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This post shows how some of the sample portfolios from earlier posts would be updated for September 2019, based on end-of-month data as of August 31, 2019.

​A Blended Portfolio
This simulated portfolio was originally described in A Portfolio with Steady Growth and Minimal Drawdowns. Its modified composition as of September 1, 2019, would be:

• Vanguard Balanced Index Admiral Shares (VBIAX), 0%.
• Vanguard Global Minimum Volatility Fund (VMVFX), 0% (because the 12-month total return fell behind that of intermediate-term Treasuries).
• Vanguard Intermediate Term Bond Index (VBILX), 20%.
• Vanguard Intermediate Term Treasury Index (VSIGX), 80%.

An All-Max Portfolio
With a goal to maximize total returns in the long run, while sometimes rotating out of stocks to limit potential drawdowns, this ETF portfolio remains more conservative than usual. Its compostion, however, is slightly revised from a month ago:

• Vanguard Total Stock Market ETF (VTI), now 25%, an increase from last month.
• Vanguard FTSE Developed Markets ETF (VEA), still 0%.
• Vanguard Long-Term Treasury ETF (VGLT): still 50%.
• Vanguard Intermediate-Term Bond Index ETF (BIV), now 25%.

An All-Min Portfolio
Unchanged this month, this portfolio is designed for low-risk income and remains as originally described:

• Vanguard Target Retirement Income Fund (VTINX), 0%
• Vanguard Intermediate-Term Treasury Index (VSIGX), 100%.

​Disclosures
Portfolios described here 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 is not a registered investment adviser and does not own, sell, or manage any of these portfolios. Alex Wilkinson may own similar portfolios in personal accounts.

In a series of posts that began in June, I've explored new ways to manage a portfolios so as to limit drawdowns while maintaining steady growth. The primary theme has been that across countries and time, a new strategy of rotating between equities and income (stocks and bonds) works much better than a traditional strategy of setting target allocations and then rebalancing periodically to maintain the target levels. A secondary theme is that low-volatility stocks can help to limit drawdowns while generating growth, except during prolonged periods of decline, such as the bear market of 2008-2009. This post combines the two themes in a blended portfolio that is both simple and powerful.

Performance: 25 Years of a Blended Portfolio
The chart above shows the simulated performance of a blended portfolio for the quarter century from July 1, 1994, to June 30, 2019. The portfolio's returns (the blue line) were better in the long run than a traditional balanced fund of 60% US stocks and 40% US bonds (the black line). Yet the blended portfolio was even more stable than holding a bond fund of safe, 10-year US Treasuries (the red line). The table below captures relevant statistics.

Composition: Building a Blended Portfolio
A blended portfolio generates growth by holding a diversity of US and international stocks when equity markets are strong; limits drawdowns by always holding some bonds, with a bias toward US Treasuries; and smooths performance by including a substantial portion of low-volatility stocks. In the example presented here, the blended portfolio holds two or three of the following mutual funds at a given time:

• Vanguard Balanced Index Admiral Shares (VBIAX), which holds 60% US equities, indexed to the total US stock market, and 40% US bonds, indexed to a broad set of corporate and government bonds with an average maturity of about eight years.
• Vanguard Global Minimum Volatility Fund (VMVFX), which invests 100% in US and international equities expected to have low volatility and, significantly, uses currency contracts to hedge the effects of fluctuating exchange rates.
• Vanguard Intermediate Term Bond Index (VBILX), which holds roughly equal amounts of US corporate and government bonds with an average maturity of about seven years.
• Vanguard Intermediate Term Treasury Index (VSIGX), which holds US Treasuries with an average maturity of about six years.
• Vanguard Short-Term Bond Index (VBIRX), which holds US corporate and government bonds with an average maturity of two to three years.

An equivalent portfolio could be constructed with Exchange Traded Funds (ETFs), instead of mutual funds. Vanguard offers an ETF corresponding to each mutual fund in the portfolio, except for VMVFX. For that, iShares ACWV could be substituted; it covers the same universe of stocks but does not hedge against currency risks. For the 25-year simulation, data for the MSCI index underlying ACWV was used until late December 2013, when VMVFX was first offered.

Management: Rotating the Portfolio's Holdings
At all times, the blended portfolio holds a target percentage in intermediate corporate and government bonds (VBILX). It thereby limits the potential impact of a sudden plunge in stock prices. For the simulation, the VBILX target was 20%. However, one could build more conservative portfolios by setting higher targets for VBILX, such as 40% or even 60%. A more aggressive version with 0% in VBLIX would be sensible in some cases, such as a retirement fund where the date to begin withdrawing funds is more than 10-to-15 years in the future.

Once a month, on a regular date (the first of the month in the simulation), a blended portfolio rotates between stocks and bonds, depending on how the mutual funds (or ETFs) have performed over the past 12 months. Specific decisions are made as follows:

• VBIAX is held if it has performed better than VSIGX since the same date a year ago; otherwise, the portion held in VBIAX goes instead to US Treasuries (VSIGX). The target allocation for VBIAX is half the amount not assigned to VBILX  (40% in the simulation).
• VMVFX is held if it has outperformed VSIGX since the same date a year ago; otherwise the portion held in VMVFX goes to US Treasuries (VSIGX). The target allocation is the other half of the amount not assigned to VBILX (40% in the simulation).
• VBIRX may be held temporarily, for a month or two, to avoid repurchasing a fund that was sold within the past month. This tactic honors the restrictions on frequent trading imposed by investment firms and avoids the tax consequences of a "wash sale" if applicable.
• On rare occasions, the portfolio is rebalanced, if the total drift from target levels has exceeded 5%. (Essentially, drift is calculated as the sum of excess percentages for funds that are above-target. Ignore those that are below target, because the negative drift must, mathematically, be equal in magnitude to the total positive drift.)

In the simulation, the total exposure to equities never exceeded 64% (40% in VBILX plus 60% of 40% in VBIAX). At times, when both US and international stocks were falling, the portfolio was invested 0% in equities, 80% in intermediate Treasuries, and 20% in mixed intermediate bonds. On average, over the entire 25-year period, the exposure to equities was 45%.

Current and Future Status
Going forward, a subscription service to be offered soon at this site will track blended portfolios and other rotation strategies, to monitor whether future results match the historical simulations.

Presently, as of August 1, a blended portfolio like the one in the simulation holds:

• 20% VBLIX
• 40% VMVFX
• 20% VBIRX (because of the sharp swings in US stock prices in June and July)

Disclosures
Portfolios described here 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 is not a registered investment adviser and does not own, sell, or manage any of these portfolios. Alex Wilkinson may own similar portfolios in personal accounts.

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.

Since being launched several years ago, ETFs and mutual funds invested in low volatility stocks have done well. Many of them have lived up to their objective to match the total return of the broad stock market while being less volatile. For example, compare the iShares U.S. Minimum Volatility ETF (USMV) and the Vanguard Total Stock Market ETF (VTI). From November 2011 through June 2019, USMV generated a slightly better annualized total return than the broad market (14.3% vs. 13.9%) and did so with less risk of loss, as measured by its maximum drawdown for the same period (-7.6% vs. -14.2%). On this data, you would surely find the low-volatility ETF attractive.

But there's a catch. Over this span, the U.S. stock market suffered some setbacks that lasted a few months, but never had a severe and prolonged decline, nothing like the dot-com collapse from 2000 to 2003, or the deep recession from 2007 to 2009. How might low-volatility funds perform, were they active during such periods?

Although no low-volatility fund or ETF was actively available at those times, back-dated results exist for the indexes that dictate stock-selections for USMV and other similar funds. The index values were generated by MSCI. They indicate what a fund currently pegged to the index might have done, had it been active since 1988 and had it been able to track the index closely. As I noted in an earlier post, retroactively generated indexes show drawdowns of about -40% for minimum-volatility stocks, both in the U.S. and internationally, between 1994 and 2019. Admittedly, broad markets were even more extreme, reaching cumulative losses of -55% or worse. Still, the index history argues that buying and holding a minimum volatility fund or ETF is no guarantee of shelter from stormy markets.

Rotating Minimum-Volatility Funds
A tsunami sinks all boats, even those more bouyant than most. To be secure when a tsunami threatens, you have to be out of the water, far inland, on high ground.

For investors exposed to financial storms, shelter is found in methods that remove most or all assets from the stock market (or in special instruments like put-options and inverse ETFs that offer downside insurance, typically with additional cost or risk). The method described here, called rotation, requires modest effort and some discipline, but is accessible to ordinary investors.

Shown below are the hypothetical results from using one specific version of a rotation strategy for the 25-year period from July 1994 through June 2019. It is not a buy-and-hold strategy. Nor is it buy-and-rebalance. Instead, it represents a portfolio that is invested, most of the time, in a specific mix of mostly U.S. and international minimum-volatility indexes, plus a small portion of long-term bonds. Sometimes, in a simple but well-defined manner, it rotates to being invested entirely in a broad selection of bonds.

The main feature of this hypothetical portfolio is that it achieved returns exceeding stocks in the long run, while exhibiting volatility similar to a benchmark of 10-year U.S. Treasury bonds. Below, I explain step-by-step how this portfolio works. Also, coming soon at this site, a subscription service will be available that provides monthly updates on the composition and performance of this and other portfolios.

Building a Rotation Portfolio
In terminology introduced in my post Time to Rotate Out of Stocks?, the strategy of the portfolio in the chart is Minimax Rotate 80-or-0, applied to minimum-volatility funds. The objecitve is a compromise between maximizing returns (by holding up to 80% in low-volatility stocks) and minimizing drawdowns (by sometimes rotating to 0% in stocks).

The data in the chart simulates this portfolio with historical data for mutual funds and index values. If implemented today with ETFs, it would be constructed as follows:

1. At all times, 20% of the portfolio is invested in BLV, a Vanguard ETF that holds a mix of long-term corporate and government bonds. The simulation constructed an equivalent fund by combining actual historical returns of two Vanguard mutual funds, VWESX (long-term investment-grade bonds) and VUSTX (long-term U.S. Treasuries).
2. Either 20% or 0% is invested in EFAV, an iShares ETF of minimum volatility stocks in developed countries outside the U.S. The simulation used the corresponding MSCI index.
3. Either 60% or 0% is invested in USMV, an iShares ETF of minimum volatility stocks in the U.S. The simulation used the corresponding MSCI index.
4. When assets are rotated out of EFAV and USMV, they are held in BND, a Vanguard ETF that tracks an index of the entire U.S. bond market. The simulation used actual historical data for VBMFX, Vanguard's equivalent mutual fund.

To manage its holdings, the portfolio follows a few simple rules:

1. Once a month, compare the 12-month total return of EFAV (non-U.S. minimum volatility stocks) to that of BND (the bond alternative). If BND has the better 12-month return but funds are currently invested in EFAV, then move the EFAV amount to BND.
2. Similarly, at the same time every month, compare the 12-month total returns of USMV (U.S. minimum volatility stocks) and BND (the bond alternative). If BND has the better 12-month return but funds are currently invested in USMV, move the USMV amount to BND.
3. If, at the same time every month, BND holds funds but has a smaller 12-month total return than EFAV, USMV, or both, transfer assets from BND to the better-performing alternative(s). For example, suppose EFAV and USMV were both at $0; both had better 12-month returns than BND; and the amount held in BMD were $10,000. Then $7500 would go USMV and $2500 to EFAV because their targets, 60% and 20%, respectively, have a 3-to-1 ratio. As another example, suppose that both EFAV and USMV had better 12-month returns than BND; that funds were already invested in USMV from a previous month, but EFAV had $0; and that BND held $3,500. Then $3,500 would be moved to EFAV.
4. At the same time every month, rebalance funds if the drift from current targets exceeds 5%. For example, suppose the targets this month were 60% BND, 20% EFAV, and 20% BLV, but the actuals were 63%, 22% , and 15% respectively. The two above-target ETFs sum to an excess of 5%. Therefore, move funds from BND and EFAV into BLV, to achieve the target percentages. In the 25-year simulation, rebalancing occurred rarely, and typically not when rotation was necessary. It can happen, however, that rotation and rebalancing are both required in the same month. For that reason, the monthly calculations should occur in a particular order. First, determine whether rebalancing is necessary; second, assess whether to rotate funds; and third, transfer amounts as needed.

In the 25-year simulation shown in the chart, the portfolio's holdings on the first trading day in July, 2019, were 21.0% in BLV (long-term bonds), 19.4% in BND (the bond alternative), and 59.6% in USMV. The drift was 1.0%, which was not enough to trigger rebalancing. The most recent rebalancing was in November 2018. (See my article on rebalancing for the reason to set the trigger at 5% and for the formula to calculate drift.)

Some Technical Details

1. Why these target percentages? For low-volatility stocks, my analysis of historical data implied that 80% is the best ceiling, and 0% the best floor, if the investor's goal is to find an optimal compromise between maximizing returns and minimizing drawdowns. The ceiling value of 80% is higher for low-volatility stocks than for broad market indexes such as the CRSP total market index or the S&P 500 (50% to 60% was best as a minimax ceiling for broad indexes). Another finding in my historical simulation was that a modest portion of non-U.S. low-volatility stocks generated better results than investing only in the U.S. version or equally in the U.S. and non-U.S. versions. Dividing the 80% ceiling into 60% U.S. and 20% non-U.S. worked well historically, although there is no guarantee that it would be the optimal mix in the future.
2. Why a 12-month window? Low-volatility stocks fall less rapidly than the average for all stocks. Consequently, a longer window is needed to detect a reliable change in outlook. The historical data implied that for low-volatility funds, 12 months worked better than shorter windows.
3. Why BND as the bond alternative? A broad bond index fund like BND has, on average, less volatility than a fund that holds long-term bonds, particularly Treasuries. To evaluate whether a bond-fund or a stock-fund is currently the better choice, the historical data favored comparing funds with similar volatilities. Thus, less volatile stock-funds like USMV and EFAV are best compared with a low-volatility bond-fund like BND.
4. Why once a month? If the decision points are too frequent, performance can decline. Although I did not have sufficient data to conduct a thorough search for the very best level of frequency across countries and times, I did conduct some analysis of recent data for the U.S. Taking action once a month tended to be better than weekly and quarterly, although sometimes every other month was virtually as good as every month. That said, the specific time of the month might not matter. My analysis used end-of-month values, but one might do equally well by checking every month on the 15th day, for example, or at some other reference point. The idea is to be consistent, every month, just once a month.
5. Do flip-flops occur? Despite the 12-month window, the simulation had rare occasions when the portfolio would have repurchased a particular ETF one month after having sold that same ETF. In such cases, the simulation temporarily held funds in the equivalent of BSV, a Vanguard index of short-term bonds. Doing so could be useful to comply with a brokerage firm's limits on frequent trading or to avoid the tax-consequences of a "wash sale." Alternatively, one could invest temporarily in a replacement fund that is similar, but that tracks a different index (for example, SPLV instead of USMV).

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 presented an analysis of floor and ceiling levels for the percent of stocks to be held in a rebalanced portfolio. Today's post presents a similar analysis for a portfolio that takes a different strategy. Instead of rebalancing toward a target percentage, it rotates strongly to stocks or to bonds, depending on which asset has recently had better returns. How strongly? Until this post, the working assumption has been to rotate the entire porfolio, going 100% to stocks or 100% to bonds. Today, the topic is whether it's best to rotate stocks to a floor higher than 0% or a ceiling lower than 100%. All these analyses are part of an on-going series that began on June 3, 2019, comparing traditional rebalancing with the alternative strategy of rotation. 

Drawdowns
The chart below summarizes 48 combinations of floor and ceiling values for rotating the portfolio between mostly or entirely stocks and mostly or entirely bonds. (For specifics about the data, see "Some Technical Details" at the end of this post.)

On average, across all floor-ceiling combinations, the trend for rotation was reminiscent of the one reported previously for rebalancing. Going to a floor of 10% in stocks was actually, perhaps counterintuitively, better than going to 0% in stocks. The margin was small, and tended to be better when the ceiling was low (as in the 40% example in the chart) than when it was high (see the 100% example). A floor of 15% was virtually as good as 0%, but above that point, drawdowns tended to accelerate.

Real Returns
​How do similar combinations of floor and ceiling values effect a portfolio's 25-year returns, adjusted for inflation? The next chart illustrates the main results, annualized.

There are two messages here. First, increasing the floor percent in stocks had little effect on annualized returns over a 25-year period. Even raising the floor to 40% reduced real returns by just a fraction of a percent compared to a floor of 0% to 15%. Second, in contrast, raising the ceiling had a big effect. Consistently applying the rotation strategy for 25 years yielded real returns that were about 2% higher when the ceiling was 100% than when it was 40%.

The average in the chart, representing a ceiling near 70%, paid handsome returns of about 6% above inflation when the floor was 10%. That result was quite close to the performance of rotating from a ceiling of 100% to a floor of 40%. As illustrated by these two examples of 70-10 and 100-40, different combinations of floor and ceiling values may produce similar long-term accumulations. They will differ, however, in potential drawdowns. That necessitates an analysis of relative returns, adjusted for drawdown risks.

Relative Returns
The story gets a bit more complicated at this point. The historical evidence indicated that three factors had to be considered together: drawdown risks, potential for real returns, and the window-size for comparing whether recent outcomes had been better for stocks or for bonds. To illustrate these dimensions, the chart below shows examples of relative returns (risk-adjusted) when large-cap stocks and 10-year Treasuries were compared over three-month and twelve-month windows.

To understand this evidence, recall how a relative return is defined (as detailed on June 17). It measures a portfolio's incremental real return, compared to investing 100% in 10-year Treasuries, after compensating for the portfolio's incremental risk of drawdowns. If a portfolio has better raw returns than Treasuries, but also has higher drawdowns, the relative return will be less than the raw increment. In fact, the relative return can diminish to virtually zero if the drawdowns are excessive.

Several points in the chart deserve emphasis:

• The relative returns for rotation portfolios were consistently high, generally above 1%. In contrast, previously reported results for rebalancing ranged from 0.3% to 0.8%. Thus, overall, rotation portfolios in these data-sets produced better risk-adjusted returns than rebalanced portfolios. (As will be noted in future posts, exceptions to this conclusion are rare.)
• Relative returns tended to be higher when the floor percent was lower. On reflection, this result makes sense. The trigger for rotating out of stocks and into Treasuries is that Treasuries, based on recent performance, are giving better returns; furthermore, their drawdown-risk is low. Therefore, reducing stock-exposure by a larger amount at such times should mean a greater reduction of potential losses. And the historical evidence says that it did.
• The best results came from portfolios with a ceiling at 50% in stocks, with a floor of 0% or 10% and a reference window at or near 3 months. Although not shown in the chart, a ceiling below 50% had somewhat lower relative returns. Very high ceilings, such as the 100% example in the chart, stayed close to the average outcome. The sweet spot may be about 50% to 60%.

Takeaways
The lessons to be drawn from these findings depend on your goals as an investor:

• If your main concern is to limit drawdowns, your lower boundary for a rotation portfolio should be 0% to 15%. This finding begs the question: "Which is better? Holding a rebalanced portfolio with a floor at 10%, or rotating a portfolio around low percentages, such as a floor of 0% and a ceiling of 15% to 25%?" My next post will examine exactly this question.
• If your main concern is to maximize real returns, then rotate your portfolio from high exposure to stocks (70% or more) to low exposure (0% to 10%).
• If you prefer a compromise on boosting returns while also limiting drawdowns, your best strategy is to rotate between about 50% to 60% in equities when they are strong, and 0% to 10% when they are weak, with the remainder in bonds. Another question is begged: "How do rotations like 50-to-0 or 60-to-10 compare to rebalancing at, say, 40-60 or 25-75?" As long-term portfolios, historically, all of these offered good risk-adjusted performance. But is any one of them distinctively better than the others for an investor who wants to optimize relative returns? This, too, will be covered in upcoming posts.

Some Technical Details
These analyses aggregated statistics and data from a large number of observations, which could be categorized in several ways:

1. Four countries: the U.S., Japan, Germany, and Australia. For all these countries, public monthly data was obtainable for (a) the total return, including reinvested dividends, for an index of large-cap stocks going back at least 25 years in local currency; (b) at least 25 years of dividend history for country-specific, constant-maturity, 10-year Treasury bonds in local currency; and (c) at least 25 years of inflation history as measured by a country-specific index of consumer prices.
2. Seven 25-year periods. Four quarter-centuries were available for the U.S., between April 1919 and March 2019, and one each in Japan, Germany, and Australia from April 1994 to March 2019.
3. Different reference windows. Generally, the analyses presented here are averages from comparing bond-returns and stock-returns over windows of three months or twelve months. Unless otherwise noted, the results were the same for these two windows. Other analyses, not presented here, also considered windows varying from one to twelve months, plus combinations of multiple window-sizes.
4. Floor-ceiling settings. The results in this post are from 48 pairs with floors of 0%, 10%, 15%, 20%, 25%, 30% or 40% in stocks and ceilings of 40%, 50%, 60%, 70%, 80%, 90% or 100% in stocks. These seven floors and seven ceilings generated 49 possible combinations. However, one of them, 40% floor and 40% ceiling, is really a rebalancing strategy, not rotation, and was therefore excluded.

​All together, the seven sets of 25-year periods for different countries, the two reference windows, and the 48 floor-ceiling settings generated 672 observation points, each of which had multiple statistics such as annualized nominal and real returns, maximum 25-year downdowns, worst-month drawdowns, and more, both for the large-cap indexes and for country-specific Treasuries.

Primary data-sources were the St. Louis Federal Reserve for Treasuries, inflation, and some stock indexes; Yahoo Finance for the historical total returns of other stock indexes; and older historical data for the U.S. as published by Robert Shiller. Data published directly by index-providers, such as the Deutsche Borse and MSCI, was sometimes used for verification  or to fill gaps.

Earlier posts this week compared rebalancing and rotation across time in a single country: 100 years in U.S. markets. Today's post takes a turn, pivoting to hold time steady while examining a varied set of countries. Time is constrained to the last 25 years; the countries are Germany, Japan, and Australia. While not having the last word, recent experience in these global markets closes one important chapter in the story that began on June 3 when I asked, What Now: Sell, Rebalance, or Rotate?

At first glance, the averages over the three countries seem familiar. The biggest drawdowns were for large-cap stocks; the smallest ones, for local 10-year Treasuries. Smoother results came from rebalancing 60% in stocks and 40% in Treasury bonds, while tempered drawdowns and the best inflation-adjusted returns were definitive for 100-or-0 Rotation. Underneath the averages, however, investors in the three countries had very different experiences in the last quarter-century.

Of the three, Germany most closely resembled the U.S. from 1994 to early this year. Stocks rose overall, though the German DAX had a deeper drawdown (-68%) than did the American S&P 500 (-51%). Bonds were more competitive with stocks in Germany, enabling a portfolio that rebalanced 40% local Treasuries against 60% local stocks, all in local currency, to keep pace with an all-stocks portfolio. While these strategies took their different paths to similar destinations, 100-or-0 Rotation ultimately found a way to take investors even farther in Germany (8.7% annualized, adjusted for local inflation) than did the same strategey in the U.S. over the same years (7.4%).

Japan's experience was sadly unique. Stocks were mostly underwater for the last 25 years. Though inflation was low, the Nikkei 225 barely kept up with it, even with dividends reinvested. Bonds and the 60-40 portfolio managed to finish about 3% and 2% above inflation, respectively, in their characteristic ways:  paddle-boarding with local Treasuries behind the harbor breakwall; and boogie-boarding to catch big surf the 60-40 way, not quite so daring as air-freaking stocks. Outmanuvering all others, once again, was 100-or-zero Rotation, which rode the good waves and avoided the rest.

Yet another distinctive pattern transpired in Australia. Nominal interest rates for local 10-year Treasuries were higher in Australia (averaging 5.7% from 1994 to 2019) than in the other countries (3.9% in Germany, 1.9% in Japan, and 4.4% in the U.S.). Had Australian investors appreciated that local inflation was tepid (2.5%), they would have been wise to prefer their Treasuries, whose 25-year run exceeded both the AX 200 index of stocks, with reinvested dividends, and a 60-40 rebalanced portfolio. The strategy of 100-or-0 Rotation was sometimes the worst, though not by much. In the end it eaked out a small victory.

Good as it was overall, 100-or-0 Rotation exhibited at least one consistent vulnerability. For the worst-month metric, it always finished in third place, better by far than stocks, but outdone both by bonds and by rebalancing. There's a simple explanation, and it has a clear message. If a strategy is 100% invested in stocks when stocks fall suddenly and dramatically in a very short period, as on Black Monday in October 1987 and in the flash-crash of 2010, then the portfolio gets the full effect. However, a portfolio invested partly or completely in Treasuries will partly or completely escape the damage. Furthermore, Treasuries will very likely rise in value at such times.

The natural question to ask is whether a better rotation would stay below some ceiling, never going to 100% in stocks. A related question might be whether 0% is, in fact, the best floor. Happily, the data of the last 100 years in U.S. markets and the last 25 internationally have clear answers for both questions. Next week's posts will show how the answers are derived.

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.

Yesterday's post examined rebalancing as a strategy for investing in Japanese stocks and government bonds over the last 25 years. Today's post applies the same analysis to the German DAX 30 index, German government bonds, and German inflation rates, all evaluated in Euros, for the same period from April 1994 through March 2019. It's part of a series that follows up my June 3 post about current U.S. markets, What Now: Sell, Rebalance, or Rotate? 

At first glance, the chart for Germany seems much like Japan's. Drawdowns were big, compared to real returns. Rebalancing, while it did not eliminate every period of distress, had some benefits as a compromise between investing wholly in stocks or in bonds.

On close inspection, however, German markets during this period, although similar in many respects to those in Japan, were also different in at least one important way.

​Yes, the maximum drawdown of -68% for a portfolio invested 100% in the DAX 30 was a debacle nearly identical to Japan's -66%. And, yes, the peak drawdown for government bonds was much easier to endure, hitting about -10% in both countries. And in both cases, a rebalanced portfolio split the difference. The biggest drawdown was about -31% for an investor who went half in stocks and half in government bonds, in the local currency, while rebalancing to 50-50 whenever the end-of-month allocation to stocks drifted past 45% or 55%.

The worst-performing months were also virtually identical in the two countries. Both had worst-month drawdowns around -25% for their all-stocks portfolios, -4% for government bonds, and -10% for 50-50 rebalanced portfolios.

What's interesting, however, is how the two countries differed on real returns, the cumulative annualized gains after adjusting for local inflation. In Japan, the rebalanced portfolio matched the performance of government bonds, which fared better than stocks. In Germany, stocks and bonds switched postions. The DAX 30 provided the better eventual outcome. And rebalancing? It went with the winner, matching German stocks this time.

Had you been a newbie investor in Germany or Japan in 1994, could you have known with any certainty whether to bet on stocks or on bonds for the next quarter century? Of course not. But if you hedged your bet by rebalancing equally across the two classes of investments, your end-result would have been as good as placing the lucky bet.

That's a powerful argument in favor of rebalancing as a strategy. But wait! Is the benefit limited to recent examples like these two, where mature markets in developed countries were all beset by asset bubbles, the Great Recession, and the financial engineering of central banks?  To expand the analysis, the next post will examine yet another example, the U.S. S&P 500 from 1944 to 1969, when the economic and financial setting was decidedly different.

This post is the first of several examining the basis of my June 3 post, What Now: Sell, Rebalance, or Rotate? Today, the topic is whether rebalancing a portfolio of stocks and bonds was an effective strategy in the past 25 years for investors in Japanese markets. In the days ahead, I'll present similar data for Germany and the U.S., and for a strategy of rotation rather than rebalancing.

The chart above summarizes total returns for three portfolios invested in Japanese markets from April 1994 through March 2019.  All the underlying data for prices, interest, total returns, and inflation are in local currency (Yen).

During this period, a prescient investor would have simply bought 10-year government bonds and held them. No stocks, no rebalancing, no worry! Why so?

At one point, government bonds were 10.5% below their previous peak for the period, as indicated by the bar for 25-year drawdown in the chart. Looking at your portfolio and seeing an unrealized loss over 10% could be troublesome. But you would have seen much worse with an all-stocks portfolio (-66.4%). A portfolio invested 50-50 in Japanese 10-year government bonds and the Nikkei 225, rebalanced monthly if it drifted to 45-55, would have mitigated the drawdown, yet remained alarming (-31.3%). In short, bonds had the least-bad losses.

Those drawdowns were not instantaneous. They evolved over several months. Could you have seen them coming, and perhaps taken some action? One way of doing so would be to monitor your portfolio every month, and assess the drawdown since the previous month. Had you done so, your worst monthly outcomes would have been -4.6% for bonds, -23.8% for stocks, and -10.7% for rebalancing. Losses of this magnitude can occur in a single day, as they did in the U.S. in 1929 and 1987. So the maximum drawdown in any month is credible as an estimate of the risk that is unavoidable for a portfolio. If you consider a potential unavoidable loss of 10% to be tolerable, then, at least for the case of recent history in Japan, rebalancing might be, for you, a strategy worth considering.

Potential drawdowns would be the only criterion that mattered if you were concerned exclusively about risks, not about benefits. Realistically, you likely have a personal preference to accept some temporary risk, provided that you get some eventual reward. Maybe you will tolerate a transient drawdown of X% if, in the long run, you stand to gain Y%.

With long-run returns, one concern (in fact, a hidden but pernicious risk) is that they may cover a period with high inflation. If your long-run return is 10% but inflation is 8%, your buying power, or real return, is just 2%. Thus, the risk-benefit calculation requires, in this data, comparing drawdowns with real (inflation-adjusted) returns.

Happily, in Japan for the last 25 years, inflation was nearly zero. In some years, the opposite occurred, with deflationary declines in prices that occasionally made bonds the indisputable investment of choice. As shown in the chart, rebalancing captured some of these benefits, matching an all-bonds portfolio over the full 25-year period; both portfolios generated real returns near +2%. Stocks, if you held them all that time, would have eventually pulled your results into the black, but only barely (+0.3% after adjusting for inflation).

In hindsight, had you been there, years ago, deciding how to invest in Japan for the next quarter-century, would you have gone all-in on government bonds? If not, and you instead opted for the compromise method of rebalancing, you would have done equally well in the end, and measurably better than by putting all your money on stocks. Along the way, however, you would have had to weather some nasty storms. In subsequent posts, I'll examine whether Germany and the U.S. were similar and whether, in all three countries, rotation would have proven superior.

NOTE: In October 2020, this post, and others on the rotation strategy, will be updated, merged into a single article, and moved to my new blog at https://likelyso.com/money.

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. 

One line in the chart shows a portfolio invested fully and continuously in a fund that tracks the S&P 500, with dividends reinvested. Another line shows full and continuous investment in a simulated fund of 10-year US Treasuries, with interest reinvested. For comparison, another line shows a simulated fund invested 60% in the S&P 500 and 40% in 10-year Treasuries, rebalanced monthly if the percentages drift to 65-35 or 55-45. The best results, however, are for a simulated fund using one version of the new method. It is invested either 90% in the S&P 500 and 10% in 10-year Treasuries, or vice versa, using a simple decision-point at the end of each month. It requires no more effort than monthly rebalancing, but generates smaller drawdowns and bigger returns.

I'll call the new method "rotation" to distinguish it from rebalancing. In brief, rotation ...

• Does not try to pinpoint the top or bottom. In fact, it is ordinarily a bit late.
• Does not prevent drawdowns. But it greatly reduces them, by design.
• Can easily be calibrated to limit tax consequences. Monthly churn is not necessary.
• Can align with personal tolerance for risk. A 90-10 split is not the only option; others, in fact, are ordinarily better.
• Has been robust, historically, across periods of high or low inflation, trending or choppy markets, and growing, stagnant, or recessionary economies in developed countries.
• Offers guidance about when and for whom the method is advisable. Sometimes, for some individuals, rebalancing may be better.

In the weeks ahead, I'll show more examples of rotation at work in various markets, with real and simulated investment funds. And, on July 1, I'll start posting monthly results using the method, allowing you to track it in real time.

Today, Mark Hulbert published a short article titled The Real Reason Why Value and Small-Cap Stocks Lag the Market.  It's a good article, as far as it goes, but overlooks some important points.

The gist of the article is this:

• In the past decade, the total return of small-cap stocks has lagged that of large-cap stocks, contrary to academic research that demonstrates the long-term superior performance of small-caps. The same is true of value stocks when compared to growth stocks over the past ten years.
• Historically, however, the long-term out-performance of small-cap and value stocks has not occurred in every time period of 1 year or 5 years or even a full decade. In fact, under-performance occurs more often than intuition might suggest.
• Therefore, investors should not abandon small-cap and value stocks merely because of their recent under-performance in the past 1, 5, and 10 year periods.

To these cogent points, I would add three more.

First, investors should not over-invest in small-cap or value stocks unless they plan to hold them for a long time, at least 10 years. For example, if you are investing in a college-savings fund for your child, it would be better (on average) to invest in broad market averages, rather than betting that the next 5 to 15 years will be one of the periods when small-cap and value stocks show their muscle.

Second, there is some evidence in academic research that the advantage of value over growth is stronger for smaller stocks, and that the value-advantage is bigger than the small-cap-advantage. Thus, in addition to planning for a very long holding period, investors should focus on the combination of small size plus good value, rather than on either factor in isolation. Because of this research, Vanguard in their recent ETF for U.S. value stocks (VFVA) has a disproportionate number of small and medium sized companies. The average market capitalization is $32B, and more than half of the holdings are mid-, small-, and micro-cap firms.  Other ETFs often do the opposite.  For example, the holdings in iShares VLUE have an average market cap of $215B, and 88% of them are large-cap companies.

Third, it not always obvious how to invest in "small" and "value" stocks as defined in the research. Funds and benchmarks often digress from the academic criteria. The S&P 600 Small-Cap benchmark, for example, has a bias toward small companies that are profitable. Thus, funds using this benchmark are perhaps most accurately described as "small quality" rather than simply "small-cap." In contrast, funds benchmarked to the CRSP or Russell definitions of "small" really are exactly that.

For "value" the problem is more pervasive. Often, "value" funds are better described as "value + quality" or "current value + expect earnings-growth" or some other composite terminology. In the original academic research, "value" meant simply a low price compared to book value. In contrast, the CRSP indices used by Vanguard define "value" by book to price plus four other metrics: forward earnings, historic earnings, price-to-dividend, and price-to-sales. Similarly, the MSCI benchmark for "Enhanced Value" uses book to price plus two more considerations: forward earnings and the ratio of a company's entire economic value to the cash it produces. Whether these divergences from the academic standards matter, favorably or unfavorably, is not the point. For investors, "value" in a fund's name simply cannot be taken at face value. To know what you are getting, you have to read the fine print.

The chart at the beginning of this post nicely illustrates these points. The combination of small value (as defined by Wilshire) has outperformed the total market since 1980. However, for the first 20 years of that period, small value stocks under-performed, largely because they were swamped by the dot-com bubble that peaked in early 2000. Not until the bottom of the 2008-2009 recession did they regain the upper hand.

Five years ago, iShares introduced ACWV, a fund of global stocks selected to be less volatile than average. Has the fund lived up to its forecast of providing returns equal to or better than worldwide stock markets, with less volatility?

In October 2011, iShares introduced a set of ETFs that tracked indexes developed by MSCI, the financial research and investment advisory firm. The most diversified of the new funds was iShares ACWV, which invested in low-volatility stocks across the globe. By design, it sought stocks that reasonably represented stock markets around the world, large and small; that approximated a standard mix of sectors such as energy, health, financials, industrials, technology, utilities, and others; and that would fluctuate in value less than average.

Theoretically, low volatility could be neutral. One can imagine that less rambunctious stocks might tend to rise or fall at the same diminished rate, gaining 5% when the broad market gains 10% and similarly losing 5% when the average loss is 10%. In reality, historical results show a favorable bias. When most stocks rise 10%, less volatile ones may gain, say, 7%; but when a 10% loss hits the broad market, less volatile stock may lose only 5%. Over a long period of time, then, less volatile stocks have tended to out-perform. They lag a bit in up-markets, but suffer far less in down-markets.

In MSCI's research, covering the period from 1988 to 2016, their global low-volatility index had a double advantage over an index of all stocks wordwide. It had better annual returns for the 28-year period, 8.75% vs. 7.26%, while also having a lower standard deviation (a measure of annual volatility), 11% vs 15%. Better returns and less risk? It seems too good to be true. Or to last forever. One can't help wondering if, as the investment world wises up, the benefits of low-volatility stocks may diminish.

Indeed, academic researchers have yet to agree on an explanation for the low-volatility effect, nor on a standard way to measure it. MSCI's method is one of several, in an area that remains new enough to capture a minor fraction of investors' dollars. It's the method I've chosen for this post because of the unique position of ACWV as having a five-year history, low costs, and global reach. (In subsequent posts, I'll review other good options.)

The table below shows results for the period from November 1, 2011, to November 30, 2016, using monthly data for two funds: iShares ACWV for global low-volatility and Vanguard VT for total global stocks. Both are invested roughly half in the U.S. and half in other countries. On all counts, ACWV did better. It had superior annual returns; scored better (lower) on standard deviation and maximum drawdown, which are measures of volatility; and thus did better, as well, on the Sharpe ratio, which adjusts returns for the amount of risk taken.

Visually, these results can be seen in two charts. The first compares weekly data from October 18, 2011, to November 28, 2016, for ACWV and a balanced portfolio. The balance was 80% invested in VT and 20% in long-term Treasury bonds (Vanguard VGLT). The rationale for the 80-20 portfolio is that mixing stocks with bonds is a traditional way to reduce volatility. Furthermore, long-term Treasuries tend to be negatively correlated with stocks; when one zigs, the other zags. One might expect the mixture to resemble low-volatility stocks, generating good returns at reduced risk. An 80-20 ratio was chosen to match ACWV on volatility; it was rebalanced when the stock portion drifted above 83% or below 77%, as recommended in our article on rebalancing. 

For the first three years in the chart, ACWV and the mixed portfolio were indistinguishable. They grew the same amount, at the same steady pace. In 2015 and 2016, however, ACWV took the lead. Over the entire period, a bit longer than five years, ACWV's original $10,000 investment grew to $15,609 while the mixed portfolio grew to $14,357. The next chart shows how these two investment strategies compared on volatility, over the same period.

The chart measures volatility in a way that may be more intuitive than, say, the standard deviation. Each marker in the chart represents an occasion when, over a four-week period, a portfolio lost value. In effect, it shows the frequency with which you might have felt some anxiety, if you inspected your portfolio monthly. The portfolio invested 100% in ACWV had 18 such occasions, or about one every four months. The mixed 80-20 portfolio had 19 of them. Both had mostly small losses of 2% or less, and both kept the maximum monthly loss under 6%.

A key takeaway from this analysis is that investing in low-volatility stocks reduces churn by about the same amount as crafting an 80-20 mix of stocks and bonds. However, during periods when stocks are rising or flat, as occurred respectively from 2012 through 2014, and from 2015 to 2016, low-volatility stocks may generate equal or better returns than a classical mix of stocks and bonds.

Importantly, this five-year analysis failed to include a time when stocks fell extremely. If stocks were to drop as sharply as they did in 2008-2009, perhaps a mixed portfolio would fare better than low-volatility stocks, because of the negative correlation with which Treasuries tend to rise as stocks panic. Still, all indications are that both a fund like ACWV and a mixed portfolio would fall in value less sharply than the broad stock market.

In subsequent posts, I'll refine this analysis by considering some addtional questions:

• What about currency risk? In ACWV, roughly half the stocks are purchased in currencies other than the U.S. dollar. Some alternatives, notably a fund from Vanguard, hedge against changes in currency exchange rates, thus potentially reducing another source of volatility.
• What if you prefer less international exposure? In that case, better options may be to craft a simple portfolio of a few funds, some of which specialize in low-volatility stocks in the U.S. or in a particular international sector.
• Finally, what about other factors? Low-volatility is but one of several methods that research has shown to be effective for building a robust portfolio of investments. Is it prudent to combine low-volatility funds with other factors, such as value, size or momentum?

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.