Martin Lettau

Resurrecting the (C)CAPM: A Cross-Sectional Test When Risk Premia are Time-Varying

This paper explores the ability of conditional versions of the CAPM and the consumption CAPM—jointly the (C)CAPM—to explain the cross section of average stock returns. Central to our approach is the use of the log consumption–wealth ratio as a conditioning variable. We demonstrate that such conditional models perform far better than unconditional specifications and about as well as the Fama‐French three‐factor model on portfolios sorted by size and book‐to‐market characteristics. The conditional consumption CAPM can account for the difference in returns between low‐book‐to‐market and high‐book‐to‐market portfolios and exhibits little evidence of residual size or book‐to‐market effects.

Understanding Trend and Cycle in Asset Values: Reevaluating the Wealth Effect on Consumption

Both textbook economics and common sense teach us that the value of household wealth should be related to consumer spending. At the same time, movements in asset values often seem disassociated with important movements in consumer spending, as episodes such as the 1987 stock market crash and the contraction in equity values that occurred in the fall of 1998 suggest. An important first step in understanding the consumption-wealth linkage is determining how closely the two variables are actually correlated, and whether there exist important movements in asset values that are not associated with changes in consumption. This paper provides evidence that a surprisingly small fraction of the variation in household net worth is related to variation in aggregate consumer spending. We use empirical techniques that allow us to quantify the relative importance of permanent and transitory innovations in the variation of consumer spending and wealth and find that transitory shocks dominate post-war variation in wealth, while permanent shocks dominate variation in aggregate consumption. Although transitory innovations are found to have little influence on consumer spending, they have long-lasting effects on wealth , exhibiting a half-life of a little over two years. The findings suggest that most macro models which make no allowance for transitory variation in wealth that is orthogonal to consumption are likely to misstate both the timing and magnitude of the consumption-wealth linkage.

Reconciling the Return Predictability Evidence

Evidence of stock return predictability by financial ratios is still controversial, as documented by inconsistent results for in-sample and out-of-sample regressions and by substantial parameter instability. This paper shows that these seemingly incompatible results can be reconciled if the assumption of a fixed steady-state mean of the economy is relaxed. We find strong empirical evidence in support of shifts in the steady-state and propose simple methods to adjust financial ratios for such shifts. The forecasting relationship of adjusted price ratios and future returns is statistically significant and stable over time. We also show that shifts in the steady-state are responsible for the parameter instability and poor out-of-sample performance of unadjusted price ratios that are found in the data. Our conclusions hold for a variety of financial ratios and are robust to changes in the econometric technique used to estimate shifts in the steady-state.

Measuring and Modelling Variation in the Risk-Return Trade-off

Are excess stock market returns predictable over time and, if so, at what horizons and with which economic indicators? Can stock return predictability be explained by changes in stock market volatility? How does the mean return per unit risk change over time? This chapter reviews what is known about the time-series evolution of the risk-return tradeoff for stock market investment, and presents some new empirical evidence using a proxy for the log consumption-aggregate wealth ratio as a predictor of both the mean and volatility of excess stock market returns. We characterize the risk-return tradeoff as the conditional expected excess return on a broad stock market index divided by its conditional standard deviation, a quantity commonly known as the Sharpe ratio. Our own investigation suggests that variation in the equity risk-premium is strongly negatively linked to variation in market volatility, at odds with leading asset pricing models. Since the conditional volatility and conditional mean move in opposite directions, the degree of countercyclicality in the Sharpe ratio that we document here is far more dramatic than that produced by existing equilibrium models of financial market behaviour, which completely miss the sheer magnitude of variation in the price of stock market risk.

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 emphasise 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.

Why is Long-Horizon Equity Less Risky? A Duration-Based Explanation of the Value Premium

This paper proposes a dynamic risk-based model that captures the high expected returns on value stocks relative to growth stocks, and the failure of the capital asset pricing model to explain these expected returns. To model the difference between value and growth stocks, we introduce a cross-section of long-lived firms distinguished by the timing of their cash flows. Firms with cash flows weighted more to the future have high price ratios, while firms with cash flows weighted more to the present have low price ratios. We model how investors perceive the risks of these cash flows by specifying a stochastic discount factor for the economy. The stochastic discount factor implies that shocks to aggregate dividends are priced, but that shocks to the time-varying price of risk are not. As long-horizon equity, growth stocks covary more with this time-varying price of risk than value stocks, which covary more with shocks to cash flows. When the model is calibrated to explain aggregate stock market behavior, we find that it can also account for the observed value premium, the high Sharpe ratios on value stocks relative to growth stocks, and the outperformance of value (and underperformance of growth) relative to the CAPM.

Euler Equation Errors

The standard, representative agent, consumption-based asset pricing theory based on CRRA utility fails to explain the average returns of risky assets. When evaluated on cross- sections of stock returns, the model generates economically large unconditional Euler equation errors. Unlike the equity premium puzzle, these large Euler equation errors cannot be resolved with high values of risk aversion. To explain why the standard model fails, we need to develop alternative models that can rationalize its large pricing errors. We evaluate whether four newer theories at the vanguard of consumption-based asset pricing can explain the large Euler equation errors of the standard consumption-based model. In each case, we find that the alternative theory counterfactually implies that the standard model has negligible Euler equation errors. We show that the models miss on this dimension because they mischaracterize the joint behavior of consumption and asset returns in recessions, when aggregate consumption is falling. By contrast, a simple model in which aggregate consumption growth and stockholder consumption growth are highly correlated most of the time, but have low or negative correlation in severe recessions, produces violations of the standard models Euler equations and departures from joint lognormality that are remarkably similar to those found in the data.

Shocks and Crashes

Three shocks, distinguished by whether their effects are permanent or transitory, are identified to characterize the post-war dynamics of aggregate consumer spending, labor earnings, and household wealth. The first shock accounts for virtually all of the variation in consumption and has effects akin to a permanent total factor productivity shock in canonical frictionless macroeconomic models. The second shock underlies the bulk of fluctuations in labor income, accounting for 76% of its variation. This shock permanently reallocates rewards between shareholders and workers but leaves consumption unaffected. Over the last 25 years, the cumulative effect of this shock has persistently boosted stock market wealth and persistently lowered labor earnings. The third shock is a persistent but transitory innovation that accounts for the vast majority of quarterly fluctuations in asset values but has a negligible impact on consumption and labor earnings at all horizons. We show that the 2000-02 asset market crash was the result of a negative transitory wealth shock, which predominantly affected stock market wealth. By contrast, the 2007-09 crash was accompanied by a string of large negative realizations in both the transitory shock and the permanent productivity shock, with the latter having especially important implications for housing wealth.

Idiosyncratic Risk and Volatility Bounds, or Can Models with Idiosyncratic Risk Solve the Equity Premium Puzzle?

This paper uses Hansen and Jagannathan’s (1991) volatility bounds to evaluate models with idiosyncratic consumption risk. I show that idiosyncratic risk does not change the volatility bounds at all when consumers have CRRA preferences and the distribution of the idiosyncratic shock is independent of the aggregate state. Following Mankiw (1986), I then show that idiosyncratic risk can help to enter the bounds when idiosyncratic uncertainty depends on the aggregate state of the economy. Since individual consumption data are not reliable, I compute an upper bound of the volatility bounds using individual income data and assume that agents have to consume their endowment. I find that the model does not pass the Hansen and Jagannathan test even for very volatile idiosyncratic income data. JEL Classification: E44, G11, G12

Statistical Estimation And Moment Evaluation Of A Stochastic Growth Model With Asset Market Restrictions

This paper estimates the parameters of a stochastic growth model with asset market and contrasts the models moments with moments of the actual data. We solve the model through log-linearization along the line of Campbell (1994) [Journal of Monetary Economics 33(3), 463] and estimate the model without and with asset pricing restrictions. As asset pricing restrictions we employ the riskfree interest rate and the Sharpe-ratio. To estimate the parameters we employ, as in Semmler and Gong (1996a) [Journal of Economics Behavior and Organization 30, 301], a ML estimation. The estimation is conducted through the simulated annealing. We introduce a diagnostic procedure which is closely related to Watson (1993) [Journal of Political Economy 101(6), 1011] and Diebold et al. (1995) [Technical Working Paper No. 174, National Burea of Economic Research] to test whether the second moments of the actual macroeconomic time series data are matched by the models time series. Several models are explored. The overall results are that sensible parameter estimates may be obtained when the actual and computed riskfree rate is included in the moments to be matched. The attempt, however, to include the Sharpe-ratio as restriction in the estimation does not produce sensible estimates. The paper thus shows, by employing statistical estimation techniques, that the baseline real business cycle (RBC) model is not likely to give correct predictions on asset market pricing when parameters are estimated from actual time series data. JEL Classification: C13; C15; C61; E32; G1; G12 Keyword(s): Stochastic growth model, Sharpe-ratio, Maximum likelihood