### How Do Investors Measure Risk?

Stanford Graduate School of Business; National Bureau of Economic Research (NBER)

University of Pennsylvania – The Wharton School; National Bureau of Economic Research (NBER)

October 1, 2015

**Abstract: **

We infer which risk model investors use by looking at their capital allocation decisions. We find that investors adjust for risk using the beta of the Capital Asset Pricing Model (CAPM). Extensions to the CAPM perform poorly, implying that they do not help explain how investors measure risk.

### How Do Investors Measure Risk? – Introduction

There is no question more fundamental to the study of investments than the question of how investors measure risk. Indeed, one could argue that the study of investments only began when the first model of risk, the Capital Asset Pricing Model (CAPM), was developed in the early 1960’s.3 In the half century that has since elapsed, the ability of the model to accurately measure risk has been questioned. In response, a number of extensions to the original model have been proposed, and in some cases, adopted as improved measures of risk.4 The principal empirical shortcoming that these extensions are designed to address is that much of the cross sectional difference in realized stock returns cannot be explained by cross sectional differences in the CAPM beta. The fact is that the relation between CAPM beta and return differences is weak in the full sample spanning 1926 to the present, and, importantly, sub periods of that sample exist, when the relation is appears to be absent altogether.

The implicit assumption underlying the literature that extends the CAPM is that a model that better explains cross sectional variation in returns necessarily better explains risk differences. But this assumption is problematic. To see why, consider the following analogy. Rather than look for an alternative theory, early astronomers reacted to the inability of the Ptolemaic theory to explain the motion of the planets by “fixing” each observational inconsistency. Just as modern financial economists added new risk factors, the early astronomers added epicycles to the theory. The net result was that by the time Copernicus proposed the correct theory that the Earth revolved around the Sun, the Ptolemaic theory had been fixed so many times it better explained the motion of the planets than the Copernican system.5 Similarly, although the extensions to the CAPM better explain the cross section of stock returns, it is hard to know, using traditional tests, whether these extensions represent true progress towards a better measure of risk or simply the asset pricing equivalent of an epicycle. To determine whether any extension to the CAPM better explains risk, one needs to confront the models with facts they were not designed to explain. That is the principal objective of this article.

To understand the basis of our new test, it is helpful to recall how prices and returns are determined in any risk model. All models of risk assume that investors compete with each other to find attractive investment opportunities. When investors find such opportunities, they react by submitting buy or sell orders and by doing so, the opportunity is removed. As a consequence of this competition, equilibrium prices are set so that the expected return of every asset is solely a function of its risk. Our key insight is that these buy and sell orders reveal the preferences of investors and therefore they reveal which risk model investors are using. By observing these orders we can infer whether investors price risk at all, and if so, which risk model they are using.

There are two criteria that are required to implement this idea. First, one needs a mechanism that identifies attractive investment opportunities. Second, one needs to observe investor reactions to these opportunities. We can satisfy both criteria if we implement the method using mutual fund data. Using this dataset we infer, from a set of candidate models, the model that is closest to the risk model investors are actually using.

Our results are surprising. We find that the CAPM is the closest model to the model investors use. None of the extensions that have been proposed better explain investor behavior. Importantly, the CAPM better explains investor behavior than no model at all, indicating that investors do price risk. Most surprisingly, the CAPM also outperforms a naive model in which investors ignore beta and simply chase any outperformance relative to the market portfolio. Investors’ capital allocation decisions reveal that they adjust for risk using the CAPM beta. The poor performance of the extensions to the CAPM implies that although these extensions might better explain cross sectional variation in realized returns, they do not help explain how investors measure risk. In short, we are no closer to understanding the risk-return relation today than we were when the CAPM was originally developed more than half a century ago.

See full PDF below.