The case of 'Less is more': Modelling risk-preference with Expected Downside Risk

TL;DR

This paper introduces Expected Downside Risk (EDR) as a new measure that better captures investor risk perception, reconciling conflicting empirical findings on the relationship between risk and return, and outperforming volatility as a predictor.

Contribution

It proposes EDR as an improved risk measure that explains the risk-return relationship within standard utility theory, resolving previous contradictions.

Findings

EDR better explains utility perception than variance.

Using EDR, both positive and negative risk-return relationships are derivable.

Empirically, EDR outperforms volatility in predicting expected returns.

Abstract

This paper discusses an alternative explanation for the empirical findings contradicting the positive relationship between risk (variance) and reward (expected return). We show that these contradicting results might be due to the false definition of risk-perception, which we correct by introducing Expected Downside Risk (EDR). The EDR parameter, similar to the Expected Shortfall or Conditional Value-at-Risk, measures the tail risk, however, fits and better explains the utility perception of investors. Our results indicate that when using the EDR as risk measure, both the positive and negative relationship between expected return and risk can be derived under standard conditions (e.g. expected utility theory and positive risk-aversion). Therefore, no alternative psychological explanation or additional boundary condition on utility theory is required to explain the phenomenon. Furthermore, we show empirically that it is a more precise linear predictor of expected return than volatility, both for individual assets and portfolios.