The Power of Dynamic Asset Allocation - · PDF fileThe Power of Dynamic Asset Allocation MIRKO CARDINALE, ... shows that a simple book-to-market ratio explains more ... approximation

THE JOURNAL OF PORTFOLIO MANAGEMENT 47SPRING 2014

The Power of Dynamic Asset AllocationMIRKO CARDINALE, MARCO NAVONE, AND ANDRZEJ PIOCH

MIRKO CARDINALE

is the head of asset allo-cation for Europe, the Middle East, and Africa at Russell Investments in London, [email protected]

MARCO NAVONE

is a senior lecturer in finance at the UTS Business School of the University of Technology, Sydney, [email protected]

ANDRZEJ PIOCH

is a multi-asset fund manager at Aviva Investors in London, [email protected]

In this article, we attempt to bridge the gap between theoretical research on equity return predictability and industry practice in portfolio management. In

fact, even though the academic community has warmed to the notion of predictability over the last 15 years, asset allocation models and software used by practitioners to calibrate optimal portfolio weights for multi-asset funds don’t yet extensively apply these con-cepts. In the practitioners’ arena, asset return predictability is often seen as an output of complex economic models whose implemen-tation rests on strong assumptions, and thus lacks practical relevance.

Although we agree that contemporary asset pricing has reached a considerable level of analytical sophistication, we also believe that a variety of relatively simple forecasting methodologies have emerged from academic research. The objective of this research is to assess whether there are material gains associ-ated with incorporating these simple method-ologies in asset allocation models, compared to the traditional approach used by most industry applications of portfolio optimiza-tion, which often rely on extrapolation of historical return patterns or equilibrium rela-tionships with limited empirical support.

We address this issue, f irst of all, by looking at the predictive power of five alter-native steady-state methodologies based on the Gordon dividend discount model, the

inverted price-to-earnings ratio, the sum of parts, the return on equity (ROE), and the book-to-market ratio model. We also build a conditional bond forecast using the initial yield to maturity. Using data on U.S. equi-ties and bonds from 1926 to 2010, we show that all of these methodologies predict future realized returns far better than do historical average returns.

We then address the issue of relevance by applying these forecasts in a dynamic asset-allocation framework with four U.S. asset classes (equities, government bonds, corpo-rate bonds, and cash). Assuming different levels of risk aversion and different investment objectives (maximization of a mean–variance utility function versus shortfall constraints), we show that a number of methodologies produce signif icantly higher risk-adjusted return than historical averages. Although we cannot reliably estimate transaction costs over such a long investment horizon, we show that these methodologies do not generate more turnover than the dynamic strategy based on historical returns.

The analysis confirms that asset returns display predictable patterns in function of valuation ratios and shows that investors can exploit these patterns by designing dynamic asset allocation strategies built to take advan-tage of time-varying expected returns.

The rest of the article is organized as follows: In the first section, we introduce our

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48 THE POWER OF DYNAMIC ASSET ALLOCATION SPRING 2014

forecasting methodologies and discuss our data; in the second section, we calculate the predictive power of our forecasts and simulate dynamic allocation strategies; and the third section concludes.

METHODOLOGY AND DATA

Equity Forecasting Models

Attempts to forecast future patterns of stock market returns have captivated investors for as long as organized stock markets have existed (e.g., The Ticker [1908]; the Dow theory formulated by Rhea [1932], and by Graham and Dodd [1934]). The classical f inancial economics paradigm (Samuelson [1965]), which relates the notion of “efficient markets” to the theory of random walks, argued that these attempts are essentially fruitless, as successive price changes are independent over time and returns at any investment horizon are unpredictable. Since the 1980s, the random walk paradigm has been challenged and the predictability of equity returns has become such a widely accepted concept in the academic community that John Cochrane [1999] referred to it as a “new fact in finance.” Ang and Bekaert [2001] even said that the asset allocation literature “often has taken predictability of the dividend yield variable as given.”

However, ten years later the debate was far from over, as highlighted by the recent CFA Institute equity premium survey (Hammond et al. [2011]), which showed disagreement among academics and market practitioners on whether the equity premium should be measured using historical averages or forward-looking models.

In this article, we consider five possible forecasting methodologies for equity returns, incorporating infor-mation contained in valuation ratios under the steady-state assumption of Campbell and Thompson [2007]. We chose these specif ic models because they feature quite prominently in the academic and practitioners’ literature and are often employed as valuation indicators in the asset management industry. Our ultimate objec-tive is to test whether asset allocators could improve long-term portfolio performance using relatively simple models that do not require complex assumptions and calibration and only rely on information that is available at each point in time.

The first approach we consider is the basic Gordon-inspired steady-state dividend discount model (Gordon [1962]), with constant expected dividend growth rate.

Following Ferreira and Santa-Clara [2011], we build the model using the dividend yield at different points in time and the 20-year moving average dividend growth rate as a measure of the expected dividend growth rate. This model is designed to represent the well-documented empirical relationship between dividend yields and sub-sequent returns (see Fama and French [1988], Hodrick [1992], Campbell and Shiller [2001], and Cochrane [2008]).

, 10 20,R

DP

gt ,t

tPP t20,= +t10 (1)

The second methodology is based on the inverted price-to-earnings (PE) ratio, or earnings yield. In prin-ciple, one can argue that when equity prices are high relative to earnings, this either signals fast growth in corporate profits or low equity returns to come. This is indeed true by definition, unless one assumes that the price/earnings ratio is not mean-reverting and can trend upward or downward indefinitely. Empirical evidence (Campbell and Shiller [1988 and 2001], Domian and Reichenstein [2009]) found that, although the PE ratio fails to predict future earnings or dividend growth, it is a reasonable predictor of future equity returns.

This simple measure has become widely used by practitioners, either as a standalone measure of expected returns or as a component in the so-called “Fed model” (see Estrada [2009]). Campbell and Shiller [1988] show that this ratio’s forecasting power increases when the current stock price or index value, in real terms, is divided by a measure of real earnings that takes into account cyclical f luctuations in corporate profits. The 10-year moving average of real earnings is considered an adequate measure of stable corporate profitability. The ratio of price to the 10-year moving average has become industry standard and is referred to as Shiller PE.

Rather than simply using a 10-year moving window, we have tested a range of measures using dif-ferent windows and smoothing techniques (e.g., con-stant growth trend versus moving average), and opted for calculating the expected real earnings growth by fit-ting a constant growth-trend model over 20-year rolling windows (see Equations 2a and 2b). This lets us capture the fact that real earnings are expected to trend upwards over time in an expanding economy. However, as a stress test, we have also used a more conventional Shiller PE definition, which employs a 10-year moving average.



Our results were not significantly affected by the choice of constant growth versus 10-year average.1

α + β τ ε τ −τ 20, 1−E t= α + β × τ + ε τ =τ (2a)

ˆ ˆ, 10R

tPt ,

tPP= α + β ×

(2b)

The third model is the sum of parts model (see Ibbotson and Chen [2003]), where the real capital gain component of equity returns is decomposed into expected real earnings growth and expected growth of the PE ratio. The model obtains a total return forecast by adding a measure of expected inf lation and the cur-rent dividend yield, as a proxy for the expected income component of equity investments. It works out real earnings growth using a constant-growth trend model fitted over 20-year rolling windows (Equation 2a). For the growth in the PE ratio, we assume a 20-year mean-reversion path that will bring the PE ratio back to an estimated long-term average level, calculated using an expanding window (i.e., with no hindsight bias). Finally, we estimate expected inf lation using the same approach adopted for real earnings growth (constant-growth trend model using a 20-year rolling window).

( )

( ) ( )

, 101R E10

DP

E g( h

E g( h E g( h

t ,t

tPP EPS

PE CPIPP

⎛⎝⎜⎛⎛⎝⎝

⎞⎠⎟⎞⎞⎠⎠

+

+ +)E(

+

(3)

The fourth model, the ROE model, revisits the basic Gordon equation and uses a well-known corpo-rate finance relationship that equates earnings’ expected growth rate to the product of retention ratio and return on equity. We define the expected return similarly to the approach used by Campbell and Thomson [2007]:2

( _ )

1

, 101R E10

DP

ratior ROE

DP

DE

ROE

t ,t

tPP t t) ROE

t

tPPt

tt

⎛⎝⎜⎛⎛⎝⎝

⎞⎠⎟⎞⎞⎠⎠

+ ⋅( )ratiorr t )

= +t −⎛⎝⎜⎛⎛⎝⎝

⎞⎠⎟⎞⎞⎠⎠

⋅

+

(4)

The last model is based on the book-to-market ratio. Pontiff and Schall [1998] show that this ratio has a significant predictive power with respect to the stock market return, as opposed to simply explaining the cross-section of equity returns, as in Fama and French [1992].

The book-to-market ratio (BM) is also closely related to Tobin’s Q, another frequently used stock market valua-tion indicator, defined as the ratio of market value to the replacement cost of companies’ assets. In fact, research shows that a simple book-to-market ratio explains more than 95% of the variability of the most commonly used approximation of Tobin’s Q (Chung and Pruitt [1994]).

Our BM model specif ication is a simple trans-formation of Equation (4), following Campbell and Thomson [2007]:

1

1

1

, 10RDP

DE

ROE

DE

EP

DE

ROE

DE

BP

ROEDE

ROE

t ,t

tPPt

tt

t

t

t

tPPt

tt

t

t

t

tPP tt

tt

= +t −⎛⎝⎜⎛⎛⎝⎝

⎞⎠⎟⎞⎞⎠⎠

⋅

= ⋅ −1+⎛⎝⎛⎛⎝⎝

⎞⎠⎟⎞⎞⎠⎠

⋅

= ⋅ ⋅ +ROEt −⎛⎝⎜⎛⎛⎝⎝

⎞⎠⎟⎞⎞⎠⎠

⋅

which can be rearranged as:

1 1, 10R R10 OE

DE

BPt , t

t

t

t

tPP⋅ROE

⎛⎝⎝⎝

⎞⎠⎟⎞⎞⎠⎠

⎡

⎣⎢⎡⎡

⎣⎣

⎤

⎦⎥⎤⎤

⎦⎦ (5)

Fixed-Income Forecasting Models

This article’s goal is to quantify the long-term ben-efit of dynamic asset allocation with noisy return fore-casts. To perform our test, we must construct forecasts for fixed-income asset classes as well.

Predictable patterns in returns have been inves-tigated in bond markets for a while. Models of bond returns since Vasicek’s [1977] seminal paper have incor-porated some degree of predictability, arising through mean reversion of short-term interest rates. It was argued that interest rates cannot rise indefinitely, as high interest rates tend to hamper economic activity, prompting mon-etary authorities to intervene by lowering rates.

Moreover, a number of studies unveiled evidence of time-varying bond risk premia in the function of fac-tors such as forward rates and yield spreads (another “new fact in finance” mentioned by Cochrane [1999]). The research seems to suggest that bond investors can do much better than naively extrapolating historical returns when making investment decisions. In fact, Ilmanen [2011] argued that the misleading nature of historical average



returns is particularly evident for Treasury yields, because a rally caused by falling discount rates will only reduce feasible expected returns, rather than raise them.

Although practitioners employ a variety of mea-sures for equity forecasts, the choices for fixed-income assets are somewhat more limited. Deriving long-term interest rate forecasts from the spot or forward yield curve (for example, in the seminal work of Ibbotson and Sinquefield [1976] or in Cochrane and Piazzesi [2005]) is not feasible when dealing with data from the early twentieth century, because full yield-curve histories are only available from the early 1960s. We have instead chosen to adopt a simpler solution proposed by Arnott et al. [2008], which takes the current yield to maturity as a proxy for the bond’s expected return, that is, implicitly assuming to hold the bond until maturity. While we rec-ognize the intrinsic limitation of this approach, we will show empirically how closely the initial yield tracks the bond index’s future performance, in particular over the long term. We will also compare this simple approach to estimates based on historical realized returns.

Benchmarks for Forecasting Models

In our test, we benchmark our forecasting models against four different benchmarks:

a. The f ive-year historical average return, which represents an investor who looks at past realized returns in order to forecast future returns. (In an alternative specification of our test, we also looked at 10-year and 20-year historical averages, with no material difference in the results.3)

b. A variation of our dividend model (the “clairvoyant model” described by Arnott et. al. [2009]), where we assume that investors can perfectly forecast the dividend yield and subsequent dividend growth. Even though perfect foresight of dividend growth is clearly not achievable in the real world, this is still a helpful benchmark, as it removes dividend-growth uncertainty from the picture. The only residual uncertainty is represented by valuation changes over the investment horizon. Obviously, this benchmark can only be computed for equity forecasts.

c. The 10-year future average realized return, which rep-resents an investor who can correctly forecast the long-term drift of the return process but cannot predict short-term deviations from the long-term trend.

d. The one-year future return, which represents an investor who can fully predict the stock market’s short- and long-term realizations.

These benchmarks represent, in ascending order, four different levels of predictive power and help us assess forecasting errors in return-prediction models that affect the performance of our dynamic asset allocation strategies.

Data

We source 1871 to 2010 U.S. equity market data from the Monthly Database for the U.S. Stock Market, com-piled by Robert Shiller, which provides historical time series covering price, dividend, earnings, and consumer price index data. We use the same dataset to calculate dividend payout ratios, total return indices, and inf la-tion rates. A dataset constructed by Goyal and Welch [2008] provides historical book-to-market data from 1921 to 1973. An estimate for the book value of equity (net worth) used for ROE calculation between 1921 and 1973 comes from the dataset compiled by Stephen Wright [2004], which covers the non-financial corpo-rate sector. We source book-to-market and ROE ratios for the S&P 500 after 1974 from a dataset compiled by Goldman Sachs Global Investment Research.

We construct total return series and historical yield for U.S. government bonds using the US Govt Bond Total Return Index, sourced from the Global Financial Database until 1980, and the 10-year Benchmark US Govt Bond Index, sourced from Datastream after that date. We also sourced corporate bonds’ total returns and yields since 1915 from the Global Financial Database, and referred to the Dow Jones US Corporate Bonds Index.

Finally, we built a cash total-return index by using the risk-free rate in the dataset constructed by Goyal and Welch [2008] until 1930, and three-month T-bill rates from the Federal Reserve thereafter.

The final sample we used for the investment simu-lation goes from April 1921 to September 2010.

INVESTMENT SIMULATION AND RESULTS

Predictive Power of Steady-State Models

We apply the previously described forecasting methodologies to our data in order to construct equity



Note: Panel A reports descriptive statistics for annual equity return forecasts from March 1921 to September 2000. Panel B reports descriptive statistics for annual fixed-income return forecasts from March 1921 to September 2000. Because the corporate bond sample starts in 1915, historical returns for corporate bonds are based on shorter expanding windows before 1925.

E X H I B I T 1Descriptive Statistics

E X H I B I T 2Correlation of Equity Forecasts

Note: The exhibit reports correlation coefficients for annual equity return forecasts from March 1921 to September 2000, as well as P-values for significance tests (in parentheses).



and fixed-income forecasts from 1921 to 2000. Exhibit 1 reports descriptive statistics for both equity and fixed-income forecasts. Exhibit 2 reports the correlation coef-ficients among the equity forecasts.

As Exhibit 1 shows, none of the models predicts single-period market swings; this is also evident from the low correlation between the one-year future returns and all other models (Exhibit 2). In fact, the volatility of pre-dictions from all forecasting models is at least four times lower than the volatility of the one-year future returns distribution (except the f ive-year historical return). However, we also observe that some of our forecasting technologies (in particular sum of parts and inverted PE) seem able to predict long-term trends and show signifi-cantly positive correlation with the 10-year future return. By contrast, the correlation between subsequent 10-year returns and the 5-year historical returns is statistically significant but negative, which suggests some degree of long-run mean reversion. This evidence alone suggests there may be some added value in considering these fore-casts as part of a dynamic asset allocation framework.

To formally confirm this intuition, we calculate the mean-squared error (MSE) for each forecasting meth-odology (and the 5-year historical return), with respect to the 10-year future return. This measure gives us an idea of how well these methodologies predict, month by

month, the subsequent 10-year realized return. Exhibit 3 reports the MSEs, as well as the Diebold and Mariano [1995]4 statistic for the differential predictive accuracy of our forecasting technologies with respect to the five-year historical return. We clearly see that a) the clairvoyant model is, not surprisingly, the best predictor of long-term subsequent return trends, and b) all of our fore-casting methodologies perform significantly better than the five-year historical return. For fixed-income assets, we also see that the current yield shows a significantly higher accuracy in predicting future return trends than does the historical average. These findings are confirmed by cumulative net square errors (NSE), shown in Exhibit A1 of the appendix. We have also replicated the analysis using longer windows (both 10 and 20 years) to calculate the historical return. Results, which are available upon request, are not significantly different.

Investment Performance of Steady-State Models in a Multi-Asset Portfolio

Optimal portfolios constructed using the con-ventional approach pioneered by Harry Markowitz (Markowitz [1952]) are particularly sensitive to estimation errors in expected returns, and the relative importance of return inputs versus other parameters (i.e., volatilities

E X H I B I T 3Mean-Squared Error Analysis

Note: The exhibit reports mean absolute error (MAE), mean positive error (MPE), mean negative error (MNE) and mean squared error (MSE) for each forecast versus the long-term perfect foresight benchmark (10-year future return) and Diebold–Mariano (DM) statistic for the test comparing the MSE of the model forecast with the MSE of the forecast, based on the five-year historical return for equities (Panel A) and fixed-income (Panel B).



and correlations) increases with investors’ risk tolerance (Chopra and Ziemba [1993]). Estimation of the variance–covariance matrix is also critical in the portfolio con-struction process, and there is an extensive literature on alternative methodologies to forecast risk and correlation (Figlewski [1997], Poon and Granger [2003], Miloudi and Moraux [2009]). However, assessing the effect of alterna-tive approaches to volatility or correlation forecasts goes beyond the scope of this article. Future research could extend this work by isolating the effect of different vola-tility and correlation forecasts on portfolio performance.

The results of the MSE analysis seem to indicate that our simple forecasting methodologies predict the stock market’s future trend better than recent (or even long-term) history. Hence, while this hardly provides an effective measure of added value for an investor, the sen-sitivity of portfolio weights to errors in expected returns suggests that these findings have important implications for investors. In order to assess this more formally, we have built a set of experiments measuring the long-term performance of different forecasting methodologies for investors with different degrees of risk aversion and dif-ferent investment goals.

The f irst experiment considers three dynamic investment strategies, optimized for investors with stan-dard mean–variance utility functions and risk-aversion coefficients equal to 0, 5, and 15, respectively. The first investor is risk neutral and will choose the portfolio with highest expected return, whereas the last two exhibit two different degrees of risk aversion. Every 12 months (from April 1921 to April 2000), investors allocate funds among equities, long-term government bonds, corporate bonds, and cash. In deciding on the optimal asset allocation, they estimate the variance–covariance matrix using a five-year return history and forecast expected returns using either forward-looking or historical average models for equities and bonds. (The choice of the five-year estimation period is con-sistent with the default option of numerous optimiza-tion software programs used by practitioners; using a longer window does not materially change the conclu-sion of this article.5) We assume that investors rebal-ance monthly to target weights, until the portfolio is re-optimized at the end of each 12-month period. For fixed-income assets, we calculate the expected return using the initial yield for all forward-looking equity models and using a f ive-year moving average in the historical average model.

For each investment strategy (high, medium, and low risk), and for each equity return forecast method-ology, Exhibit 4, Panel A, reports the average Sharpe ratio and the P-value of equality of the mean test between the Sharpe ratio of each forward-looking model versus the historical average benchmark. The Sharpe ratio is calculated as the average return in excess of cash, divided by the excess return volatility, both calculated using the full 80-year sample.

The exhibit shows that a perfect forecaster (able to accurately predict returns every year) will generate asset allocations that deliver far superior Sharpe ratios, compared to all forward-looking forecasting method-ologies. This is not a surprise, but an important sanity check for the experiment’s results. The key result is that, for medium- and low-risk investors, any of the proposed steady-state models would have generated significantly better Sharpe ratios than the historical average bench-mark. Steady-state models (in particular the inverted PE) also produced better Sharpe ratios than the historical average for high-risk investors. Interestingly, the other two benchmark models (the 10-year future average and, in particular, the clairvoyant model) do not deliver consistently higher Sharpe ratios compared to steady-state models, which do not require hindsight knowl-edge. This highlights the fact that steady-state models do a relatively good job at predicting changes in the long-run drift and demonstrates that perfect foresight on dividend growth does not necessarily translate into better Sharpe ratios. The latter suggests that long-run return patterns are also driven by long-term shifts in valuation multiples. It is worth noting that the dividend model that uses an imperfect backward-looking forecast for dividend growth produces better Sharpe ratios than does the clairvoyant model. This implies some degree of correlation between errors in dividend growth forecasts and shifts in valuation multiples. In other words, strong historical dividend growth may affect investors’ expecta-tions boosting price–earnings multiples, even if history is an imperfect forecast of future growth patterns.

Exhibit 5, Panel A, reports average equity weight and mean annual equity turnover, defined as absolute change in equity weight between rebalancings. The results show that in most cases, steady-state models generate lower equity weights, compared to the historical average bench-mark. This provides a glimpse of how better Sharpe ratios have been generated, given mean-reversion patterns (negative correlation between historical and subsequent



returns) shown in Exhibit 2. Investors relying on his-torical averages would often be misled into extrapolating strong equity returns into the future and over-allocate to the asset class at the wrong time, i.e., when steady-state models would instead warn that valuations have become stretched. This is evidenced by Exhibit A2 in the appendix, which shows a snapshot of allocations chosen using different models at a particular point in time: April 1999. The chart shows that the historical average model would have extrapolated the bull market of the 1990s into the future and allocated 100% to equities, even for risk-averse investors. By contrast, steady-state models would rather allocate a large chunk to fixed income, particularly for low- and medium-risk investors.

We have also replicated this exercise using 10- and 20-year historical moving averages as benchmarks (results available upon request), and the results are not materially

different. Finally, the exhibit also shows that average equity turnover generated by steady-state models as a result of changes in optimal portfolio weights is gener-ally lower than those produced by the historical average model. This unveils another shortcoming of relying on historical averages: Chosen portfolio weights are likely to be unstable, leading to excessive turnover. This is also consistent with the patterns shown in Exhibit 1, as five-year rolling-average estimates are more volatile than those produced by steady-state models.

In the second experiment, we rely on the same underlying inputs (expected returns and variance–cova-riance matrix) to build the efficient frontier, but consider an investor with a slightly different decision-making pro-cess: Instead of maximizing an expected utility function, she has a shortfall constraint. Specifically, we consider three investors with maximum acceptable loss (with 99%

Notes: The exhibit reports Sharpe ratios calculated over the entire sample between 1921 and 2000, using monthly returns of nine dynamic allocation strate-gies optimized for investors with different risk-aversion coefficients γ (Panel A) and different shortfall constraints expressed as a percentage of expected equity volatility (Panel B). The exhibit also shows the difference between the Sharpe ratios of the different strategies and the historical return strategy, together with the P-value of the t-test on that difference.

E X H I B I T 4Dynamic Portfolio Performance (1921–2000)



confidence level) equal to 50%, 100%, and 200% of the expected equity volatility, backed out from the same five-year history used to estimate the variance–covariance matrix. The choice of a market-dependent shortfall con-straint is without loss of generality and has the advantage of avoiding situations in which the constraint cannot be satisfied. This second experiment captures the behavior of an investor whose decision process is characterized by a safety-first approach (Roy [1952]). The investor will choose the portfolio with the highest expected return, subject to a lower than 1% probability of producing a loss of more than the maximum acceptable level.

The results for the second experiment, displayed in Exhibit 4, Panel B, are not materially different from the first experiment’s results. However, it is worth noting that the clairvoyant model performs slightly better than steady-state models under the shortfall constraint. Still, most of the proposed models significantly outperform the historical average. Exhibit 5, Panel B, displays results

on average equity weight and turnover, which are also consistent with the first experiment. Overall, the Gordon-inspired dividend model and the inverted PE model are the most consistent performers, even if they do not outperform the clairvoyant benchmark in this experiment.

CONCLUSION

Using historical averages to back out expected returns for equities and other asset classes is a widespread practice in the industry and the default option of most commercial optimization software. It is also very common to disregard the more distant past using the argument of structural breaks, or use the same argument to build a common evaluation sample that includes asset classes with shorter histories (i.e., corporate bonds in Europe, hedge funds, and so forth).

E X H I B I T 5Dynamic Portfolio Allocation and Turnover (1921–2000)

Notes: The exhibit reports the equity component and the average annual turnover of nine dynamic allocation strategies shown in Exhibit 4, optimized for investors with different risk aversion coefficients γ (Panel A) and different shortfall constraints expressed as a percentage of expected equity volatility (Panel B). The exhibit also shows P-values of the differences in the equity component and turnover between the various strategies and the historical return strategy.



This article provides fresh evidence on the poor pre-dictive power of historical average returns, in both equity and fixed income. The analysis also shows that forward-looking models that rely on steady-state equations for equities and initial yields to maturity for bonds are far better predictors of markets’ long-run direction. These findings are consistent with the literature on long-horizon predictability, a notion hailed back in 1999 as a “new fact in finance” (Cochrane [1999]), but still not universally accepted by academics and industry practitioners.

Using a long-term U.S. sample (1926 to 2010), we also find that predictability translates into significantly better risk-adjusted performance for dynamic asset-allocation strategies that rely on forward-looking inputs, as opposed to historical average returns. The results are robust to different assumptions on investors’ risk aversion and preferences (utility versus safety first). This con-firms the crucial importance of reliable expected return assumptions in estimating optimal portfolio weights

in a Markowitz setting. Future work could extend our approach to assess the effect of alternative volatility and correlation forecasts on portfolio performance.

Our results provide strong evidence that asset allo-cators should disregard static risk-premia assumptions that hinge on historical average returns and instead calibrate the optimal asset mix using well-proven relationships between long-term return trends and market fundamen-tals such as dividend yields, cyclically adjusted PE ratios, or long-term bond yields. Given that these inputs can change significantly over the space of just a few months, the findings’ broader implication is that institutional investors, such as pension funds and endowments, should move away from the traditional approach to strategic asset allocation, which involves infrequent reviews once every two or three years and static policy weights in between. Instead, they should embrace a more dynamic approach to take advantage of changes in long-run expected returns and the composition of the optimal portfolio mix.

A P P E N D I X

E X H I B I T A 1Cumulative Net Square Error



Notes: The exhibit shows cumulative net square errors for the clairvoyant model and five equity forecasts, versus the five-year historical average return of equities (Panel A) and for initial yield versus five-year historical average of fixed-income assets (Panel B). Net square error (NSE) is calculated as the difference in a square of the forecast error of the historical five-year average return and the square of the forecast error of a given forecasting model. Both errors are estimated versus a subsequent 10-year average realized return. The higher the NSE, the better the forecasting model’s forecast, relative to the historical average. Cumulative NSE for a given month is the sum of net square errors since 1921 until that point in time. Hence, it tracks the cumulative performance of each model over time, versus a five-year historical average. As a point of reference, we show cumulative NSE for a clairvoyant model in all equity exhibits, to ease comparison across different equity forecasts.

E X H I B I T A 1 (Continued)

E X H I B I T A 2Allocations Comparison (Last Optimization April 1999)



ENDNOTES

Marco Navone acknowledges financial support from CAREFIN, the Centre for Applied Research in Finance of Bocconi University in Milan, Italy.

1Stress test results are available upon request.2We calculate retention ratio as one minus a 20-year

historical average payout ratio. The product of ROE and this measure of retention ratio seems to be a better estimate of future earnings growth, because the model based on the historical average of payout ratios showed higher predictive power than the model using only current payout levels.

3Results using the 10-year historical average and the 20-year average as benchmarks are available upon request.

4Diebold and Mariano [1995] propose a f lexible meth-odology to develop an asymptotical distribution for a variety of loss-of-accuracy measures. Given an actual series, i.e., a realized subsequent 10-year equity return calculated for each

month, the test applies a loss criterion (we chose a mean-squared error for its widespread use in the related literature) and calculates multiple measures of predictive accuracy that let us test the null hypothesis of equal accuracy. In par-ticular, the DM statistic tests the hypothesis that the mean difference between the loss criteria for the two predictions is zero, using a long-run estimate of the variance of the difference series.

5Results using 10 years of historical returns in esti-mating the variance–covariance matrix are available upon request.

REFERENCES

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E X H I B I T A 2 (Continued)



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