In December, able2pay.com will have a fresh analysis of value and volatility in the stock and bond markets. This post is a preview of the topics to be covered.

Always timely, questions like these seem particularly germane now. Stocks are over-valued by many of the traditional metrics; interest rates on bonds imply dismal future returns; and cash has languished below inflation rates for a painfully long period. If no investment has obvious value, does something have to give, and if it does, is there any prudent shelter from the ensuing volatility?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

​

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

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

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

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

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

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

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

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

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

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

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

First, consider the good points.

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

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

Now, the weak points:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Stock markets across the globe have been plunging lately, prompting all the news media and investment firms to speculate on reasons why and what to do. One sensible journalist, for example, concluded that the reasons are, alas, unknowable. And good investment firms like Betterment and Vanguard have sprinkled their websites with reassuring advice to stay on plan and not sell in a panic.

My take on the matter centers on this line of argument:

1. Volatility is a factor intrinsic to markets and economies. They occasionally suffer steep plunges, so-called "corrections" in markets and recessions in economies, sometimes in concert, sometimes not. Between the drastic dives, they more commonly grow in a positive and orderly fashion. But the dives will happen, sooner or later.
2. Predicting when they will happen, in advance, is hard. Maybe a few prescient souls can do it accurately for a while, but logically, if many of us could do it consistently, our collective actions would neutralize the effect or at least diminish it. We would be richer than we are.
3. Although we can't predict in advance, we can respond intelligently after the fact. One rational response is to rebalance. As Andrew Ang explains in his fine textbook, Asset Management, rebalancing a portfolio is, for strictly mathematical reasons, a counterweight to volatility. One good way to implement a rebalancing strategy is to monitor your portfolio monthly or quarterly, and realign it to your target allocations if the overall percentage of stocks has drifted 3% to 5% from your objective. Another way is to invest at a low-cost firm like Betterment or Wealthfront that does so automatically. (Learn more by reading our article on rebalancing.)
4. Additionally, volatility can be countered, somewhat, by investing in funds that specialize in finding low-risk stocks. Ang's book has more on this topic, and you'll find an overview in our article on factor investing.

To illustrate these ideas, consider the chart below. It shows three portfolios, all for the period from December 31, 2013, to January 20, 2016 (essentially, the last two years, up to the day before this post).

• Custom RB3% is a custom set of five low-cost mutual funds, rebalanced at the end of the month, if the portfolio's allocations drift by 3% from their targets. It was rebalanced twice previously, at the end of January and May 2015, and meets the criterion for rebalancing now.
• Custom RB5% is the same mutual funds, rebalanced monthly if the drift is more extreme, 5% or more beyond the target allocations. It was never rebalanced over the two-year period, but just now meets its 5% criterion for the first time.
• VSMGX is an all-in-one fund similar in composition to the custom fund. It has even lower costs than the custom portfolios, and is constantly rebalanced.

One implication from the chart is that rebalancing was effective when the custom portfolio drifted more than 3% to 5%, as compared to the VSMGX baseline. Granted, this one example would scarcely be adequate evidence, by itself. It aligns, however, with extensive historical analysis as reviewed in our article on rebalancing and with mathematical analysis as explained in Ang's textbook.

A second implication from the chart is about factor investing, which was the strategy used to select funds for the custom portfolios. Employing ideas outlined in two articles, Diversify! and Factor Investing (both on the Portfolios menu above), the custom portfolios consisted of:

• Vanguard Global Minimum Volatility (15%)
• iShares All-Country World Minimum Volatility ETF (15%)
• Vanguard Strategic Equity (15%)
• Vanguard U.S. Value (15%)
• Vanguard Long-Term Government Bond Index (40%)

This combination of funds is weighted for low-risk and for value and momentum, especially in smaller companies. Overall it is invested 15% in international stocks, 45% in U.S. stocks, and 40% in long-term Treasuries. Although well diversified, it is more selective than a broadly indexed strategy, as represented by VSMGX, Vanguard's LifeStrategy Moderate Growth fund. That fund currently invests 24% in a total index of international stocks, 36% in a total index of U.S. stocks, and 40% in two bond indexes representing all U.S. bonds and international government bonds. (In 2014 and early 2015, it had somewhat smaller international allocations.)

Although both the custom and VSMGX portfolios have a 60-40 split between stocks and bonds, and both implement a rebalancing strategy, their results in the recent two-year period were quite different, as the chart illustrates. Don't jump to conclusions, however. Future years may turn out differently than the last two, and the usual cautions apply: Diversification does not guarantee a positive return; any investment strategy can lose money; and your results may differ from those depicted here. The ideas in this post are presented for information only and are not meant to endorse a particular firm or security. Please read our full disclosures.

Taxes are such a headache.

Still, despite the pain, it's dumb to be dumb about taxes on your investments.

​I've assembled a new article, Being Tax-Wise, that tries to capture the main points to consider when planning your investments, so as to make them a notch more tax-savvy.

Some of the ideas are obvious: Save for retirement in an IRA or your employer's plan. Others, not so obvious: should you have both an IRA and your employer's plan?

Some ideas may be surprising: Did you know you can be the beneficiary of a 529 college savings plan you establish for your own graduate degree, and possibly get a state-tax rebate for doing so?

And, yes, some ideas are downright convoluted: Being tax-smart about retirement spending will keep you mentally fit, if your frontal lobe is ready to be exercised.

The article closes with suggestions on where to turn for tax-advice and second-opinions. In an area like taxes, where you are the one ultimately accountable for the decisions, professional advice and second-opinions would be smart for everyone. You can find the full article on the Investing menu.

The Portfolios menu has been expanded with new and updated articles on how to build a diversified portfolio of investments. The main ideas are in Diversify!, which uses specific examples to illustrate how to diversify across stocks and bonds, domestically and globally. Factor Investing digs deeper, showing how retail investors can build simple portfolios to capitalize on factors from academic research, such as value, momentum, and low-risk. And Finding Value explains how to use the able2pay.com calculators to adjust stock and bond allocations if U.S. stocks are over-valued (as they are today) or under-valued (as might happen in the future).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

It's been a few decades since inflation was much of a problem. As shown in the chart below, spiking inflation and plunging deflation occurred with disturbing frequency throughout most of the 20th century. The cliffs and canyons in the chart are daunting. In the last 30 years, however, consumer prices have been relatively calm. Producer prices, which are more closely linked to commodities, have been more volatile. Yet even they seem less craggy than in earlier decades. Not coincidentally, during the recent period of moderate inflation, recessions (shown in gray) have been spaced farther apart.

Should we stop worrying about inflation? Or is the recent quiescence a fool's paradise, certain to be ravaged some day with cyclonic fury? If we only knew.

But we don't know. And the recent moderation poses a problem. To judge whether an investment or strategy might protect a portfolio against inflation, we need to look back at least to the 1970's, but many investments, including TIPS and commodity-linked ETFs, don't go back that far. We have to rely on logic and theory more than on data. Or we have to assume that what works now when inflation and deflation are tame will continue to work, should the extreme tumult of past decades revive.

Just before the last big surge in consumer prices, in late 1975, suppose you saw inflation perking up and purchased some hard assets as a hedge. You bought a barrel of crude oil (it still resides in your garage) and a gold bar (it remains encased in your foam mattress). The next chart shows how these possessions fared in the nearly 40 years you have held them in storage. For comparison, I've added your other two investments, a boring fund of 2-year Treasury bonds and a plain-vanilla fund of the total U.S. stock market.

Your gold bar and barrel of oil were fabulous in 1980, as consumer prices peaked. Then, however, the Federal Reserve mercilessly raised interest rates, causing inflation to subside, and your winners went south. Zoom ahead to August 2015, and the picture is very different. Your barrel of oil is worth exactly what you paid for it (the chart adjusts for inflation each year). Your bar of gold is worth a bit more than its original price, in real purchasing power, but your boring 2-year Treasuries have done equally well, with a lot less drama. Best of all, by a whopping margin, is your stock fund, whose purchasing power has grown more than 10-fold.

The message of the last 40 years is very clear. The best long-run protection against inflation comes from stocks, tempered perhaps by some bonds if volatility is a concern. Had we done a similar analysis of other 40-year periods, the conclusion would have been the same, going back well into the 19th century.

Spot commodities, like the barrel of oil in your garage and the bar of gold in your mattress, are passive investments. Would more active strategies, such as funds that manage baskets of commodities or real-estate properties, do any better? Let's see. We'll look at three other options: commodity funds, real-estate funds, and a simple strategy based on stock-sectors.

Some exchange-traded funds (ETFs) and mutual funds specialize in managing baskets of commodities. Unlike investors who buy a spot commodity, most of them don't hold hard assets in storage (although some do, especially gold funds). Instead, they manage contracts for future delivery of hard assets. The head-fake is that they never take delivery. Instead, they roll the contracts, selling one that will soon expire and buying another with a future date. As collateral for their transactions, they deposit enough cash-equivalents (usually T-Bills) to cover their contractual obligations. Thus, these funds generate returns in three ways:

• Spot values on the commodities they have contracted to purchase.
• Cash returns in the form of interest earned on the collateral they have posted.
• Roll returns, or the difference in price between expiring contracts closed and replacement contracts opened.

Andrew Ang (Asset Management, Chapter 11, section 5.3) analysed the spot, cash, and roll components of one commodity index (GSCI) for the 42-year period from 1970 through 2011. I've reproduced his findings in the following chart, after adjusting for inflation.* Over the entire period, the spot and cash returns were about equal, and the roll return was slightly negative, for a total return of 6.6% above inflation. That value is similar to the very long-run real return on U.S. stocks. Significantly, commodity indexes such as GSCI tend to have low correlations with both stocks and bonds. The combination of a good return and a low correlation argues in favor of managed commodity funds as a long-term inflation hedge for a diversified portfolio. There are some caveats, however. 

First, as the chart shows, the spot component varies substantially. In the 1970s, when inflation was consistently high, the returns were handsome. From 1980 to 2000, however, virtually all the return came from cash collateral (interest on T-Bills or other cash-equivalents) and none from spot values. That's consistent with the earlier chart of spot-returns on gold and crude oil. In fact, if you compare the two charts, the elements coded in green are similar investments, short-term interest from Treasury notes or bills. Thus, a key reason why a managed fund may offer better inflation-protection than spot commodities is that it buys more than commodities. The fund also purchases short-term interest payments from the U.S. Treasury, which nicely hedge inflation (or deflation) when spot returns are poor.

Second, commodity funds differ in the commodities they track. Some track just one commodity (such as gold or crude oil) or one sector (such as energy or precious metals). Others track a basket of commodities, with energy-related components such as oil, gas, and coal getting more or less weight depending on the fund. Ang presents evidence that energy deserves to be weighted strongly because its correlation with inflation is higher than other classes of commodities.

Finally, the fees on commodity-related funds are sometimes high, close to 1%. 

With these points in mind, here are some options to evaluate, as you consider whether to allocate a modest portion of your portfolio to a commodity fund.

• Many of the largest and most liquid commodity-linked funds specialize in a single asset (spot gold with GLD or IAU, for example, or current crude oil with USO). Their low fees may be attractive, but they are poor diversifiers, unless you pick several of them to create your own basket.
• GSG, from iShares, tracks the more diversified S&P GSCI index, which is about 70% energy-related. While not the largest commodity fund, it is large enough to offer reasonable liquidity.
• DBC, from Invesco-Powershares, gives 55% weight to energy, with the remainder divided about equally between agriculture and metals. The fund has an active strategy intended to optimize roll returns. It is a very large fund and very liquid.
• USCI, from United States Commodity Funds, samples multiple commodities in a manner intended to capture momentum and value (see my post on factor investing). Momentum is gained by selecting commodities whose spot returns have recently been the best. Value is earned by selecting commodities whose contracts currently offer the most favorable roll returns. The fund's exposure to a particular sector, such as energy, will systematically rise or fall as the sector gains or loses either momentum or value.

Should you invest in commercial real estate to diversify your holdings? And will commercial real estate help to guard your portfolio against inflation? It's important to acknowledge that these are two different questions. They may have different answers.

Before trying to answer them, let's consider your options for investing in commercial real estate. For most retail investors, the options are limited.

• Real Estate Investment Trusts (REITs) are companies whose stock you can purchase in a brokerage account, mutual fund, or ETF, sometimes within a 401(k) or 403(b) retirement plan. A REIT owns, operates, or finances real property. For example, it may own office buildings, shopping centers, apartment complexes, hotels, timber land, nursing homes, storage facilities, commercial mortgages, or other income-producing land or structures. Only a small fraction of U.S.commercial property is held by REITs. The great majority is privately owned. By U.S. law, REITs must be listed on a stock exchange and must pay 90% of their taxable income as dividends to shareholders.
• TIAA Real Estate is a unique fund structured as a variable annuity. It may only be available if you have a qualified retirement plan at TIAA-CREF. This fund is not a REIT. It is not listed on a stock exchange, and therefore cannot be bought and sold with the same liquidity and frequency as a REIT. By investing in this fund, you own shares in the real-estate portfolio that TIAA-CREF uses to manage its insurance operations. In addition, the fund holds some cash reserves and may purchase shares in true REITs. Mostly, however, it comprises the office buildings, shopping centers, and apartment complexes from which TIAA-CREF generates income to run its own business. The values of these properties are assessed infrequently, which means that the share-values are less volatile than those of a publicly traded REIT. The fees are also higher than, say, a REIT index fund.

Returning to the key questions, will either of these forms of commercial real estate diversify a portfolio that already has stocks and bonds? The answer is a weak yes.

• REITs are mid-cap value stocks. Their average size is the same as the average mid-cap stock, and their factor profile (see this earlier post) is very similar to a mid-cap value index. Thus, where a small-cap or mid-cap value fund would diversify your portfolio, a REIT index fund such as VGSIX or VNQ from Vanguard will do much the same. One sensible strategy would be to assign half your U.S. stock allocation to U.S. large caps (such as the S&P 500) and split the other half equally between U.S. small-cap value and a REIT index. By doing so, you might see a small boost in return, maybe 0.2%, compared to using just U.S. large caps and small-cap value.
• TIAA Real Estate, in nearly 20 years since its inception, has generated returns mid-way between bonds and stocks. The trend-line went smoothly upward from 1995 to 2008, then fell 40% during the financial crisis, then resumed a steady rise from 2010 to 2015 (see this chart from Morningstar). In contrast, the trend-line for intermediate bonds was upward throughout this period, while the pattern for stocks was a double-crash, first from 2001 to 2003, then again in 2008-2009. Because of the different historical patterns, a portfolio that contains some TIAA Real Estate, plus stocks and bonds, would be better diversified than stocks and bonds alone. A reasonable strategy might be to replace a small portion of stocks (maybe 5%) and a small portion of bonds (maybe another 5%) with an investment in the real estate fund (10% in this example).

By diversifying in this manner, will your portfolio be better sheltered from inflation? The answer this time is yes, but not strongly enough to matter. Both REITs and TIAA Real Estate have tended to rise when inflation is slowly rising. Sweet! Both collapsed, however, because of the brief but intense deflation that occurred in late 2008. Sorry! In the long run, to be fair, both have bested inflation. The return of REITs surpassed inflation by 5.25% since 1972; those of TIAA Real Estate did so by 4.17% since 1995. While these returns are good, the total stock market did even better in both cases. Thus, commercial real estate may add little inflation-protection above and beyond what stocks generally provide, in the long run. (Ang's analysis led to a similar conclusion.)

The evidence reviewed to this point suggests:

• Stocks, combined with some bonds, offer excellent protection against long-run inflation.
• Commodity funds may add value, too, but are volatile and often expensive.
• Real estate may diversify stock holdings, but won't boost stocks' capacity to outlast inflation.

There's one final idea to consider. It may be the best of the lot.

The chart above shows, on the right-hand scale, that by the summer of 2015, it cost $2.31 to purchase consumer goods and services that would have cost $1.00 in May 1984. Over the same period of time, as shown on the left-hand scale, an "All Weather" fund rose from $1.00 to $17.52. Two attributes of this fund are significant:

• The rate of return far exceeded inflation. The $17.52 generated by the fund in 2015 would have bought more than seven times the goods and services of the original dollar invested in 1984, even at 2015's inflated prices.
• The pattern of growth corresponded nicely to the inflation profile, as shown by the close alignment of the two lines in the chart. The correspondence seems especially clear in the past 15 years, when the Consumer Price Index has been reported with increasing precision, compared to its earlier computation.

The All Weather fund is exceedingly simple. It's a one-third allocation to global energy stocks and two-thirds to 10-year U.S. Treasury bonds, rebalanced monthly. The rationale for energy stocks and intermediate Treasuries is sound. It's based on both logical and statistical considerations.

Logically, there are two ways in which consumer prices may change: inflation (the cliffs) and deflation (the canyons). Ideally, one wants protection from both extremes. But it is implausible that any ordinary security would rise in value when inflation spikes, equally rise in value when deflation plunges, and otherwise stay neutral. In a (long-only) commodity fund, this problem is partially solved by jointly holding commodity contracts, which tend to rise with inflation and fall with deflation, and cash collateral, which may mitigate deflationary trends during a recession. In the All Weather fund, energy stocks coupled with intermediate Treasuries offer an analogous solution. When inflation occurs, energy companies know how to prosper; in times of recession and deflation, Treasury bonds become a safe haven for investors. Yet, if held long enough, both energy stocks and Treasury bonds have returns that exceed the rate of inflation.

Among sectors of the stock market, energy correlates most strongly with inflation. One way to compute the correlation is to use the annual change in price from the end of December in a given year to the end of the following December. The U.S. energy sector, as measured by the XLE, the SPDR Energy ETF over the 16 years ending from 1999 to 2014, correlated 0.72 with corresponding annual changes in the Consumer Price Index. No other sector was even close. Second place went to Utilities (0.42). REITs did worse (0.14), as did spot gold, a surrogate for a gold ETF (0.26). If computed over three years, the correlation was again highest for Energy (0.73), with Utilities a distant second (0.48). Admittedly, the period from 1998 through 2014 saw generally mild changes in consumer prices, except for a few months of sharp deflation at the end of 2008. So this evidence has to be taken with a bit of caution.

Treasury bonds, in contrast, tend to have a decreasing correlation with inflation, the longer the maturity of the bonds (see Ang's chapter 9, section 3.3). In the data I examined from the last three decades, bonds with maturities of 10 years or longer correlated with consumer prices at values between zero and 0.2. The same bonds, over the same three decades, tended to be negatively correlated with stocks. Thus, if stocks fell, particularly when deflation or recession occurred, intermediate and long-term Treasuries often rose. It's been the perfect recipe. These bonds didn't pay much attention to consumer prices, except when we really needed them to, when stocks were getting slammed.

Note that intermediate TIPS don't dish up the same tasty meal. Because they are indexed to inflation, they will be marked down in value when deflation hits. Something like that happened during the financial panic of late 2008 and early 2009, when intermediate TIPS fell and Treasuries rose. That's why, for the intermediate or long term, Treasuries are better than TIPS in an All Weather fund. Despite the "P" in their name, intermediate TIPS protect less well against inflation than energy stocks do, for holding periods of a few years, and during deflation they hurt more than they help.

One final chart may serve to illustrate these points. Shown below are three portfolios. One is the same All Weather fund as in the previous chart. Another is like the All Weather fund, except that a U.S. REIT index replaces the global energy stocks. The third fund invests 100% in an index of the total U.S. stock market. All three portfolios are adjusted continuously for changes in consumer prices. Over the 31 years depicted in the chart, the All Weather fund had a compound real return of 6.7%, while the real return of REITs plus 10-year Treasuries was somewhat lower (6.0%), and the total stock market, noticeably higher (8.2%). Although, by this metric, the fund fully invested in stocks was best at exceeding inflation, all three were very good, and the all-stocks option was beset with volatility.

The three funds in the chart correlated with consumer prices in a manner consistent with the logical and statistical analysis presented above. For the all-stocks fund, correlations from 1984 to 2015 were virtually zero for continuously rolling 12-month periods (.04) and 36-month periods (.07). For REITs plus 10-year Treasuries, the correlations were no better, -.03 at 12 months and .00 at 36. Only the All Weather fund with its energy stocks and 10-year Treasuries had positive correlations at 12 months (0.40) and at 36 (0.55). In short, the All Weather fund best achieved inflation-beating returns at a pace that emulated yearly changes in consumer prices.

If the relatively mild inflation of the past 30 years continues, your portfolio may not need any special strategy to keep abreast of consumer prices. Simply including a reasonable dose of stocks in your portfolio may suffice. Then again, if rousing inflation and deflation come back to plague us, we cannot be sure that strategies tested on data from the past 30 to 40 years will continue to work. Still, those strategies are the best options available.

• Investing in real estate is not one of them, although it might be productive as a way to add mid-cap value to your stock-holdings.
• Purchasing a multiple commodity fund or ETF may diversify your portfolio and, over a decade or more, achieve inflation-beating returns comparable to stocks. But pay close attention to the costs, and limit your exposure to a minor portion of your total portfolio.
• Alternatively, instead of purchasing commodity-linked funds, consider creating your own All Weather fund with global energy stocks and intermediate or long-term Treasury bonds. For global energy, Vanguard offers a mutual fund, VGENX, which was used for the analyses presented above; iShares IXC is a similar ETF. Both have somewhat higher fees than a U.S.-only energy ETF, which could work equally well. Vanguard and iShares both offer intermediate and long-term Treasury funds, all at low fees. A sensible strategy would be to set aside 10% to 25% of your portfolio for your All Weather fund, allocating a third of it to energy stocks and two-thirds to Treasuries with intermediate or long maturities. 

* For other purposes, a different metric of inflation might be preferable. A manufacturer, for example, might prefer producer prices or a GDP deflater, rather than consumer prices. I'm assuming that, like me, if you cash in your commodity shares, you'll use the proceeds to buy more coffee, splurge on some spiffy jeans, get a nice surprise for someone you like, or take a trip to someplace warm and friendly.

Data sources: Yahoo Finance for historical prices of mutual funds and ETFs. FRED for Treasuries, spot WTI crude oil, spot gold, the Wilshire 5000 index of total U.S. stocks, and CPI-U.  Morningstar for variable annuity prices of TIAA Real Estate. Andrew Ang for GSCI index price history. For those interested in technical details, a forthcoming article to be published at this site will explain how the measurements here were constructed and compare them to other possible methods of analysis.

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