Understanding Risk and Return

Campbell, John Y. “Understanding Risk and Return.” Journal of Political Economy Vol. 104, No. 2 (Apr. 1996), pp. 298-345

The author seeks to address some of the failings and critiques of prominent asset pricing models by deriving a model of his own. He begins by asking two fundamental questions:

1.       How should we measure risk?

2.      What determines the how much an investor should be compensated for bearing that risk?

Previous models:

CAPM:

This model measures the risk of an asset by its covariance with the market return.

1.       Merton (1973) says it should be measured by its covariance with the marginal utility of investors.

2.       Roll (1977) questions the validity of using stock market return as a proxy for the “true” market return. (i.e. we can’t truly test the CAPM because we don’t know the market return.

In the CAPM, the price of risk is determined by the risk aversion of the investors.

Multi-Factor Models:

These models measure the risk of an asset by its covariance with common factors which have broad explanatory power in asset returns.

1.       These models are very weak on theory and, thus, give little guidance as to what factors should be used. Therefore, factors could just come from spurious correlations as an artefact of the sample being used.

Multi-Factor models have nothing to say about the question of what determines the price of risk.

CCAPM:

This model measures risk by an asset’s covariance with consumption.

1.       In particular, the model performs poorly when being tested empirically.

The price of risk is determined by the risk aversion of a representative investor.

To attempt to better address the critiques of the CAPM than the other models have, the author derives a “multi-factor model” of his own which brings in both changing investment and human capital. He then tests the model empirically. He assumes Epstein and Zin (1989, 1991) preferences and begins with a budget constraint:

The preferences contain both a coefficient of relative risk aversion, γ, and elasticity of intertemporal substitution, σ. Through process of derivation and substitution he eliminates consumption and, therefore, σ from the final model. The main equation from his derivation is:

The left-hand side is the expected excess return on an asset with an adjustment for Jensen’s Inequality. The right-hand side is a weighted average of covariances of the asset with the stock market, good news about current and future labor income, and good news about future expected returns on the market, respectively. As we see, only the coefficient of relative risk aversion, γ, enters the final equation.

This derivation motivates the choice of variables which have some ability to predict market returns and labor income growth as well as to explain the cross-section of asset returns. He tests for this by estimating Vector Autoregressions to show both time series and cross-sectional explanatory power. Having done that the author comes to the main takeaway for asset pricing in Table 8.

Here we see that RVW (the stock market factor) is the most important determinant of stock market portfolio returns by far. For bond portfolio returns, columns 3, 6, and 7 are the most important where columns 6 and 7 are the short-term rate and long-term spread, respectively. Despite the theoretical derivation of a multi-factor model, this table ultimately shows that the CAPM does still explain most of the variation in stock returns, at least for those portfolios here. As for the intertemporal model then, the author states, “its main contribution is to explain why investors use covariance with an aggregate stock index to determine expected returns on assets.”