Redefining risk: an investigation into the role of sequencing

Abstract

Mehra and Prescott's (1985) equity premium puzzle has stirred continued debate on just why the average return on equity has been so high relative to the risk-free rate. Recent work by Backus, Gregory, and Zin (1989), Knez and Snow (1992), and Trainor (1992) have also documented a liquidity premium puzzle. In addition, Fama and French (1992) have found that beta has no explanatory power in explaining an asset's excess return.

These studies point out that current financial models are unable to explain even the most basic premise that assets with greater risk have higher returns. The question that now arises is why are these financial models failing to explain excess returns? One obvious answer to this question which has been completely ignored is that the proxy being used to define risk is wrong.

It is the contention of this proposal that investors are concerned about buying into an asset and subsequently experiencing a sequence of below average or negative returns. Under this premise, using the variance of returns as a measure of risk is inadequate and a new risk measure must be derived. This study demonstrates that measuring the deviation of an investor's wealth level from buying a risky asset in relation to what an investor's wealth level would have been from buying a risk-free asset discerns both the deviation of returns and the propensity of returns to sequence.

It is then shown that sequencing risk and the slope of the term structure are integrally related. Specifically, the steeper the yield curve, the greater sequencing risk will be priced since a negative sequence could result in forced borrowing by investors when rates are high to maintain a constant consumption rate.

Empirically, it is shown that measuring an asset's risk by the contribution it makes to a portfolio's propensity to sequence rather than to a portfolio's variance more accurately explains portfolio returns within a CAPM type framework. Additionally, size does not usurp the explanatory power of this new beta. Surprisingly, it is found that the explanatory power of the traditional beta and size are contingent upon the slope of the term structure being fairly flat. The wealth beta seems to be unaffected. The conclusion of the study suggests that current financial models are seriously flawed due to the erroneous definition and mis-measurement of risk.