Monday, August 27, 2012

Permanent Portfolio Shakedown Part II

In Part I of the Permanent Portfolio Shakedown we investigated the history of the approach, tracing it back to Harry Browne in 1982. The company he helped to found, The Permanent Portfolio Family of Funds, has been running their version of the strategy in a mutual fund for almost 30 years, with fairly impressive results.

Harry's thoughts about the portfolio are worth repeating in this second instalment:
Established in 1982, in an era of stagnant economic growth and rampant inflation, Permanent Portfolio seeks to provide a sound structure and disciplined approach to asset allocation. The Fund was born in an environment where investors didn’t know where to turn. Regardless of what an investor did, they were losing money. Harry Browne, one of the founders of the fund stated, “It’s easy to think you know what the future holds, but the future invariably contradicts our expectations. Over and over again we are proven wrong when we bet too much on our expectations. Uncertainty is a fact of life.” No one can accurately predict the future.
[The] Permanent Portfolio recognizes this limitation and seeks to invest a fixed “Target Percentage” of its assets to six carefully chosen, diverse and “non-correlated” investment categories. Such diversification in a single mutual fund seeks to mitigate risk regardless of the economic climate. [Emphasis ours]
Harry's critical revelation was that no amount of knowledge about markets or economies will enable  an investor to accurately see into the future, so investors should balance portfolios between diversified asset classes to 'mitigate risk regardless of the economic climate'. This is consistent with the broad intention of Ray Dalio's 'All Weather' portfolio and the 'Risk Parity' paradigm he spawned, with important differences that we will address later in this article. 

Later in his career, Harry suggested that a permanent portfolio could be constructed very simply with equal allocations to stocks, Treasuries, t-bills and gold. We explored this simple mix in Part 1 to discover how well this portfolio has done since 1970 relative to other common allocation strategies, such as 60/40, and discovered that the 'Simple Permanent Portfolio' approach has delivered relatively impressive results over the past 40 years.

Simple vs. Complex Permanent Portfolio

The Permanent Portfolio Family of Funds has been running their Permanent Portfolio mutual fund since 1983, so we wanted to explore the performance of the actual fund versus the simple version since the fund's inception. The Permanent Portfolio Family of Funds only provides annual returns to the mutual fund since inception, so the chart reflects annual returns to both approaches.

Chart 1. Permanent Portfolio mutual fund (PRPFX) vs. Simple Permanent Portfolio
Source: Permanent Portfolio Family of Funds, Ken French, Shiller, FRED

You will note visually that the simple portfolio tracks the mutual fund quite well, and indeed the correlation between them is 0.70 over the period, which suggests that the simple portfolio explains about 50% of the returns to the mutual fund over the period. PRPFX had a miserable year in 1984, losing about 13% that year while the simple portfolio held in with a return that year of about 4%, but PRPFX made up for it from 2002 - 2007 with substantially higher returns than the simple portfolio, perhaps because of its exposure to real estate.

The annualized returns to the fund are 6.8% vs. 7.8% for the simple version, but this difference would be accounted for by the fund's 0.76% MER and the fees one would incur to purchase the indices in the simple portfolio in ETF form. After accounting for this, the returns are effectively the same. The volatility of the simple portfolio is lower however, at least using annual return data. PRPFX has a realized annual volatility of 8.3 vs. 5.3 for the simple version, which means the return/risk ratio is lower for the mutual fund: 0.82 vs. 1.45.

The rest of this article will utilize daily long-term data for each of the four asset classes in the simple version of the approach going back to 1970. The simple permanent portfolio delivered the following return and risk profile going back to 1970 (a review from Part 1). You will note annualized returns of 8.55%, a return/volatility ratio of 1.25, and a maximum drawdown of about 18%, with 93% of rolling 12-month periods delivering positive nominal returns (right bottom corner of data table). We will benchmark all subsequent tests against this basic profile.

Chart 2. Simple Permanent Portfolio, rebalanced quarterly, 1970 - 2012
Source: Ken French, Shiller, FRED

Volatility Management

The Permanent Portfolio approach has a faithful following, and for good reason, but we are going to risk introducing a few simple overlays to the basic approach in an effort to improve risk adjusted returns.

The most obvious first step, at least for us, is to introduce a volatility management overlay to maintain a consistent risk profile in all market environments. In our experience, we have yet to examine a portfolio management approach where the return/risk profile is not improved by intelligent volatility management.

The long-term ex-post observed volatility of the basic simple permanent portfolio is 7%, so we will use this target to actively manage the portfolio volatility using the exact same 25% capital allocation to each of the four asset classes. As a reminder, we target portfolio volatility by measuring the volatility of the portfolio at each rebalance period and adjusting total portfolio exposure lower if observed volatility is too high by adding cash.

Chart 3. Simple Permanent Portfolio, 7% target volatility, rebalanced quarterly, 1970 - 2012
Source: Ken French, Shiller, FRED

The volatility targeting approach seems to add some value, raising returns from 8.55% to 8.8% annualized, and reducing the maximum drawdown to 12.4% from 18%, or about one third. This seems like a simple, coherent, and intuitive improvement that is worthwhile implementing.

Risk Parity

Risk Parity proponents will protest that the current incarnation of the simple approach has a massively skewed risk profile. Chart 4. shows the return and risk contributions for each of the 4 asset classes in the basic equal weight approach - you may have to click on the image for a readable version. IRX is the t-bill (cash) index.

Chart 4. Marginal Return and Risk contributions 1970 - 2012
Source: Ken French, Shiller, FRED

You can see that stocks and gold (VTILT and GLDLT respectively) contribute about 5x - 8x as much marginal volatility to the portfolio as Treasuries (IEFLT), though they only contribute about 25% more returns.

The marginal risk contribution accounts for the risk each asset contributes to the portfolio after accounting for the asset's diversification potential. While Treasuries are structurally less volatile than stocks or gold over the long-term, they also provide stronger diversification than either stocks or bonds within the portfolio. As a result, Treasuries 'hit above their weight class' in the portfolio in terms of the diversification they provide relative to the risk they introduce. This explains why the marginal risk contribution of stocks and gold is greater than either's proportional volatility, while the risk contribution of bonds is lower than bond's proportional volatility.

Adherents to the risk parity philosophy aim to create portfolios where each asset class contributes an equal amount of volatility to the portfolio rather than an equal amount of capital. Chart 5. approximates a risk parity approach using stocks, gold and Treasuries, with a 7% risk target. The cash allocation is dynamic where cash expands and contracts in the portfolio in order to keep the portfolio volatility close to our 7% target. 

Chart 5. Simple Permanent Portfolio, Risk Parity, 7% target volatility 1970 - 2012
Source: Ken French, Shiller, FRED

The 7% target volatility risk parity version above delivers similar returns to the traditional simple approach, with 13% lower volatility and 35% lower drawdown. However, the ex-post allocation to cash at a 7% volatility target is just 8%. In order to have a 25% average allocation to cash over the period, in keeping with the traditional simple approach, we need to apply a 5% risk target instead.

Chart 6. Simple Permanent Portfolio, Risk Parity, 5% target volatility, 1970 - 2012
Source: Ken French, Shiller, FRED

The realized ex-post volatility of the 5% target volatility risk parity permanent portfolio is just 4.84%, and the largest drawdown was just 8.4%, for which investors would have been compensated with a 7.89% annualized return. Pretty amazing for a portfolio with half the volatility and just 25% of the drawdown of a typical bond portfolio!

A Tactical Permanent Portfolio

We'll really be treading on thin ice with the die-hard permanent portfolio crowd with these next simulations, but I hope they will forgive our impiety in our perpetual pursuit of a 'better way'. 

The potential problem, as we see it, with any static asset allocation, including the permanent portfolio's permanent equal weight allocations to stocks, bonds, gold and cash, is that sometimes everything is expensive all at once, and returns to all asset classes have the potential to be low or negative in tandem. The current environment may represent one of these periods, where certainly bonds and cash are more expensive than they have ever been, with yields on Treasuries lower than at any other time in the last 220 years (source: Bank of America). Cash yields essentially zero. We think stocks are expensive as well (see here and here), and gold is at best a wildcard, having rallied by 500% or more from its lows in 2001. 

If we are right, and the permanent portfolio is vulnerable to synchronized losses, then it makes sense to explore some tactical or dynamic overlays to help avoid investing in asset classes in sustained downtrends. 

Mebane Faber is credited with bringing moving averages to the masses with his Quantitative Approach to Tactical Asset Allocation whitepaper in 2005. In it, he describes an approach that applies a 10-month moving average to basket of 5 asset classes: stocks, Treasuries, commodities, REITs and international stocks. While there is nothing magical about the 10-month moving average, this approach is ubiquitously cited elsewhere, and in our testing we observed no material difference with other moving averages. The following simulations apply monthly rebalancing.

Chart 7. Simple Permanent Portfolio, 10-Month MA, 1970 - 2012
Source: Faber, Ken French, Shiller, FRED

Chart 7. delivers a pretty compelling equity line. You will note that returns rise above 10% annualized over the period while volatility and drawdowns remain similar to the original simple approach. The majority of losses to this approach occurred during the tumultuous 1970s and 1980, with the largest drawdown occurring in March of 1980 as gold and stocks collapsed at the same time while both were far above their respective 10-month moving averages. 

We stated above that risk adjusted returns are almost always improved by managing portfolio level volatility, so below we tested the Faber 10-month moving average approach but also applied a 7% target volatility overlay. Chart 8 shows the results of this combination.

Chart 8. Simple Permanent Portfolio, 10-Month MA, 1970 - 2012
Source: Faber, Ken French, Shiller, FRED

Now we are really cooking! While the absolute performance of the approach drops by about 0.4 percentage points per year, the risk profile drops dramatically; volatility drops to 5.5% annualized and the maximum drawdown drops to 9% from 19%. Even better, investors would have realized positive results over 98% of rolling 12-month periods!


Permanent Portfolio adherents are right to be proud of the performance of their approach over the past 40 years. Of all the static asset allocation approaches we have tested, the PP ranks near the top of the list in terms of risk-adjusted returns. Further, the philosophy behind its construction is consistent with the goal of resilience in the face of any economic environment. 

Even PP zealots would be silly not to consider some of the simple volatility-based overlays that we presented however. Simple volatility management techniques are philosophically and empirically coherent, and deliver similar results with much smaller drawdowns.

While risk management is important, it does not address the most important challenge to the traditional portfolio: what happens next. That is, how will the traditional model behave going forward in the current environment, where all assets have been artificially inflated at once via coordinated global central bank intervention. Will the portfolio prove resilient to a period of sustained global deflation with Treasury yields already at record lows?

Tactical overlays to the traditional approach may help address this problem by systematically exiting asset classes that are exhibiting strong and/or sustained negative price trends.

The simple Faber moving average approach on its own does not seem to deliver much value above the profile of the traditional PP approach. However, combining a tactical moving average approach with simple volatility management delivers similar high returns, but without the major drawdown characteristics of the simple MA approach.

Further, this approach delivered positive returns over 98% of periods since 1970.

Monday, August 20, 2012

Permanent Portfolio Shakedown Part 1

The Permanent Portfolio is an asset allocation concept first introduced by Harry Browne in 1982. The Permanent Portfolio Family of Funds website has this to say about the strategy, which they have been running in mutual fund format for about 20 years.
Established in 1982, in an era of stagnant economic growth and rampant inflation, Permanent Portfolio seeks to provide a sound structure and disciplined approach to asset allocation. The Fund was born in an environment where investors didn’t know where to turn. Regardless of what an investor did, they were losing money. Harry Browne, one of the founders of the fund stated, “It’s easy to think you know what the future holds, but the future invariably contradicts our expectations. Over and over again we are proven wrong when we bet too much on our expectations. Uncertainty is a fact of life.” No one can accurately predict the future. 
[The] Permanent Portfolio recognizes this limitation and seeks to invest a fixed “Target Percentage” of its assets to six carefully chosen, diverse and “non-correlated” investment categories. Such diversification in a single mutual fund seeks to mitigate risk regardless of the economic climate. [Emphasis ours]
The Permanent Portfolio mutual fund purports to invest in 6 major asset classes according to the fixed prescribed weights in Chart 1, but the asset classes in Chart 1 leave a lot of 'wiggle room',  so we performed a factor analysis to determine asset class exposures over the past 3 years (Chart 2).

Chart 1. PRPFX weights from the fact sheet.

Source: Permanent Portfolio Family of Funds

The factor analysis below is the product of a multiple regression analysis whereby the daily performance of the Permanent Portfolio mutual fund is regressed on a basket of global risk factors. The factors in Chart 2. were statistically significant in explaining the performance of the portfolio over the past 3 years; non-significant factors were rejected.

Chart 2.
Source: Yahoo finance

You can see that the performance of the Permanent Portfolio can largely be attributed to high-grade U.S. bonds (AGG), U.S. stocks (VTI), and Gold (GLD) over the past three years, with each contributing about 20% to performance. All 8 factors together explain over 90% of portfolio returns for the period (see R-Squared = 0.92885).

On several occasions, Mr. Brown indicated that a simple equal allocation to stocks, gold, Treasuries, and T-bills would probably achieve the same goals as the more complex portfolio used in his mutual fund.  Empirically, these four assets have worked very well together in portfolios for at least one reason: the long-term ex-post pair-wise correlations between the assets is essentially zero over the past 40 years, which means they offer superb long-term diversification potential.

A High Hurdle

Before we investigate the performance of the Permanent Portfolio, let's set the stage by taking a look at the performance of some more conventional approaches using daily total return data back to 1970. All multi-asset portfolios are rebalanced quarterly.

Chart 3. U.S. Total Stock Market
Source: Ken French

Chart 4. 60/40 Stocks/Treasuries
Source: Ken French, Shiller

Equities and the 60/40 portfolio have delivered essentially the same 9.6% total returns since 1970, (an astonishing blow to CAPM), but the 60/40 portfolio delivered its returns with almost 40% less volatility (10% vs. 17%) and drawdown (30% vs. 53%).

Chart 5. Permanent Portfolio (Equal Weight stocks, gold, Treasuries, and cash), 1970 - 2012
Source: Ken French, Shiller, CRB

The Permanent Portfolio provided returns of 8.55% per year over the same period, which is over 1% per year lower than either stocks or the 60/40 portfolio. However, because of the low correlations between the assets, this portfolio had substantially lower risk than 60/40. Ex-post volatility averaged less than 7% versus 10.4% for 60/40, and the maximum drawdown was reduced by almost half (18% vs. 30%)

The plain-vanilla version of this strategy is quite compelling on its own, and tough to beat. Unfortunately, the approach faces the same challenge as other static allocation approaches in the current environment: record low interest rates and expensive stocks and commodities, which suggests that returns to this approach may not be as strong over the next several years.

In Part 2 of this series we are going to explore some simple techniques that might further improve the performance of this approach, including volatility management, risk parity, moving averages and finally Adaptive Asset Allocation.

Friday, August 10, 2012

Focus On What You Can Control

Andrew Ang has published online draft versions of some sections from his forthcoming book, Asset Management, and from what I've read so far it promises to be a treasure trove, at least for the narrow sliver of investment managers that care about evidence over theory.

His chapter on 'Equities Market Level' is especially interesting to us, as it explores two areas of research that we have also explored at length in many articles on this blog: statistical forecasting of long-term stock market returns, and; the observation and management of portfolio volatility.

The chapter is 50 pages long, and well worth reading (here), but for brevity I want to highlight a few critically important findings:

1. Volatility is very forecastable, and it is therefore possible to effectively manage risk in portfolios.

In fact, using standard volatility forecasting methods, the correlation between the volatility estimate at the beginning of any month, and the realized volatility over the subsequent month, is 63%, which suggests more than 12x greater forecast-ability for volatility relative to returns.
Long-time readers will recall that we have posted many articles that deal with this topic, and we would encourage new readers to examine some of this research.

Ang used an intuitive (but somewhat complicated) method to test the performance of a strategy which actively manages the volatility of a portfolio of U.S. stocks through time based on the VIX implied volatility index, so that when the VIX is high, the portfolio holds a higher cash (t-bill) position in order to maintain the expected volatility of the portfolio in the face of large changes in the volatility distribution through time.
From Ang:
If volatility is so predictable, then volatility trading should lead to terrific investment gains. It does. Despite my pessimism on predicting expected returns of the previous section, I am far more enthusiastic on strategies predicting volatilities.
...[The chart below] shows that the cumulated returns (left-hand axis) of [a] volatility timing strategy largely avoided the drawdowns of the static strategy during the early 2000s and the 2008 financial crisis. During these periods VIX (right-hand axis) was high and the volatility timing strategy shifted into T-bills. It thus avoided the low returns occurring when volatility spiked.
The mean of the static 60%-40% strategy in [the chart below] is 7.9% and its reward-to-risk ratio is 0.82. In contrast, the volatility timing strategy has a mean of 10.1% and a reward-to-risk ratio of 1.95. Volatility strategies have good performance. 
 Source: Ang (2012)

2. It is really difficult to forecast equity returns over time horizons that are meaningful for most investors.

While equity returns over the very long term are about 9% nominal and 6.6% real, the range of possible equity returns is very wide over shorter time frames out to 20 years or more. The following chart from our AAA whitepaper shows the distribution of rolling 20-year real returns to stocks using Professor Shiller's database, which has stock and bond return information back to 1871.
Source: Shiller (2012)

The following table from Ang quantifies the degree to which a wide variety of valuation, economic and trend-based factors explain equity returns over periods from 1 quarter to 5 years. Ang confirms our discovery that the Shiller PE is a robust explanatory variable for stock returns, with statistical significance at all horizons studied.

The only other statistically significant factor tested by Ang was the Consumption-Wealth ratio, though the author correctly highlights the 'look-ahead' bias embedded in this measure, which means it can not be used effectively for contemporaneous forecasting.

 Source: Ang (2012)

Ang provides a superb summary of the implications of this analysis on forecasting stock returns for investors, and I feel it's worth re-publishing here in its entirety.

Note that the first point pertains directly to our Estimating Future Returns report, as Ang highlights the spurious confidence implied by R-squared values in studies with long-term overlapping periods. We would definitely agree with Ang's caution, but we would also point out that estimates generated by our model are still likely to prove to be much more accurate than simple long-term average estimates in forecasting stock market returns going forward.
There are time-varying risk premiums, but they are difficult to estimate. If you attempt to take advantage of them, do the following:
  • Use good statistical techniques. Overstating statistical significance, for example by using the wrong t-statistics and thereby making predictability look “too good,” will hurt you when you implement investment strategies. One manifestation of spuriously high R2 in fitted in samples is that the performance deteriorates markedly going out of sample. Consistent with the spurious high R2 s, Welch and Goyal (2008) find that the historical average of excess stock returns forecasts better than almost all predictive variables. Use smart econometric techniques that combine a lot of information, but be careful about data mining, and take into account the possibility of shifts in regime
  • Use economic models. Notice that the best predictors in Table 7 were valuation ratios. Prediction of equity risk premiums is the same as prediction of economic value. If you can impose economic structure, do it. Campbell and Thompson (2008), among others, find that imposing economic intuition and constraints from economic models help.
  • Be humble. If you’re trying to time the market, then have humility. Predicting returns is hard to do. Since it is difficult to statistically detect predictability, it will also be easy to delude yourself in thinking you are the greatest manager in the world because of a lucky streak (this is self-attribution bias) and this overconfidence will really hurt when the luck runs out. You will also need the right governance structure to withstand painful periods that may extend for years. Note there are very few who have skill, especially among those who think they have skill.

3. Cash (t-bills) represent a much better hedge against inflation than stocks.
This revelation will probably come as a major shock to equity investors who believe that their equity portfolio represents their best shot at hedging against an inflationary shock from misguided central bank intervention.

The following chart from Ang clearly illustrates this point. Ang performed a robust pearson correlation analysis between, stock, bond and cash returns and inflation. Stocks exhibit negative correlation vs. inflation in absolute terms over periods less than 3 years; that is, when inflation increases, stocks react negatively in the short term. After 3 years, stocks are relatively agnostic to changes in inflation, as inflation estimates change in response to changes in inflation regime. 

On the other hand, t-bill yields adapt fairly quickly to changes in inflation, with correlations rising toward 0.5 after about a 3 year horizon, where they find a plateau. Conversely, when stock returns are adjusted for t-bill yields to represent excess returns, they exhibit a negative correlation vis-a-vis inflation for the entire horizon out to 10 years in the range of -0.1 to -0.2.

The incontrovertible message from this analysis is that investors should hold a healthy slug of cash in portfolios to hedge against inflation - in diametric opposition to prevailing investment dogma.

Source: Ang (2012)


There a few big ideas here. 

First: focus on what you can control, and budget for what you can't.

You can’t control the long-term returns to markets, and the evidence above strongly suggests that you can’t even make a very good forecast about what to expect.  You can observe, measure, and to a very large degree control the volatility of your portfolio, however. And it happens that by controlling for volatility in the right way, you will have a high probability of achieving higher absolute returns.

Even if controlling for volatility doesn’t deliver higher returns over your investment horizon, it will definitely achieve two important goals:

1. You will enjoy a more stable investment experience with less anxiety, and therefore be much less likely to make highly detrimental behavioural errors under situations of extreme pressure
2. You will improve the sustainability of your retirement plan because you will substantially narrow the range of potential negative market outcomes. For more on this, we strongly encourage you to read this important article.

The other important takeaway is that investment dogma is often (dare I say, mostly?) wrong, and that it is important to verify the empirical validity of many basic investment concepts before putting real money to work.

For example, the volatility management tests revealed what we have known for some while: higher returns do not necessarily require higher risk. In fact, smart low risk strategies often outperform high-risk strategies in both absolute and risk-adjusted terms. 

Further, evidence from the above examination of correlations between stocks, t-bills and inflation directly contradicts one of the most popular myths in finance: that is, that stocks will protect your portfolio in the event of an inflationary shock, while cash will become worthless. Certainly, cash under the mattress is much more vulnerable to inflation, but cash held in cash-like instruments like high quality government Treasury bills actually offer better protection than stocks, which are likely to lose value after adjusting for inflation.

Wednesday, August 8, 2012

Estimating Future Stock Market Returns: August 2012 Update

"Mankind are so much the same, in all times and places, that history informs us of nothing new or strange in this particular. Its chief use is only to discover the constant and universal principles of human nature." - David Hume

Long-time readers will know that we do not make predictions in the normal sense. That is, we endorse the decisive evidence that markets and economies are complex, dynamic systems which are not reducible to normal cause-effect analysis. However, we are willing to acknowledge the likelihood that the future is likely to rhyme with the past. Thus, we apply simple statistical models to discover mean estimates of what the future may hold over meaningful investment horizons (10+ years), while acknowledging the wide range of possibilities that exist around these averages.
There are several reasons why it may be useful to have a more robust estimate of future expected returns on stocks:
  • People who are approaching retirement need to estimate probable returns in order to budget how much they need to save.
  • A retiree's level of sustainable income is largely dictated by expected returns over the early years of retirement.
  • Investors of all types must make an informed decision about how best to allocate their capital among various investment opportunities.
Many studies have attempted to quantify the relationship between Shiller PE and future stock returns. Shiller PE smoothes away the spikes and troughs in corporate earnings which occur as a result of the business cycle by averaging inflation-adjusted earnings over rolling historical 10-year windows.
This study contributes substantially to research on smoothed earnings and Shiller PE by adding three new valuation indicators: the Q-Ratio, total market capitalization to GNP, and deviations from the long-term price trends. The Q-Ratio measures how expensive stocks are relative to the replacement value of corporate assets. Market capitalization to GNP accounts for the aggregate value of U.S. publicly traded business as a porportion of the size of the economy. In 2001, Warren Buffett wrote an article in Fortunewhere he states, "The ratio has certain limitations in telling you what you need to know. Still, it is probably the best single measure of where valuations stand at any given moment." Lastly, deviations from the long-term trend of the S&P inflation adjusted price series indicate how 'stretched' values are above or below their long-term averages.
These three measures take on further gravity when we consider that they are derived from four distinct facets of financial markets: Shiller PE focuses on the earnings statement; Q-ratio focuses on the balance sheet; market cap to GNP focuses on corporate value as a proportion of the size of the economy; and deviation from price trend focuses on a technical price series. Taken together, they capture a wide swath of information about markets.
We analyzed the power of each of these 'valuation' measures to explain inflation-adjusted stock returns including reinvested dividends over subsequent multi-year periods. Our analysis provides compelling evidence that future returns will be lower when starting valuations are high, and that returns will be higher in periods where starting valuations are low.
This last point may seem obvious, but I want to emphasize a critical point about traditional wealth management of which most investors are not aware:
Traditional investment planning does not account for whether markets are cheap or expensive. An investor who visited a traditional Investment Advisor at the peak of the technology bubble in early 2000 would, in practice, be advised to allocate the same proportion of his wealth to stocks as an investor who visited an Advisor near the bottom of the markets in early 2009. This despite the fact that the first investor would have had a valuation-based expected return on his stock portfolio from January 2000 of negative 2% per year, while the second investor would expect inflation-adjusted compound annual returns of 6.5%. For an investor with $1,000,000 to invest, this would represent a difference of more than $1.26 million in cumulative wealth over a decade.
Said differently, traditional wealth advice is rooted in the assumption that the best estimate of future returns is the average long-term return to stocks. No matter where markets are on the continuum from very cheap to very expensive, traditional Advisors will make recommendations on the assumption that investors should expect 6.5% inflation adjusted returns on stocks over all investment horizons.
John Hussman at Hussman funds is careful to qualify the value of this analysis: "Rich valuation is strongly associated with weak subsequent returns, but only reliably so over periods of 7-10 years. In contrast, the present syndrome of overvalued, overbought, overbullish, rising-yield conditions is typically associated with abrupt and often steep losses, but is more commonly resolved over a period of months rather than years." (Hussman, Feb 14, 2011). Thus, we are not making a forecast of market returns over the next several months; in fact, markets could go substantially higher from here. However, over the next 10 to 15 years, markets are very likely to revert to average valuations, which are much lower than current levels. This study will demonstrate that investors should expect 6.5% returns to stocks only during those very rare occasions when the stock market passes through 'fair value' on its way to becoming very cheap, or very expensive. At all other periods, there is a better estimate of future returns than the long-term average, and this study will quantify that estimate.
Investors should be aware that, relative to meaningful historical precedents, markets are currently expensive and overbought by all three measures, indicating a strong likelihood of low inflation-adjusted returns going forward over periods as long as 20 years.
This prediction is also supported by evidence from an analysis of corporate profit margins. In his recent book, Vitaly Katsenelson provided in Chart 1 of long-term profit margins to U.S. companies. Companies have clearly been benefitting from a period of extraordinary profitability.
Source: Vitaly Katsenelson (2011) The profit margin picture is critically important. Jeremy Grantham recently stated, "Profit margins are probably the most mean-reverting series in finance, and if profit margins do not mean-revert, then something has gone badly wrong with capitalism. If high profits do not attract competition, there is something wrong with the system and it is not functioning properly." On this basis, we can expect profit margins to begin to revert to more normalized ratios over coming months. If so, stocks may face a future where multiples to corporate earnings are contracting at the same time that the growth in earnings is also contracting. This double feedback mechanism may partially explain why our statistical model predicts such low real returns in coming years. Caveat Emptor.

Modeling Across Many Horizons

Many studies have been published on the Shiller PE, and how well (or not) it estimates future returns. Almost all of these studies apply a rolling 10-year window to earnings as advocated by Dr. Shiller. But is there something magical about a 10-year earnings smoothing factor? Further, is there anything magical about a 10-year forecast horizon?
Kitces (2008, PDF format) demonstrated that "the safe withdrawal rate for a 30-year retirement period has shown a 0.91 correlation to the annualized real return of the portfolio over the first 15 years of the time period". So there is clearly merit in studying a 15-year forecast horizon as well. Further, the tables below will demonstrate that statistical models have the greatest explanatory power at the 15-year horizon.
This study will attempt to address the question of 'perfect forecast horizon', perfect valuation factor, and 'perfect earnings smoothing factor', by analyzing the explanatory power of earnings, the Q-Ratio, and regressed historical stock returns, over return horizons from 1 to 30 years. We will also put all of the factors together to construct an optimized model.
Table 1. below provides a snapshot of some of the results from our analysis. The table shows estimated future returns based on several factor models over some important investment horizons. The "Best Fit Multiple Regression" is by far the most accurate model, but other results are provided for context.
Table 1. Factor Based Return Forecasts Over Important Investment Horizons
Source: Shiller (2011), (2011), Chris Turner (2011), World Exchange Forum (2011), Federal Reserve (2011), Butler|Philbrick & Associates (2011)
You can see from the table that every single valuation factor model generates results which suggest a very low future return environment for stocks. Further, the 'Best Fit Multiple Regression', which has historically provided a surprising degree of forecast accuracy, confirms this outlook with a high degree of confidence (see explanation below). Those who are not interested in our process can skip to the bottom sections, 'Putting the Predictions to the Test', and 'Conclusion'.


The following matrices show the R-Squared ratio, regression slope, regression intercept, and current predicted forecast returns for each valuation factor. The matrices are heat-mapped so that larger values are reddish, and small or negative values are blue-ish. Click on each image for a large version.
Matrix 1. Explanatory power of valuation/future returns relationships
Source: Shiller (2011), (2011), Chris Turner (2011), World Exchange Forum (2011), Federal Reserve (2011), Butler|Philbrick & Associates (2011)
Many analysts quote 'Trailing 12-Months' or TTM PE ratios for the market as a tool to assess whether markets are cheap or expensive. If you hear an analyst quoting the market's PE ratio, odds are they are referring to this TTM number. Our analysis slightly modifies this measure by averaging the PE over the prior 12 months rather than using trailing cumulative earnings through the current month, but this change does not substantially alter the results. As it turns out, TTM average earnings have very mild explanatory value over periods greater than 8 years. However, the explanatory power of TTM earnings is substantially less reliable than all other factors studied in this analysis, so investors may wish to pay little heed to this indicator of whether stocks are cheap or expensive.

Forecasting Expected Returns

The next matrices provide the slope and intercept coefficients for each regression. We have provided these in order to illustrate how we calculated the values for the final matrix below of predicted future returns to stocks.
Matrix 2. Slope of regression line for each valuation factor/time horizon pair.
Source: Shiller (2011), (2011), Chris Turner (2011), World Exchange Forum (2011), Federal Reserve (2011), Butler|Philbrick & Associates (2011)
Matrix 3. Intercept of regression line for each valuation factor/time horizon pair.
Source: Shiller (2011), (2011), Chris Turner (2011), World Exchange Forum (2011), Federal Reserve (2011), Butler|Philbrick & Associates (2011)
Our final matrix below shows predicted future real returns over each time horizon, as calculated from the slopes and intercepts above, by using the most recent values for each of the 13 earnings series, the Q-Ratio, and the return series as inputs. For statistical reasons which are beyond the scope of this study, we have substituted the ordinal rank for the nominal value for each factor in running our analysis. Therefore, when we solve for future returns based on current monthly data, we apply the monthly rank in the equations.
For example, the 15-year return prediction based on the current Q-Ratio can be calculated by multiplying the current ordinal rank of the Q-Ratio (969) by the slope from Matrix 2. at the intersection of 'Q-Ratio' and '15-Year Rtns' (-0.0000894), and then adding the intercept at the same intersection (0.1202323) from Matrix 3. The result is 0.0336, or 3.36%, as you can see in Matrix 4. below at the same intersection (Q-Ratio : 15-Year Rtns).
Matrix 4. Modeled forecast future returns using current valuations.
Source: Shiller (2011), (2011), Chris Turner (2011), World Exchange Forum (2011), Federal Reserve (2011), Butler|Philbrick & Associates (2011)
Finally, at the bottom of the above matrix we show the forecast returns over each future horizon based on our best-fit multiple regression from the factors above. We began testing the multiple regression against the Q-ratio, the 15-year Shiller PE, the price regression, and the market cap to GNP as a 4 factor model. However, we discovered that the 15-year PE provided more noise than signal to the regression (that is, these factors were not statistically significant and reduced the F-score), so we narrowed the regression to include just the Q ratio, market cap/GNP, and the real price series over each forecast horizon.
We provided the R-squared for each multiple regression at the bottom of each forecast horizon column in Matrix 4.; you can see that at the 15-year forecast horizon, our regression explains 82% of total returns to stocks. Further, the regression is very highly statistically significant, with a p value of effectively zero.
Chart 2. below demonstrates how closely the model tracks actual future 15-year returns. The red line tracks the model's forecast annualized real total returns over subsequent 15-year periods using the Q ratio and deviation from price regression as inputs at each period. The blue line shows the actual annualized real total returns over the same 15-year horizon.

Chart 2. 15-Year Forecast Returns vs. 15-Year Actual Future Returns

Source: Shiller (2011), (2011), Chris Turner (2011), World Exchange Forum (2011), Federal Reserve (2011), Butler|Philbrick & Associates (2011)
You can see that 15-year "Regression Forecast" returns are 0.69% per year and 10-year returns are forecast to be 2.49% per year using market valuations as of July 30, 2012.

Putting the Predictions to the Test

A model is not very interesting or useful unless it actually does a good job of predicting the future. To that end, we tested the model's predictive capacity at some key turning points in markets over the past century or more to see how well it predicted future inflation-adjusted returns.
Table 2. Comparing Long-term average forecasts with model forecasts
Source: Shiller (2011), (2011), Chris Turner (2011), World Exchange Forum (2011), Federal Reserve (2011), Butler|Philbrick & Associates (2011)
You can see we tested against periods during the Great Depression, the 1970s inflationary bear market, the 1982 bottom, and the middle of the 1990s technology bubble in 1995. The table also shows expected 15-year returns given market valuations at the 2009 bottom, and current levels. These are shaded green because we do not have 15-year future returns from these periods yet. Note real total return forecasts of 5.92% annualized from the bottom of the market in February 2009. This suggests that prices just approached fair value at the market's bottom, but they were nowhere near the level of cheapness that markets achieved at bottoms in 1932 or 1982. As of the end of July 2012, annualized future returns over the next 15 years are expected to be less than 1 percent.
We compared the forecasts from our model with what would be expected from using just the long-term average real returns of 6.5% as a constant forecast, and demonstrated that estimates form long-term average returns yield over 433% more error than estimations from our model over these 15-year forecast horizons (1.28% annualized return error from our model vs 5.55% using the long-term average). Clearly the model offers substantially more insight into future return expectations than simple long-term averages, especially near valuation extremes.


The 'Regression Forecast' return predictions along the bottom of Matrix 4. are robust predictions for future stock returns, as they account for over 100 different cuts of the data, using 3 distinct valuation techniques, and utilize the most explanatory statistical relationships. The models explain up to 82% of future returns based on R-Squared, and are statistically significant at p~0. It is worth noting, however, that even this model has very little explanatory power over horizons less than 6 or 7 years, so almost anything is possible in the short-term.
Returns in the reddish row labeled "PE1" in Matrix 4 were forecast using just the most recent 12 months of earnings data, and correlate strongly with common "Trailing 12-Month" PE ratios cited in the media. Note that our Matrix 1. proves that this trailing 12 month measure is not worth very much as a measure for forecasting future returns over any horizon. However, the more constructive results from this metric probably helps to explain the general consensus among sell-side market strategists that markets will do just fine over coming years. Just remember that these analysts have no proven ability whatsoever in predicting market returns (see herehere, and here). Further, it can be argued that their firms have a substantial incentive to keep their clients invested in stocks.
Investors would do much better to heed the results of robust statistical analyses of actual market history, and play to the relative odds. This analysis suggests that markets are currently expensive, and asserts a very high probability of low returns to stocks (and possibly other asset classes) in the future. Remember, any returns earned above the average are necessarily earned at someone else's expense, so it will likely be necessary to do something radically different than everyone else to capture excess returns going forward.