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.     

Rejoinder

This paper provides a formula for a commonly used measure of the economic value of asset return predictability. In doing this, we find that there is a strong connection between this measure and a traditional statistical measure of predictive quality. In particular, we demonstrate that the maximum amount an investor is willing to pay for predictability knowledge (the performance fee) is a simple transformation of the R ² statistic associated with the predictor equation. We illustrate the use of these results with an application to the Ibbotson US bond and equity data (and a set of pertinent predictors), and via application to the results published in Fama and French [1988. Dividend yields and expected stock returns. Journal of Financial Economics 22: 3–25], Balvers, Cosimano, and McDonald [1990. Predicting stock returns in an efficient market. Journal of Finance 45: 1109–28], Lettau and Ludvigson [2001. Consumption, aggregate wealth and expected stock returns. Journal of Finance 56: 815–49], and Santa-Clara and Yan [2010. Crashes, volatility, and the equity premium: Lessons from S&;P 500 options. Review of Economics and Statistics 92: 435–51].     

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.     

Output and expected returns

This paper shows for 1929–2003 U.S. data and also for international G-7 data that the ratio of share prices to GDP tracks a large fraction of the variation over time in expected returns on the aggregate stock market, capturing more of that variation than do price–earnings and price–dividend ratios and often also providing additional information about excess returns. The price–output ratio tracks long-term U.S. cumulative stock returns almost as well as the cay-ratio of Lettau and Ludvigson [2001a. Journal of Finance 56, 815–849, 2005. Journal of Financial Economics 76, 583–626], although the cay-ratio tracks variation in U.S. excess returns better. The price–output ratio, however, involves no parameter estimation and is easily constructed for non-U.S. countries.     

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.     

On the predictive power of the surplus consumption ratio

This paper shows that the surplus consumption ratio, specified by Campbell and Cochrane [1999. Journal of Political Economy 107, 205–251], is a good predictor of excess returns at long horizons. We also provide empirical evidence that this variable captures a component of expected returns, not explained by the proxies for the consumption to wealth ratio, cay and cdy, proposed by Lettau and Ludvigson [2001a. Journal of Finance 56, 815–849; 2001b. Journal of Political Economy 109, 1238–1286; 2005. Journal of Financial Economics 76, 583–626]. Moreover, used as a conditioning information for the Consumption based Asset Pricing Model (C)CAPM, the resulting linear model helps to explain for the variation in average returns across the Fama–French (25) portfolios sorted by size and book-to-market characteristics.     

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.     

The second moment matters! Cross-sectional dispersion of firm valuations and expected returns

Behavioral theories predict that firm valuation dispersion in the cross-section (“dispersion”) measures aggregate overpricing caused by investor overconfidence and should be negatively related to expected aggregate returns. This paper develops and tests these hypotheses. Consistent with the model predictions, I find that measures of dispersion are positively related to aggregate valuations, trading volume, idiosyncratic volatility, past market returns, and current and future investor sentiment indexes. Dispersion is a strong negative predictor of subsequent short- and long-term market excess returns. Market beta is positively related to stock returns when the beginning-of-period dispersion is low and this relationship reverses when initial dispersion is high. A simple forecast model based on dispersion significantly outperforms a naive model based on historical equity premium in out-of-sample tests and the predictability is stronger in economic downturns.     

Profitability,investment and average returns

Valuation theory says that expected stock returns are related to three variables: the book-to-market equity ratio (B_t/M_t), expected profitability, and expected investment. Given B_t/M_t and expected profitability, higher expected rates of investment imply lower expected returns. But controlling for the other two variables, more profitable firms have higher expected returns, as do firms with higher B_t/M_t. These predictions are confirmed in our tests.     

Asset pricing in production economies with extrapolative expectations

Introducing extrapolative bias into a standard production-based model with recursive preferences reconciles salient stylized facts about business cycles (low consumption volatility, high investment volatility relative to output) and financial markets (high equity premium, volatile stock returns, low and smooth risk-free rate) with plausible levels of risk aversion and intertemporal elasticity of substitution. Furthermore, the model captures return predictability based upon dividend yield, Q, and investment. Intuitively, extrapolative bias increases the variation in the wealth–consumption ratio, which is heavily priced under recursive preferences; adjustment costs decrease the covariance between marginal utility and asset returns. Empirical support for key implications of the model is also provided.     

Predictability and the earnings–returns relation

This paper studies the effects of predictability on the earnings–returns relation for individual firms and for the aggregate. We demonstrate that prices better anticipate earnings growth at the aggregate level than at the firm level, which implies that random-walk models are inappropriate for gauging aggregate earnings expectations. Moreover, we show that the contemporaneous correlation of earnings growth and stock returns decreases with the ability to predict future earnings. Our results may therefore help explain the apparently conflicting recent evidence that the earnings–returns relation is negative at the aggregate level but positive at the firm level.     

The Consumption–Income Ratio,Entrepreneurial Risk,and the U.S. Stock Market

The owners of small noncorporate businesses face substantial and largely uninsurable entrepreneurial risk. They are also an important group of stock owners. This paper explores the role of entrepreneurial risk in explaining time variation in expected U.S. stock returns in the period 1952–2010. It proposes an entrepreneurial distress factor that is based on a cointegrating relationship between aggregate consumption and income from proprietary and nonproprietary wealth. This factor, referred to here as the cpy residual, signals when entrepreneurial income is low in relation to aggregate consumption and other forms of income in the economy. It is highly correlated with cross‐sectional measures of idiosyncratic entrepreneurial and default risk, and it has considerable forecasting power for the expected equity premium. However, the correlation between cpy and the stock market started to decline at the beginning of the 1980s. The decline in this correlation can be associated with increased stock market participation and with the progress of U.S. state‐level bank deregulation. This pattern is consistent with the view that entrepreneurial risk became more easily diversifiable in the wake of U.S. state‐level bank deregulation.     

A new approach to measuring riskiness in the equity market: Implications for the risk premium

We introduce a new approach to measuring riskiness in the equity market. We propose option implied and physical measures of riskiness and investigate their performance in predicting future market returns. The predictive regressions indicate a positive and significant relation between time-varying riskiness and expected market returns. The significantly positive link between aggregate riskiness and market risk premium remains intact after controlling for the S&P 500 index option implied volatility (VIX), aggregate idiosyncratic volatility, and a large set of macroeconomic variables. We also provide alternative explanations for the positive relation by showing that aggregate riskiness is higher during economic downturns characterized by high aggregate risk aversion and high expected returns.     

Time Variation in the Covariance between Stock Returns and Consumption Growth

The conditional covariance between aggregate stock returns and aggregate consumption growth varies substantially over time. When stock market wealth is high relative to consumption, both the conditional covariance and correlation are high. This pattern is consistent with the “composition effect,” where agents' consumption growth is more closely tied to stock returns when stock wealth is a larger share of total wealth. This variation can be used to test asset‐pricing models in which the price of consumption risk varies. After accounting for variations in this price, the relation between expected excess stock returns and the conditional covariance is negative.     

Measuring investor sentiment with mutual fund flows

We investigate a proxy for monthly shifts between bond funds and equity funds in the USA: aggregate net exchanges of equity funds. This measure (which is negatively related to changes in VIX) is positively contemporaneously correlated with aggregate stock market excess returns: One standard deviation of net exchanges is related to 1.95% of market excess return. Our main new finding is that 85% (all) of the contemporaneous relation is reversed within four (ten) months. The effect is stronger in smaller stocks and in growth stocks. These findings support the notion of “noise” in aggregate market prices induced by investor sentiment.     

Consumption,asset wealth,equity premium,term spread,and flight to quality

We link transitory deviations of consumption from its equilibrium relationship with aggregate wealth and labor income to equity returns on the one hand, and to two characteristics of bond investors—the premium demanded to hold long‐term assets, and “flight to quality” behavior—on the other hand. Using a panel of 10 euro area countries over the period 1984Q1–2017Q4, we show that a rise in the consumption–wealth ratio predicts both higher equity returns and the future term spread, while a fall in the consumption–wealth ratio explains a large fraction of the rise in the spread between the “risky” and the “safe‐haven” bond.     

Time-varying risk premia and the cost of capital: An alternative implication of the Q theory of investment

Evidence suggests that expected excess stock market returns vary over time, and that this variation is much larger than that of expected real interest rates. It follows that a large fraction of the movement in the cost of capital in standard investment models must be attributable to movements in equity risk-premia. In this paper we emphasize that such movements in equity risk premia should have implications not merely for investment today, but also for future investment over long horizons. In this case, predictive variables for excess stock returns over long-horizons are also likely to forecast long-horizon fluctuations in the growth of marginal Q, and therefore investment. We test this implication directly by performing long-horizon forecasting regressions of aggregate investment growth using a variety of predictive variables shown elsewhere to have forecasting power for excess stock market returns.     

Stock price synchronicity and analyst coverage in emerging markets

This paper examines the relation between the stock price synchronicity and analyst activity in emerging markets. Contrary to the conventional wisdom that security analysts specialize in the production of firm-specific information, we find that securities which are covered by more analysts incorporate greater (lesser) market-wide (firm-specific) information. Using the R² statistics of the market model as a measure of synchronicity of stock price movement, we find that greater analyst coverage increases stock price synchronicity. Furthermore, after controlling for the influence of firm size on the lead–lag relation, we find that the returns of high analyst-following portfolio lead returns of low analyst-following portfolio more than vice versa. We also find that the aggregate change in the earnings forecasts in a high analyst-following portfolio affects the aggregate returns of the portfolio itself as well as those of the low analyst-following portfolio, whereas the aggregate change in the earnings forecasts of the low analyst-following portfolio have no predictive ability. Finally, when the forecast dispersion is high, the effect of analyst coverage on stock price synchronicity is reduced.     

A consumption-based model of the term structure of interest rates

This paper proposes a consumption-based model that accounts for many features of the nominal term structure of interest rates. The driving force behind the model is a time-varying price of risk generated by external habit. Nominal bonds depend on past consumption growth through habit and on expected inflation. When calibrated to data on consumption, inflation, and the aggregate market, the model produces realistic means and volatilities of bond yields and accounts for the expectations puzzle. The model also captures the high equity premium and excess stock market volatility.     

Aggregate insider trading: Contrarian beliefs or superior information?

We decompose realized market returns into expected return, unexpected cash-flow news and unexpected discount rate news to test the relation between aggregate market returns and aggregate insider trading. We find that (1) the predictive ability of aggregate insider trading is much stronger than what was reported in earlier studies, (2) aggregate insider trading is strongly related to unexpected cash-flow news, (3) market expectations do not cause insider trading contrary to what others have documented, and (4) aggregate insider trading in firms with high information uncertainty is more likely to be associated with contrarian investment strategy. These results strongly suggest that the predictive ability of aggregate insider trading is because of insider’s ability to predict future cash-flow news rather than from adopting a contrarian investment strategy. These results hold even after we control for non-informative trades and information uncertainty.