Interpreting the predictive power of the consumption–wealth ratio

Lettau and Ludvigson [Lettau, M., Ludvigson, S.C., 2001a. Consumption, aggregate wealth and expected stock returns. Journal of Finance 56, 815–849] find that the estimated consumption–wealth ratio (cay) is a strong predictor of U.S. stock returns, while Brennan and Xia [Brennan, M.J., Xia, Y., 2005. tay's as good as cay. Finance Research Letters 2, 1–14] argue that the predictive power of cay arises from a look-ahead bias. In a unified framework, we examine how the presence of deterministic time trends affects the estimation and forecasting power of cay. We show that ignoring the presence of a deterministic time trend in estimating the cointegrating relationship among consumption, asset wealth, and labor income leads to a biased estimate of the consumption–wealth ratio. In the presence of a deterministic time trend, cay is a combination of the highly persistent bias component and the unbiased cointegrating residual, and most of the predictive power of cay is attributable to the bias component, casting doubt on the robustness of the forecasting power of cay.     

tay's as good as cay

The empirical evidence that the consumption–wealth ratio, cay, has strong in-sample predictive power for future stock returns has been interpreted as evidence that consumers take account of future investment opportunities in planning their consumption expenditures. In this paper we show that the predictive power of cay arises mainly from a “look-ahead bias” introduced by estimating the parameters of the cointegrating regression between consumption, assets, and labor income in-sample. When a similar regression is run, replacing the log of consumption with an inanimate variable, calendar time, the resulting residual, which we label tay, is shown to be able to forecast stock returns as well as, or better than, cay. In addition, both cay and tay lose their out-of-sample forecasting power when they are re-estimated every period with only available data.     

The empirical risk–return relation: A factor analysis approach

Existing empirical literature on the risk–return relation uses relatively small amount of conditioning information to model the conditional mean and conditional volatility of excess stock market returns. We use dynamic factor analysis for large data sets, to summarize a large amount of economic information by few estimated factors, and find that three new factors—termed “volatility,” “risk premium,” and “real” factors—contain important information about one-quarter-ahead excess returns and volatility not contained in commonly used predictor variables. Our specifications predict 16–20% of the one-quarter-ahead variation in excess stock market returns, and exhibit stable and statistically significant out-of-sample forecasting power. We also find a positive conditional risk–return correlation.     

Consumption growth and time-varying expected stock returns

When the consumption growth rate is measured based upon fourth quarter data, it tracks predictable variation in future excess stock returns. Low fourth quarter consumption growth rates predict high future excess stock returns such that expected returns are high at business cycle troughs and low at business cycle peaks. The consumption growth rate loses predictive power when it is measured based upon other quarters. This is consistent with the insight of Jagannathan and Wang [2007. Journal of Finance 62, 1623–1661] that investors tend to review their consumption and investment plans during the end of each calendar year, and at possibly random times in between. The consumption growth rate measured based upon fourth quarter data is a much stronger predictive variable than benchmark predictive variables such as the dividend–price ratio, the term spread, and the default spread.     

Forecasting Japanese Stock Returns with Financial Ratios and Other Variables

This paper extends the previous analyses of the forecastability of Japanese stock market returns in two directions. First, we carefully construct smoothed market price–earnings ratios and examine their predictive ability. We find that the empirical performance of the price–earnings ratio in forecasting stock returns in Japan is generally weaker than both the price–earnings ratio in comparable US studies and the price dividend ratio. Second, we also examine the performance of several other forecasting variables, including lagged stock returns and interest rates. We find that both variables are useful in predicting aggregate stock returns when using Japanese data. However, while we find that the interest rate variable is useful in early subsamples in this regard, it loses its predictive ability in more recent subsamples. This is because of the extremely limited variability in interest rates associated with operation of the Bank of Japan’s zero interest policy since the late 1990s. In contrast, the importance of lagged returns increases in subsamples starting from the 2000s. Overall, a combination of logged price dividend ratios, lagged stock returns, and interest rates yield the most stable performance when forecasting Japanese stock market returns.     

tay's as good as cay: Reply

In a recent comment on our published work [Lettau, M., Ludvigson, S., 2001. Consumption, aggregate wealth, and expected stock returns. Journal of Finance 56, 815–850], Michael Brennan and Yihong Xia [2005. tay's as good as cay. Finance Research Letters 2, 1–14] advance the following argument: A “mechanistic” variable tay, where t is a linear time trend, forecasts stock returns. Since “t has no foresight,” the argument goes, the predictive power of this variable must be attributable to what they call “look-ahead bias.” The authors assert that cay is subject to the same look-ahead bias (generated because we use the full sample to estimate the cointegrating parameters in cay), implying that its forecasting power must be spurious. In this response, we explain why this critique is misplaced.     

Expected returns and expected dividend growth

We investigate a consumption-based present-value relation that is a function of future dividend growth and find that changing forecasts of dividend growth are an important feature of the post-war U.S. stock market, despite the failure of the dividend–price ratio to uncover such variation. In addition, dividend forecasts are found to covary with changing forecasts of excess stock returns over business cycle frequencies. This covariation is important because positively correlated fluctuations in expected dividend growth and expected returns have offsetting effects on the log dividend–price ratio. The market risk premium and expected dividend growth thus vary considerably more than is apparent using the log divided–price ratio alone as a predictive variable.     

Capital Gains, Dividend Yields, and Expected Inflation

One explanation for the negative relationship between short-horizon stock returns and inflation is that inflation proxies (inversely) for expected future real output. In this paper, I examine the possibility that inflation also proxies for variation in real price/dividend ratios (excess returns). I show that when the covariance between real price/dividend ratios and inflation is nonzero, the relationship between returns and expected inflation differs for the two components of returns: dividend yields and capital gains returns. My empirical evidence demonstrates that dividend yields and capital gains are related differently to expected inflation in U.S. and foreign markets.     

Relation between time-series and cross-sectional effects of idiosyncratic variance on stock returns

Consistent with the post-1962 US evidence by Ang et al. [Ang, A., Hodrick, R., Xing Y., Zhang, X., 2006. The cross-section of volatility and expected returns. Journal of Finance 51, 259–299], we find that stocks with high idiosyncratic variance (IV) have low CAPM-adjusted expected returns in both pre-1962 US and modern G7 data. We also test in three ways the conjecture that IV is a proxy of systematic risk. First, the return difference between low and high IV stocks – that we dub as IVF – is a priced factor in the cross-section of stock returns. Second, loadings on lagged market variance and lagged average IV account for a significant portion of variation in average returns on portfolios sorted by IV. Third, the variance of IVF correlates closely with average IV, and the two variables have similar explanatory power for the time-series and cross-sectional stock returns.     

Consumption, (dis)aggregate wealth,and asset returns

In this work, I show, from the consumer's budget constraint, that the residuals of the trend relationship among consumption, financial wealth, housing wealth and labor income (summarized by the variable cday) should predict better U.S. and U.K. quarterly stock market returns than a variable like cay from Lettau and Ludvigson (2001), which considers aggregate wealth instead.I find that the superior forecasting power of cday is due to: (i) its ability to track the changes in the composition of asset wealth; and (ii) the faster rate of convergence of the coefficients to the “long-run equilibrium” parameters.In addition, the results suggest that, while financial wealth shocks are mainly transitory, fluctuations in housing wealth are very persistent. Moreover, they highlight that expectations about future returns are “synchronized” across countries.     

The Risk‐Return Relation in International Stock Markets

We investigate the risk‐return relation in international stock markets using realized variance constructed from MSCI (Morgan Stanley Capital International) daily stock price indices. In contrast with the capital asset pricing model, realized variance by itself provides negligible information about future excess stock market returns; however, we uncover a positive and significant risk‐return tradeoff in many countries after controlling for the (U.S.) consumption‐wealth ratio. U.S. realized variance is also significantly related to future international stock market returns; more importantly, it always subsumes the information content of its local counterparts. Our results indicate that stock market variance is an important determinant of the equity premium.     

Predictable Stock Returns in the United States and Japan: A Study of Long-Term Capital Market Integration

This paper uses the predictability of monthly excess returns on U.S. and Japanese equity portfolios over the U.S. Treasury bill rate to study the integration of long-term capital markets in these two countries. During the period 1971–1990 similar variables, including the dividend-price ratio and interest rate variables, help to forecast excess returns in each country. In addition, in the 1980's U.S. variables help to forecast excess Japanese stock returns. There is some evidence of common movement in expected excess returns across the two countries, which is suggestive of integration of long-term capital markets.     

Earnings and Expected Returns

The aggregate dividend payout ratio forecasts excess returns on both stocks and corporate bonds in postwar U.S. data. High dividends forecast high returns. High earnings forecast low returns. The correlation of earnings with business conditions gives them predictive power for returns; they contain information about future returns that is not captured by other variables. Dividends and earnings contribute substantial explanatory power at short horizons. For forecasting long-horizon returns, however, only (scaled) stock prices matter. Forecasts of low long-horizon stock returns in the mid-1990s are caused not by earnings or dividends, but by high stock prices.     

What Moves the Stock and Bond Markets? A Variance Decomposition for Long-Term Asset Returns

This paper uses a vector autoregressive model to decompose excess stock and 10-year bond returns into changes in expectations of future stock dividends, inflation, short-term real interest rates, and excess stock and bond returns. In monthly postwar U.S. data, stock and bond returns are driven largely by news about future excess stock returns and inflation, respectively. Real interest rates have little impact on returns, although they do affect the short-term nominal interest rate and the slope of the term structure. These findings help to explain the low correlation between excess stock and bond returns.     

Consumption, Aggregate Wealth, and Expected Stock Returns

This paper studies the role of fluctuations in the aggregate consumption–wealth ratio for predicting stock returns. Using U.S. quarterly stock market data, we find that these fluctuations in the consumption–wealth ratio are strong predictors of both real stock returns and excess returns over a Treasury bill rate. We also find that this variable is a better forecaster of future returns at short and intermediate horizons than is the dividend yield, the dividend payout ratio, and several other popular forecasting variables. Why should the consumption–wealth ratio forecast asset returns? We show that a wide class of optimal models of consumer behavior imply that the log consumption–aggregate wealth (human capital plus asset holdings) ratio summarizes expected returns on aggregate wealth, or the market portfolio. Although this ratio is not observable, we provide assumptions under which its important predictive components for future asset returns may be expressed in terms of observable variables, namely in terms of consumption, asset holdings and labor income. The framework implies that these variables are cointegrated, and that deviations from this shared trend summarize agents' expectations of future returns on the market portfolio.     

Consumer expectations and short-horizon return predictability

Lettau and Ludvigson [Lettau, M., Ludvigson, S, 2001. Consumption, aggregate wealth and expected stock returns. Journal of Finance 56, 815–849] argue that fluctuations from the equilibrium ratio of consumption to wealth (cây) reflect changing expectations of asset returns and document significant short-horizon predictability based on cây. This paper further explores the role of consumer expectations in modeling time variation of expected equity returns by considering two measures of consumer expectations: (i) consumer behavior as reflected in cây, and (ii) a more-direct measure of expectations captured by the Index of Consumer Sentiment (ICS). We report strong regression-based evidence of return predictability based on cây, which remains evident even after accounting for various sources of estimation risk. However, the regression-based evidence of predictability does not necessarily imply that shifts in aggregate consumption and the components of aggregate wealth give rise to economically significant investment signals. The survey-based measure of expectations (ICS) is shown to complement the behavioral measure (cây) but has no apparent stand-alone predictive value in forecasting equity returns.     

Investment Plans and Stock Returns

When the discount rate falls, investment should rise. Thus with time-varying discount rates and instantly changing investment, investment should positively covary with current stock returns and negatively covary with future stock returns. Aggregate nonresidential U.S. investment contradicts both these implications, probably because of investment lags. Investment plans, however, satisfy both implications. These investment plans, from a U.S. government survey of firms, are highly informative measures of expected investment and explain more than three-quarters of the variation in real annual aggregate investment growth. Plans have substantial forecasting power for excess stock returns, showing that time-varying risk premia affect investment.     

The risk return tradeoff in the long run: 1836–2003

Previous studies typically find a statistically insignificant relation between the market risk premium and its expected volatility. Further, several of these studies estimate a negative risk return tradeoff, contrary to the predictions of mainstream theory. Using simulations, I demonstrate that even 100 years of data constitute a small sample that may easily lead to this finding even though the true risk return tradeoff is positive. Small-sample inference is plagued by the fact that conditional volatility has almost no explanatory power for realized returns. Using the nearly two century history of U.S. equity market returns from Schwert [1990. Indexes of United States stock prices from 1802 to 1987. Journal of Business 63, 399–426], I estimate a positive and statistically significant risk return tradeoff. Finally, exploratory analysis suggests a role for a time-varying relation linked to the changing nature of the U.S. economy.     

Habit formation,surplus consumption and return predictability: International evidence

On an international post World War II dataset, we use an iterated GMM procedure to estimate and test the Campbell and Cochrane (1999, By force of habit: a consumption-based explanation of aggregate stock market behavior. Journal of Political Economy 107, 205–251.) habit formation model with a time-varying risk-free rate. In addition, we analyze the predictive power of the surplus consumption ratio for future stock and bond returns. We find that, although there are important cross-country differences and economically significant pricing errors, for the majority of countries in our sample the model gets empirical support in a variety of different dimensions, including reasonable estimates of risk-free rates. Further, for the majority of countries the surplus consumption ratio captures time-variation in expected returns. Together with the price-dividend ratio, the surplus consumption ratio contains significant information about future stock returns, also during the 1990s. In addition, in most countries the surplus consumption ratio is also a powerful predictor of future bond returns. Thus, the surplus consumption ratio captures time-varying expected returns in both stock and bond markets.     

International diversification strategies: Revisited from the risk perspective

Following Roll [Roll, R., 1992. Industrial structure and comparative behaviour of international stock market indices. Journal of Finance 47, 3–42] and Heston and Rouwenhorst [Heston, S.L., Rouwenhorst, G.K., 1994. Does industrial structure explain the benefits of international diversification. Journal of Financial Economics 36, 3–27], researchers have decomposed stock returns into country and industry components. Evidence suggests that industry components have become more important in recent years, but the reasons for this are unclear. Existing research concentrated mainly on stock returns in industrial countries. In this paper we consider instead the decomposition of stock risks within emerging equity markets. We provide a rationale for this procedure and its relationship to return decompositions. The results provide new firm-specific evidence on the debate over country and industry components, their stability over time, and the implications for portfolio diversification.