MODELING

All active management strategies—whether they are based on stocks, factors or markets—rely on forecasts, and all active managers employ some forecasting methodology. The quest to predict financial market returns and the debate over the futility of this endeavor will likely endure forever.

Samuelson argues that stock markets are efficient at the micro level, but inefficient at the macro level.³³ Although equity prices are known to exhibit an excessive degree of volatility relative to their fundamentals,³⁴ equity markets do appear very efficient at the micro level in the sense that individual stock dividend yields forecast future dividend growth rates in a manner consistent with the simple efficient markets model. That is, high dividend yields indicate low future dividend growth and low dividend yields signify high future dividend growth. Shiller and Jung find that evidence supportive of Samuelson's apparent paradox;³⁵ their empirical tests reveal that the dividend yield has significant predictive power for forecasting future dividend growth rates for individual firms, although measures of an aggregate dividend yield exhibits no significant relationship with future aggregate dividend growth and the coefficient is often of the wrong sign. They interpret these results as evidence in favor of Samuelson's thesis. Campbell and Shiller demonstrate that aggregate stock market returns are forecastable using various valuation metrics and show that the dividend yield for the aggregate U.S. stock market does not forecast dividend growth in a manner consistent with theory.³⁶

Whatever the forecasting technique, the seemingly paradoxical combination of macro inefficiency and micro efficiency suggests that portfolio management strategies based on selective exposure to various macro factors may be more effective than those based purely on bottom-up security selection techniques. While individual security selection may present more opportunity to enhance returns due to greater breadth³⁷—the number of securities in the global market is much larger than the number of countries, industries, or asset classes—there is plenty of evidence highlighting the difficulty associated with achieving excess returns via traditional security.

Fundamental Valuation–Based Methods

A large literature examines the use of valuation ratios (e.g., book-to-price, dividend yield, earnings yield, etc.) in forecasting future stock returns. Most of this research suggests that valuation ratios are extremely useful forecasting metrics, especially at the aggregate level.³⁸

The most basic model of stock valuation is the dividend discount model, which is commonly attributed to Gordon.³⁹ The derivation of this model begins with the representation of the price (P) of a stock in any period as the sum of the discounted value of the sum of the expected dividend (D) received at the end of the current period plus the expected stock price in the following period:

A close inspection of equation (14.9) reveals that it is nothing more than the definition of return. Assuming that (P_t+_K) is bounded, then the recursive substitution for (P_t+1) reveals that the current stock price is equal to the present discounted value of all future dividends:

With a constant dividend growth rate, the expected return of a stock (E(r)) may be written as the sum of the current dividend yield and the expected growth rate (g):

Often, an aggregate version of the Gordon model is used to model the return spread between two categories or indexes of stocks. For instance, it is possible to use this approach to model relative expected returns for two stocks, styles, or asset categories by writing the expected return spread as the sum of the difference in dividend yields and the difference in expected growth rates:

Using an aggregated version of equation (14.12) based on stock-level data and a composite value metric based on earnings, sales, and dividends, Asness, Friedman, Krail, and Liew examine the usefulness of this type of methodology for forecasting style return spreads in the United States and find that both fundamental value spreads—(Dⁱ/Pⁱ – D^j/P^j)—and growth spreads—E(gⁱ – g^j)—are important determinants of the future return spread between value and growth stocks.⁴⁰ They find that these metrics jointly account for almost 40% of the variability in the following year's style return spread. Periods when value stocks offer larger than average yield premiums relative to growth stocks and growth stocks offer lower than average premiums in terms of expected growth are particularly good for value. In their study of country-level timing based on value factors, Asness, Krail, and Liew find that the value spread for country equity indexes identifies opportunities to earn above average expected returns by focusing on countries with lower than normal book-to-market values.⁴¹ Cohen, Polk, and Vuolteenahoalso find that the times series variation in the spread between the average return on growth stocks and value stocks is related to the so-called value spread;⁴² abnormally high value spreads are predictive of higher expected returns from value strategies relative to growth strategies.

Momentum-Based and Trend-Sensitive Methods

Although valuation-based trading strategies offer some promise and fit well with the fundamental theoretical model of Gordon and the mental framework of many investors, there remains a great deal of interest in momentum strategies. Why might financial markets exhibit momentum and why might momentum strategies work? Two primary reasons to expect the presence of momentum and the success of trend-based strategies are the possibility that market participants systematically underreact to news—good or bad—or the possibility that market participants are subject to a herd mentality of some sort. While there is some evidence suggesting that market participants systematically overreact to new information, leading to mean reversion in stock market returns,⁴³ many believe these results are driven by systematic risk factors such as style and size premiums, and there is now widespread agreement among financial economists and practitioners on the existence of momentum effects exist in financial markets and the efficacy of momentum strategies.

Jegadeesh and Titman find that momentum strategies—that is, strategies that buy stocks past winners (those that have performed well in the recent past) and sell past losers (that have performed poorly in the recent past)—generate significant positive returns over 3- to 12-month holding periods.⁴⁴ Chan, Jegadeesh, and Lakonishok also study momentum effects and find that past returns and earnings surprise are both predictive of future returns and that these effects are not explained by market risk, size, or style effects.⁴⁵ Rouwenhorst studies international equity markets and finds evidence of momentum, showing that an internationally diversified portfolio of recent winners outperforms recent losers by more than one percent per month.⁴⁶ While momentum is related to firm size, Rouwenhorst finds evidence of momentum across the size spectrum, indicating that momentum is not entirely explained by the size effect.

Momentum models differ in the forecast horizon and the time lags used to measure trends. They can be built at the individual stock level or on some aggregate basis. However, at the heart of any momentum model, there is a relationship of the following form:

In equation (14.13), f(.) is assumed to be increasing in past values of (rⁱ − r^j), suggesting that future return spreads are a positively related to past return spreads. Generally, momentum models are designed to forecast returns a reasonably high frequency (e.g., days, weeks, or months) since value (or mean-reversion) appears to dominate over long time periods.

Momentum and trend-based strategies are attractive because of their simplicity. Indeed, the ability to forecast future returns based on nothing more than past returns is appealing—if for nothing else because of its absurdity. These models are similar to mathematical or statistical versions of technical analysis, which basically attempts to forecast future prices based on charts of past prices behavior. When employing these techniques, care must be taken to avoid data mining, spurious correlations, and chasing after cycles that are merely artifacts of a particular smoothing process.⁴⁷

Combined Methods

Value strategies tend to trade early because financial market prices often exhibit a pattern of overshooting their fundamental value. This pattern implies that value strategies often appear foolish in the short run due to their tendency to purchase unloved securities that continue to fall in price and sell glamour securities that continue to increase in price. Momentum and trend-driven strategies by definition must trade late, and, if market cycles are characterized by the largest return spreads near the beginning of a regime shift, slow-moving momentum strategies may fail to deliver superior returns.

EXHIBIT 14.2 The Timing of Value and Momentum Strategies

Exhibit 14.2 illustrates these points. The line in the figure depicts both the relative value and relative return of two assets. When asset X is cheap relative to asset Y (and vice versa) value strategies sell asset Y(X) in order to buy asset X(Y). These instances are depicted in points A and B. When momentum shifts in favor asset X at the expense of asset Y, momentum strategies sell asset Y in order to buy asset X; conversely, when momentum shifts in favor of asset Y at the expense of asset X, momentum strategies sell asset X in order to buy asset Y. These instances are depicted in points C and D. Neither strategy is a perfect timing device. That is, neither the value strategy nor the momentum strategy precisely identifies the local peaks and troughs in the relative returns of the two assets. The value strategy is generally early, and the momentum strategy is—by definition—always late.

Grantham argues that an appropriate balance between momentum effects and value effects is one of the central aspects of successful portfolio management.⁴⁸

Models incorporating a combination of valuation and momentum strategies are designed to remedy these problems, by allowing momentum to dominate when valuations have not yet reached an extreme position and valuations to dominate when momentum breaks down. Although it is rare in practice, the concurrence of valuation signals and momentum signals is a powerful indicator, since both momentum and valuation have been shown to be predictive of future returns.

There is some empirical evidence suggesting that valuation approaches and momentum approaches may be complementary. Asness argues that the interaction of value and momentum strategies is important for understanding the success of both value and momentum strategies.⁴⁹ He shows that the efficacy of value strategies is greatest for low momentum stocks and the success of momentum strategies is greatest among expensive stocks. Because of the instability in the forecasting content of valuation ratios and the presence of serial correlation in country-level and regional stock returns, Farr advocates the use of a combination of valuation and momentum methods.⁵⁰

Other Techniques

During the 1980s and 1990s, quantitative portfolio managers began to employ models to forecast portfolio risk and tracking error (the volatility of a portfolio's excess return relative to its benchmark). These risk models are basically multifactor regression models used to isolate the past determinants of volatility and project future volatility.

Haugen and Baker turn a return attribution model into a return forecasting model by assuming investors have a form of adaptive preferences and expectations which are influenced by the recent past.⁵¹ This type of model is truly agnostic in the sense that it does not reflect any belief about the elemental importance of fundamental or technical factors. While it does rely on the assumption that investors have a form of adaptive expectations (and hence the presence of momentum in factor payoffs)—it lets the data do the talking as to which factors are most important at any given time.

Haugen and Baker begin with a return decomposition of the following form, which depicts the return for stock i at date t is a function of a set of factors and the payoffs to each factor:

In (14.14) PAYOFF_i,t is the estimated regression coefficient for factor i at date t, and FACTOR_j,i,t-1 is the exposure to factor i for stock j at date t − 1. The model is a standard multifactor return attribution model incorporating time-varying payoffs. A version of this type of model is commonly used as a portfolio attribution model or as a portfolio risk model (used to forecast the active risk of a portfolio relative to a passive benchmark).

If one can forecast the date t payoff values at date t − 1, then it is possible to transform equation (14.14) from a return attribution model into a return forecasting model. Haugen and Baker use a simple 12-month smoothing to project the next period's payoff values,

so that the expected return for stock i at date t is projected as

The model in equation (14.15) is closely related to the investor preference theory of Stevens, Borger, and Reynolds.⁵² They argue that since broadly recognized factor returns—e.g., value and size—are likely to be arbitraged away and investor preferences evolve slowly over time with changes in market conditions, a dynamic model of investor preferences (and hence expected returns) is necessary. The primary drawback of these models is their lack of parsimony, and thus their tendency to fall victim to the criticism of data mining.