 to 2015. This historical period had three very different, 20-year phases. The first saw rising interest rates; the second had high inflation coupled with rates that rose then started to fall; and the last enjoyed steadily falling rates. Beware of advice based exclusively on any newer, shorter time period. Most questionable are recommendations from data that starts after 1982. That's an exuberant period of falling interest rates, rising bond prices, and low inflation overall, which was biased in favor of bonds.

My analysis of the longer period from 1953 to 2015 suggests that three bond funds can diversify your stock investments. At any given time, one or two of them will suffice, depending on your circumstances.

• Long -Term U.S. Government. The fund should invest in bonds from the U.S. Treasury and other federal agencies, with average maturities longer than 10 years, preferably near 20. Examples: VUSTX or VGLT from Vanguard, or TLH or TLT from iShares. 
• Long-Term Corporate. The fund should hold 10-to-30 year bonds issued by well-rated (investment-grade) U.S. companies. Examples: VWESX or VCLT from Vanguard, or LQD from i-Shares.
• Short-Term U.S. Government. In this fund you should find Treasuries and bonds from other federal agencies, with average maturities of 2 to 3 years. Examples: VSGBX, VGSH, or VFISX from Vanguard, or SHV from iShares.

(In a taxable account, you should consult your tax-adviser about using a short-term or long-term municipal bond fund, perhaps for your state, instead of the funds listed above.)

To determine which fund to use, if you plan to hold your investments for five years or longer, consult the table below. For example, when Able to Pay's calculator (or some other method) says you should invest 70% in stocks, then the table advises you to put the remaining 30% in long-term government bonds. But if your stock-allocation is below 40%, the table assigns the rest to long-term corporates. The 40% threshold is not absolute. You could reasonably use an even split of long-term government and corporate bonds for stock-allocations near 40%.

For holding periods of one to five years, two changes should occur. Your stock-allocation should decrease, to reduce the risk of loss. Concurrently, your bond-holdings should shift toward short-term government issues, both to control losses and to respond, if necessary, to inflation.

The next table lays out guidelines for a forward-looking, middle-of-the-road investor, one who aims both to achieve some gains and to limit possible losses, and who plans to spend 100% of her savings one to five years from now. Consistent with the preceding table, long-term bonds are allocated to corporates if the overall stock-allocation is under 40%; otherwise, the long-term portion goes to government-issued bonds. One could do about equally well by putting bonds in an intermediate-term index, such as a "total bond market" fund, when the stock percentage is below 40% and the holding period is five years or less.

For values fine-tuned to your preferences and circumstances, use Able to Pay’s calculators, which take into account two aspects of your holding period: when you will start spending, and how many years you will continue spending. The best allocations for you may be different from the tables above if your spending starts farther in the future or lasts more than five years. And bear in mind that any funds you need to spend within 12 months (a zero-year holding period) should be kept in bank savings, T-Bills, or a money-market fund.

These are the basic recommendations. To get the full details, read on!

To develop recommendations for corporate and long-term bonds, I began by asking whether various bonds could beneficially diversify a portfolio that already held U.S. stocks. This analysis entailed a new concept, investment factors. Where macro-factors apply to big forces that affect an entire economy or many markets, an investment factor is more narrow. It affects the investments in a particular market.

Academic research has identified several investment factors affecting bonds. The two most important, for our purposes, are term structure and credit risk.

• Term refers to the number of years a bond pays interest (its years to maturity). Short-term bonds have maturities less than 5 years; intermediate-term bonds, 5-10 years; long-term bonds, 10-30 years. As Ang’s book explains (chapter 9, section 3.3), the interest rates of short-term bonds are heavily influenced (about 70%) by inflation; they are much less influenced by economic growth, monetary policies, and other macro-factors. For long-term bonds, the opposite holds true. They are weakly influenced by inflation (32%) and strongly influenced by other factors. The influences on intermediate-term bonds are much like those for long-term bonds. It may be promising, therefore, to diversify between short-term and long-term bonds, omitting or de-emphasizing the intermediate term.

• Credit refers to the risk of default. Will the issuer of the bond make good on the promise to pay dividends and to return all the principal (the face value) when the bond matures? With U.S. Treasuries, the risk of default is extremely low, and is often assumed to be zero. In contrast, bonds issued by corporations (and government agencies other than the U.S. Treasury) have some risk of default. Investors who held bonds from General Motors in 2009, for example, or from the City of Detroit a few years later, faced the very real risk of not being repaid the full amount they had invested. Credit risk can be mitigated by buying bonds from many issuers, just as the risk of bankruptcy can be mitigated for stocks by purchasing shares in many companies. Because corporate bonds have credit risk and U.S. Treasuries do not, diversifying across the pair of them may be advantageous.

Taking guidance from the investment factors of term and credit, let’s apply the diversification criteria to short-, intermediate-, and long-term Treasuries and corporates.

• Are they objectively different? When contrasted with stocks, corporate bonds depend on the financial health of the companies, as stocks do. Treasuries don’t. They depend, instead, on the good faith and credit of the U.S. government. Thus, Treasuries should get more weight as diversifiers, because they differ from stocks to a greater extent than corporate bonds do. Among bonds, the biggest differences are between short-term Treasuries and long-term corporates, as they differ on both factors. Perhaps these two will diversify each other, while they also diversify stocks.
• Are there new risks? Technically, the credit risk of a company’s bonds is somewhat less than the risk of loss from investing in the same company’s stock. Why? Because if the company fails, bond-holders may partially recoup their investments, while stock-holders lose everything. Because of this, and because the default-risk of U.S. Treasuries is extremely low, the incremental risk of adding any bonds to a portfolio is minimal. That’s good for diversification! (A caveat: Low-rated bonds, which have high credit-risk, may add little value.)
• Are the returns equal or better? No. In general, the returns on bonds are less than on stocks. However, long-term bonds come closest to the compound return of stocks, thus arguing for them as the best of a set of tepid choices.
• What’s the correlation? Historically, the correlation between Treasuries and stocks has tended to be zero or somewhat negative, making Treasuries attractive diversifiers for a stock-portfolio. Corporate bonds tend to have low positive correlations with stocks, low enough to make them candidates for diversification, but less compelling than Treasuries.

Clearly, no single type of bond scores highly on all the diversification criteria. A mix of Treasuries and corporates looks promising, because it would diversify across the credit factor, but the mix must also diversify across term. To find a good mix, I analyzed portfolios ranging from 10% to 90% in S&P 500 stocks, and the remainder in a single type of bonds. I did so for data from 1953 to mid-2015, for each of the following: 

• 2 Year Treasuries (short-term)
• 5 Year Treasuries (intermediate-term)
• 10 Year Treasuries (intermediate-term)
• 20 Year Treasuries (long-term)
• 20-30 Year A-Rated Corporates (long-term, with favorable credit-risk)
• Simulated Intermediate-Term Index*

The chart above shows the results, applying the same investment goals used earlier in this series. For building real wealth and keeping pace with inflation, long-term bonds, both Treasuries and corporates, best diversified a portfolio that already had stocks. They generated the biggest portfolio returns. For limiting downside volatility, however, 2-year Treasuries were the best addition, because they had the smallest portfolio losses. In comparison, intermediate 5- and 10-year Treasuries and a simulated intermediate-term index were middling, neither best nor worst.

This finding poses a dilemma. Is it possible to add both long-term bonds and short-term Treasuries without nullifying their respective benefits? Or does one cancel the other, making the combination no more effective than simply using intermediate-term bonds, perhaps chosen broadly to represent the entire bond market? The solution to the dilemma turns on your goals as an investor.

Long-Run Goals
Continuing with the same broad goals used earlier in this series, let’s first consider investments you plan to hold longer than five years. For these, your weights would be:

• Grow wealth: High
• Protect buying power: High
• Avoid losses, near-term: Low

With many years left before you spend your investments, you could ride out near-term losses, provided that your portfolio’s long-term trend was to grow faster than inflation and also, if possible, faster than the economy. In this case, your portfolio should have 40% to 90% invested in stocks, by our models, with the specific percentage depending on your spending plans and tolerance for market swings. The rest of your portfolio should be in long-term government-issues, because they exhibit no correlation with stocks, historically, and their low risk of default differentiates them from economically vulnerable corporate securities.

The evidence is in the chart above. It is like the previous chart, but limited to portfolios with 40% or more invested in stocks.** In the top two panels, which correspond to the high-weighted goals, notice the bump-out for 20-year Treasuries. Even for the lower-weighted goal of limiting near-term losses, in the bottom panel, 20-year Treasuries did virtually as well as most other bonds, for these long-run portfolios.

The advantage of 20-year Treasuries was consistent. They ranked first or a very close second at all stock-allocation levels from 40% to 90%. That said, they were not necessarily tops in any given year, and the paths taken through particular 20-year periods were variable.

What if you prefer to invest less in stocks for the long run than our models recommend? In that case, at stock allocations from 10% to 30%, long-term corporates would have been your best diversifier, historically. This makes sense intuitively because a smaller allocation to economically sensitive stocks encourages a modest exposure to the credit risk of corporate bonds. The next chart has the evidence. Now the bump-out in the top two panels is for long-term corporates.

Near-Term Goals
Bear in mind that the foregoing results are for holding stocks and long-term bonds for many years. What if you hold them for shorter periods? Then your goals are different, something like this:

• Grow wealth: Low
• Protect buying power: High
• Avoid losses, near-term: High

As implemented in our calculators, if you plan to spend your investments over the next one to five years, a portion of your portfolio gets transferred from stocks to bonds. The transfer goes increasingly to safer, short-term government bonds as you get closer to the year when you will start spending. But they don't go there completely. Some bonds remain in longer-term securities. Should those be long-term corporates, as argued above, or something more cautious?

The next chart answers the question with two good options. It displays average results over all of the 20 unique combinations generated by our calculators where the holding period is five years or less and the recommended allocation to stocks is under 40%.

Yes, keeping the remainder in long-term corporates is a good option. Virtually as good, however, is assigning the rest to a fund that indexes intermediate-term corporate and government bonds (“total bond market” funds, for example). The real return is slightly worse with the intermediate option, but the risk of loss compensates with a marginally better reading, and this is the more important goal. All in all, both choices work well.

Long-Run Example
Recall that the historical data covered three 20-year periods during which bonds performed very differently. Using the previous example of a long-run portfolio with 66% in stocks (the S&P 500), the following chart illustrates what happened in each period when the the remaining 34% went to long-term Treasuries. The journeys were disparate, but the outcomes, very similar.

Near-Term Example
Previously, when looking at basic portfolios, we examined non-overlapping, three-year holding periods for investments cautiously allocated 25% to S&P 500 stocks, 20% to 10-year Treasuries, and 55% to 2-year Treasuries. Let's take a fresh look at those periods, with these updates:

• Long-term corporates replace 10-year Treasuries.
• The investor, using Able to Pay's calculators in the intended manner, updates allocations annually as the years ramp down from three remaining to two and then to one. By the final year, the allocations are 10% S&P 500 stocks, 10% long-term corporates, and 80% 2-year Treasuries.
• Instead of periodic rebalancing, the portfolio is simply set to its new allocations at the end of each year.

The outcomes, shown in the chart below, are somewhat more consistent (less dispersed at the end), and the losses are smaller in the two worst cases, 1972-1974 and 1978-1980. An apt way to summarize the pattern is that for an investor whose goal is to minimize losses, this ramp-down strategy for bond-allocations resulted in a low 10% chance of losing 10% in buying power over three years. (And nominal dollars, not adjusted for inflation, exhibited no loss at all in any of these time periods.)

* The Simulated Intermediate-Term Index was a weighted average of 10% 2-year Treasuries, 50% 10-year Treasuries, and 40% 20-30 year corporates. This value had virtually the same compound return and standard deviation as Vanguard's Intermediate Bond Index fund since it was initiated in 1994. 
** While 40% was chosen as a threshold because of Able to Pay’s model for long-run portfolios (held five years or longer), it was optimal by another criterion, as well. In a linear regression seeking to optimize returns, 40% was the point above which 20-year government bonds emerged as the best long-term diversifiers. Below 40%, long-term corporates were better.

Data sources: Shiller for S&P500, 10-Year Treasuries, and CPI inflation. FRED for 2-year, 5-year, and 20-year Treasuries, and A-rated long-term corporates; some missing data-points were interpolated with regression models. BEA for real GDP annually in the U.S. For those interested in technical details, a forthcoming article to be published at this site will explain how the measurements here were constructed and compare them to other possible methods of analysis.

Disclaimer: Historical data cannot guarantee future results. Although a mixture of bonds and stocks may be safer than investing exclusively in one class of assets, diversification cannot guarantee a positive return. Losses are always possible with any investment strategy. Nothing here is intended as an endorsement, offer, or solicitation for any particular investment, security, or type of insurance.

An annuity that gives you guaranteed payments, for the rest of your life, may seem attractive. But it likely comes with fees and restrictions that may be hard to decipher. Furthermore, the net benefit to you may be less than you think, and more expensive than other options. Still, for some, certain annuities make sense. The key questions are:

• What's an annuity, and do you need one?
• How can you find the best annuities from the best companies?
• What annuities should be avoided, because better alternatives are available?

For answers, click here to read our article on annuities, which is located on the Retirement tab. Or, for detailed examples based on our research, continue reading the post below.

Here are some examples of Single-Premium Immediate Annuities (SPIAs) and other options. They are based on actual quotes and real products, for a hypothetical married couple in their late 60's, seeking to invest $100,000 from an existing retirement account, with 100% benefits to be paid as long as either spouse lives. Although the quotes and products are genuine, I've made the companies anonymous because they may not operate in the state where you live, your age and other variables may differ, and the companies may impose contractual stipulations that depart from the quotes and website-data available to me. These examples should not be construed as recommendations to buy any particular security or insurance product. Rather, they are intended to illustrate how you might examine and evaluate annuity options applicable in your circumstances.

• SPIA-3%. This immediate income annuity raises its payments by 3% each year. The first year's payment is $4544, a 4.54% rate on the $100,000 deposit. With a COMDEX rank of 96, the insurer is among the top 30.
• SPIA-CPI. Also an immediate income annuity, this one increases its payments by the same percentage as the previous year's increase in the Consumer Price Index. Its first year payment is $4349, or 4.34%. The insurance company's COMDEX rank is 90, which puts it solidly in the top 100.
• Rider. This variable annuity is a partnership between a well established, highly regarded investment firm and an insurance company with a COMDEX rank of 92 (the top 60). Underlying the annuity is a mutual fund invested 60% in domestic and international stocks, and 40% in domestic and international bonds. The mutual fund, if purchased by itself, would have fees under 0.2%. Purchased as a variable annuity, it has additional fees of 0.29%. A guaranteed income rider adds 1.2% more. The total fees are pro-rated as 0.127% deducted automatically every month. In year one, for a $100,000 purchase, the annuity pays you $4500 (4.5%). Net, every month that year, the insurer deducts $501.67 from your account, paying $375.00 to you and $126.67 to itself. These values may change, depending on the performance of the mutual fund. It's possible for the annuity fees to increase while the payments to you remain flat. On the other hand, a legal rider to the annuity contract guarantees that payments to you will never decrease, and stipulates a formula by which they will increase if the underlying investments rise above their value at the time of purchase.
• Self-CPI. This option is not an annuity. It's a direct investment in the same mutual fund that underlies the Rider option. But the fees are lower, under $16 monthly, because none of the annuity fees apply, and the fund is held in an IRA account with no employer-related fees. It's a self-managed plan, where the investor uses the "collared inflation" method described here and implemented in our retirement income calculator. This method starts with an initial payment of $4020 (4.02%) because of the age of the hypothetical couple. It increases the payment each year by the smaller of (a) 6.7% or (b) last year's change in the Consumer Price Index. The limit of 6.7% is a "collar" which, historically, has been necessary to protect against depleting the fund in the worst case of 40+ years in retirement with inflation initially at extreme levels.

I was able to obtain market data since 1972 for the domestic stock, international stock, and domestic bond indices underlying the Rider and Self-CPI options (but not for the international bond index, which was added to the mutual fund only very recently). This data was used to simulate what would have happened if an investor had begun each of the options above under three scenarios:

• From January 1972 to December 2014, a 43-year retirement with wide variation in markets and inflation.
• A 21-year retirement starting in 1973, when stocks crashed then rose, and inflation started very high.
• A 21-year retirement starting in 1994, when stocks and bonds both rose and fell, but inflation was low.

The simulations are necessarily conjectures. The annuities being simulated were not available to be purchased during these time-periods, and had they been, their prices, interest rates, and contractual terms might have been different from what is sold today. Thus, the analyses reported below must be viewed as suppositions about what might happen if today's annuity products were to experience future markets for stocks, bonds, and interest rates resembling markets of the past.

First, the good news. All four options provided payments every year for 43 years. Even better, the Self-CPI option had a residual value of $209,650, adjusted for inflation, in 2014. Yes, you read that right. With the money left in 2014, the investor's heirs would have had twice the buying power of the couple's original $100,00 investment in 1972. The annuities, as annuities, had no residual value. Instead, any profits went to the insurers.

However, because 43 years is a long time, because inflation was high in the 1970's, and because the period included multiple large swings in the values of stocks and bonds, the four options paid out very different amounts from year to year. The chart below shows how they differed, over time. It's important to note that in the chart, all values are inflation-adjusted to show constant buying power, pegged to January 1972.

Viewed in terms of buying power, the SPIA-CPI option was the clear winner. When adjusting for last year's inflation, it sometimes lost a bit of buying power if current-year inflation was high. But over the long term, it guaranteed constant income, in real, inflation-adjusted dollars. 

The SPIA-3% option underestimated the high inflation of the 1970's and never caught up. Had this annuity been purchased with a 4% annual increase instead of 3%, the initial payment would have been a bit smaller, but the decline during high inflation would have been more limited. Eventually the initial buying power would have been nearly restored, as the compound rate of inflation for the entire 43-year period was 4.14%.

The Self-CPI option, because of its 6.7% cap on annual increases, fell behind inflation in the 1970's, but leveled out from 1980 onward. In effect, this method made a trade-off. It kept a large bequest as a result of cautious withdrawals.

The Rider option, when adjusted for inflation, fell short on its promise that payments would never decrease. Yes, in nominal dollars, the same amount was paid every year throughout the 1970's, but within a decade, inflation cut the buying power of those dollars in half. When huge bull markets in stocks and bonds began in 1982, the Rider option swiftly recovered, only to lose ground again after the dot-com bubble burst in 2000. Of all four options, this one had the least consistent payouts, adjusted for inflation.

The foregoing analysis comes with a big caveat. It's for a very long retirement in a unique historical period. Your experience in retirement will almost certainly be different. Consider, then, two other examples, both 21 years in length, one from January 1973 to December 1993; the other, from January 1994 to December 2014.

During these two periods, the underlying mutual fund of the Rider and Self-CPI options had compound, inflation-adjusted returns a bit higher than 5% per year. In this respect, the stock and bond markets were, overall, about average during both periods, despite some dramatic swings along the way.

At 21 years, both periods were also average in another sense. They fit the joint life-expectancy of a couple in their late 60's.

A key difference, however, is that in the first period, 1973-1993, inflation was abnormally high (6.05%), while in the second, 1994-2014, inflation was much lower (2.30%). Because of inflation, the SPIA-CPI option did the best job of maintaining payments at constant buying power in the 1973-1993 period; the other methods lost about 25%, falling close to $3000, inflation-adjusted. In the low-inflation period from 1994 to 2014, however, all the options preserved buying power, and the SPIA-3% and Rider payments actually bettered inflation. The chart below displays the average payments, after adjusting for inflation.

As shown in the next chart, only SPIA-CPI generated annual increases that kept pace with the 6% rate of inflation in the first period, while all the options matched or beat the tame 2.3% rate of inflation in the second period.

Finally, as with the 43-year analysis, the Self-CPI option was unique in preserving a bequest. Adjusted for inflation to reflect constant buying power, Self-CPI preserved principal approximately equal to the initial investment, in both 21-year periods: $90,756 at the end of 1972-1993, and $144,631 at the end of 1994-2014. The three annuities, by design, left nothing.

The examples presented here are for selected options and time periods. As such, they cannot be taken as guarantees of future performance or as definitive recommendations of certain products. Your results may differ, and will, as with any investment, entail a risk of loss. With those important cautions in mind, consider the following key insights from these examples:

• If one's goal were to guarantee constant buying power, SPIA-CPI would have been the best of the options examined above. A SPIA with a 4% or 5% annual increase might have performed comparably for periods of high inflation, but would have been more than necessary under normal levels of inflation.
• If one's goals were to preserve constant buying power and also leave a bequest, Self-CPI would have been the best of the options studied here. However, it would require active management by the investor (or by a paid adviser), which sets it apart from the annuity options.

When my father retired, he was fortunate to have inherited assets from my mother, who had died too young several years earlier, and from his own father. I remember my father saying his goal was to live on the interest and leave the principal for my three siblings and me. There was no way he could have known that the next decade would bring constant inflation and poor markets. A frugal spender who had no formal knowledge of finance or economics, he was happy, I suspect, to see the dollars in his account hold firm over the years, unaware that adjusted for inflation, they were worth much less than when his retirement began. I'm not complaining. He richly deserved every penny he spent, and then some.

Looking back on my father's experience and thinking ahead to my own retirement, I would reframe his twin goals of living on interest and preserving principal. Instead, for any retiree, I see the objectives as a triplet:

• Covering expenses. As noted earlier in this series, insured income from Social Security, possibly supplemented by a lifetime, inflation-adjusted annuity, may partially achieve this goal. The rest would come from managed investments.
• Holding emergency reserves. Unless one's retirement accounts are very large, some portion should be managed separately for unplanned expenses such as uninsured medical costs, accidental damage to property, or dependents' unforeseen needs.
• Leaving a bequest. For those lucky enough to have assets exceeding their own needs for normal expenses and emergency reserves, the remaining funds may be managed as future gifts, donations, or inheritances.

Historical data on U.S. stock and bond markets implies that one method of money-management may work best for emergency reserves. This post covers that method. For living expenses and bequests, a different method may be better, so those goals are covered separately, in the post on finance strategies.

Previously, I described a set of historical data on U.S. stock and bond markets since 1924, with which I studied the experience of hypothetical investors, all of whom retired at age 65 and lived to 95. The analysis had 62 cohorts, each starting in January of a year between 1924 and 1985, and ending 30 years later in December of a year between 1974 and 2015. For these cohorts, I considered three methods of managing retirement funds.

• Flat Percentage. Annually, a fixed percentage is withdrawn from a retirement account, while the remainder is left to grow over time. Variants of this method turn out to work best for managing emergency reserves. The method is similar to how universities and foundations typically manage their endowments.
• Required Minimum Distributions (RMD) . As dictated by the Internal Revenue Service, retirees at 70.5 years and older must withdraw a portion of their traditional IRA, 401(k), 403(b) or 457 accounts annually and pay taxes on the amount withdrawn. Each year, the mandatory portion increases, because the tax-collectors want their due. Consequently, the RMD method works poorly for emergency reserves and bequests. By design, it depletes the accounts of those who live long lives. It won't preserve a surplus for unexpected needs or posterity. Furthermore, if reserves or gifts are held in Roth or taxable accounts, as may be advantageous, then withdrawals are not obligatory, and the RMD method is irrelevant.
• Inflated 4%. This method withdraws 4% of an account's initial value at the start of retirement, then increases the withdrawn dollars each year by the same percentage as the previous year's inflation in consumer prices, or, less commonly, decreases it by the amount of deflation. It's really a variant of the flat-percentage method, but one that risks depletion of the account if inflation runs high for many years. For this reason, it's a non-starter for all except very short retirements.*

With flat-percentage as the method of choice, I ran simulated retirements for the 62 cohorts from 1924-1953 to 1985-2014, across withdrawal rates that ranged from 0% to 5% annually.

I first looked at a portfolio with 35% in U.S. stocks, 50% in 10-year U.S. treasury bonds, and 15% in 2-year U.S. treasury notes. Allocating 35% to stocks was a compromise between capturing the long-term, inflation-beating power of stocks and earning the shorter-term, stable return of bonds. In my previously reported study of inflation, a 35% allocation was a good choice for funds likely to be spent five to six years in the future, which seems reasonable as a planning target for retirement reserves. Coincidentally, the retirement income funds offered by most investment firms allocate 30% or 40% to stocks. Perhaps they should be renamed "retirement reserve funds" and relegated to the emergency-reserve portion of one's portfolio.

The chart below summarizes the simulated outcomes at the end of a 30-year retirement, for withdrawal rates ranging from 0% to 5% annually. The blue line labeled "35% Steady" shows the amount remaining after 30 years, for the middle cohort, using the 35% allocation to stocks and steady withdrawals every year. Half the cohorts did better than the blue line; half did worse. For example, at Flat0%, where nothing was ever withdrawn, the middle cohort's reserve fund had nearly tripled in buying power after 30 years. Even for Flat3%, where each year the retiree spent 3% of the reserves, the middle cohort kept 100% of its original buying power. Nice!

For comparison, I ran simulations for two additional portfolios as depicted in the chart. One, called "20% Steady" and shown by the red line, had a more conservative allocation: 20% stocks, 60% 10-year bonds, and 20% 2-year bonds. Because of the lower allocation to stocks, the returns tended to be a bit lower. Even so, after 30 years of withdrawing 3% annually, the middle cohort had virtually all its original buying power.

The final portfolio, shown by the green line labeled "35% Cautious," was the best of all. It had exactly the same allocations to stocks and bonds as the 35% Steady portfolio, but the method of withdrawal was modified. If, in the previous year, the portfolio had fallen in value, then no withdrawal was taken. However, if the previous year had positive returns, then 1% to 5% was withdrawn, as depicted in the chart. This method simplifies more elaborate strategies that many endowments use to moderate their withdrawals depending on the results of prior years. It's also what your instincts might guide you to do. After a down year, you might find yourself taking no discretionary withdrawals, while waiting for your funds to recover. That's exactly how the "35% Cautious" simulation worked, with favorable results. 

Because of normal, non-discretionary expenses, you might not be able to delay withdrawals from the rest of your retirement assets after a bad year. But non-emergency withdrawals from your reserve fund are truly discretionary. They allow you to redirect surplus funds to a vacation, to charitable donations, or to your fund for future bequests. When markets are falling, you can skip them.

If an emergency requires you to spend your reserves, it matters little what they might hypothetically earn after 30 years. You need them now. What matters, from this perspective, is the least amount you can expect to be available at any point during your retirement, not the cumulative total at the end. Accordingly, my simulations calculated the low-point for each payout method, over all 62 portfolios and all 30-year periods. For a given method, that's the lowest of 62 times 30 or 1860 outcomes. It's truly a worst-case metric, one that's lower than the other 99.95% of the method's historical results. The next chart shows this metric for each simulation.

As one example, for the 35% Steady portfolio and 2% withdrawals every year, the most dismal cohort sank to about 65% of its original buying power at one point during its 30-years of retirement. One might think that a more conservative portfolio, with less allocated to stocks, would be less volatile and thus suffer less depletion. Not so! Comparing the red and blue lines in the chart, it's clear that the more conservative 20% portfolio actually sank to lower lows than the 35% portfolio. How could this be? The reason, in brief, is that during periods of high inflation, the interest rate on bonds has often been less than the current inflation rate. A heavier allocation to bonds, if it lasts long enough during such times, will reduce inflation-adjusted returns.

The best strategy for limiting losses, across all the simulations, turned out to be the same as the one that was best for promoting gains. It was the 35% Cautious method.

This analysis has several implications for retirees.

• The retirement income funds offered by many investment firms, with about 30% to 40% allocated to stocks, may be a good match for funds you set aside as emergency reserves during retirement. This does not mean you should put all your assets in such funds, just the portion necessary for emergencies.
• If the future is like the past, then in most years you may be able to spend a modest percentage of your reserve fund, without losing any of its purchasing power, long-term. About 1% to 3% may be prudent.
• Your instinctive tendency to scale back spending after a bad year may be wise, at least for discretionary withdrawals from your reserve fund.

To learn more about reserve funds for retirees, read this related article.

* Endowments sometimes use cost-increases or inflation as part of their strategy for determining withdrawals. However, to curtail the risk of depletion, they add "collars" that prevent the withdrawn amount from growing faster than a certain rate compared to previous years. Should you be inclined to try such methods, you can find a very simple, very effective version in the post on finance strategies, or more elaborate versions here for Yale University and here for three other institutions.

Although a mixture of bonds, stocks, and guaranteed benefits may be safer than investing exclusively in one class of assets, diversification cannot guarantee a positive return. Losses are always possible with any investment strategy. Nothing here is intended as an endorsement, offer, or solicitation for any particular investment, security, or type of insurance.

Do you see your Social Security benefits as a retirement account? Your view, perhaps, is that you made deposits into a personal account with payroll taxes, and, when the time comes, you will withdraw from that account. Actually, Social Security was devised not as a government-sponsored retirement account, but as a form of insurance for retirees, the disabled and their children, and widows and widowers. Payroll taxes are premiums that are paid into a pooled fund, and payments to retirees and other qualified individuals are benefits to insure them against lost income. 

Viewed as insurance, Social Security benefits should be postponed to the latest possible age, because doing so maximizes the amount of the benefit. By waiting longer to collect your benefit, you get more insurance against loss of income later in life. You might need it if you live longer than expected or have large unplanned expenses. One excellent source of information is the website, Maximize My Social Security. For a modest fee, it provides a sophisticated online calculator to compute your best option for collecting benefits.

As detailed in other posts in this series, it is difficult to use stock and bond investments to construct a retirement portfolio that will last a lifetime and reliably protect against inflation. Social Security benefits address this difficulty because they are both adjusted for inflation and paid until you depart. There's a flip-side, of course. You can't bequeath your Social Security benefits to an heir (although a spouse, former spouse, or child may be entitled to benefits of their own, because of their relationship to you). Your stock and bond investments, however, can be bequeathed to a charity or a person, if any assets remain in your estate. Because of their complimentary nature, you need both Social Security and some investments. The following list spells out the reasons, based on the payout risks likely to be of concern to a retiree:

Inflation: Will it erodes your income?

• Social Security: Guaranteed protection.
• Investments: Some protection, depending on your investment strategy, but no guarantee. Read this post for details.

Payout Volatility: Can you rely on sufficient income every year?

• Social Security: Guaranteed delivery of the same inflation-adjusted amount, every month.
• Investments: Likelihood of higher payouts some years, lower ones other years.

Longevity: Will your income sources last as long as you do?

• Social Security: Guaranteed to last your lifetime.
• Investments: May last your lifetime if you adopt a good strategy, but failure is possible.

Emergency: What if you are struck by a costly event or illness?

• Social Security: No help here. Your benefits won't increase if you suddenly need more.
• Investments: If you are wise with your strategy, you can set aside some retirement savings as a reserve or contingency fund.

Bequest: Will you be able to leave an inheritance to your heirs or charity?

• Social Security: No help here. You have guaranteed benefits to you, not to your heirs. There's no account balance that would go to your estate.
• Investments: Again, it depends on your strategy. It's possible, as other posts in this series explain, to follow a plan that has a high probability of leaving something for your estate, provided you avoid emergency payouts.

If you have both Social Security benefits and retirement investments, do you also need an annuity? For many retirees, an annuity of any kind may add little value. 

To see why, consider a typical retiree. Her actual Social Security benefits might cover 40% or more of her pre-retirement income (see, for example, a classic study by Munnell and Soto). This figure would rise if she maximized her Social Security benefits, because the actual practice, as noted in the reported studies, is that most retirees minimize their annual benefits by taking them too soon. As it happens, 46% is about how much of a typical household income is paid for housing and food expenses, according to the most recent survey by the U.S. Department of Labor. Your circumstances may differ. Still, to a good approximation, Social Security benefits may suffice to pay for your most critical expenses.

Thus, your income from investments, although it may vary from year to year, may only need to cover about 60% of your budget. If your investment income were to fall by, say, 30% in a given year, that's really 30% of 60%, or 18% of your total income. The key question is whether your budget can sustain a drop of 18% or so. If you have a reserve fund or can reduce some optional expenses or have ample investments, the answer may be yes. If not, you may want to consider annuitizing some (not all) of your investments, thereby raising your guaranteed income to a higher percentage than the 40% or so that Social Security might cover. 

Should you chose to buy an annuity, it would be sensible to get one that resembles Social Security benefits. As explained in a related article, the best annuity is fixed (not a variable annuity); it pays for your lifetime (not for a limited period); and it's inflation-adjusted.

While your individual circumstances must guide your decision, you might, as a rule of thumb, consider your options very carefully before locking up more than two-thirds of your budget in the total of Social Security plus guaranteed annuities. Certainly, if your retirement investments are more than adequate to cover your income needs beyond what Social Security insures, then converting those investments to annuities would have little value. Other posts in this series provide some guidance on making such decisions.

Disclaimer​: Although a mixture of bonds, stocks, and guaranteed benefits may be safer than investing exclusively in one class of assets, diversification cannot guarantee a positive return. Losses are always possible with any investment strategy. Nothing here is intended as an endorsement, offer, or solicitation for any particular investment, security, or type of insurance.