Increasing return response to changes in risk

• Date: 01 January 2019
• Author: Mehmet F. Dicle
• Published date: 01 January 2019
• DOI: http://doi.org/10.1002/rfe.1032

SPECIAL ISSUE ARTICLE

Increasing return response to changes in risk

Mehmet F. Dicle

College of Business, Loyola University

New Orleans, New Orleans, LA

Correspondence

Mehmet F. Dicle, College of Business,

Loyola University New Orleans, New

Orleans, LA, USA.

Email: mfdicle@gmail.com

Abstract

Risk aversion theory is based on an individual's choice among risky assets with

expected utility in its foundation. It is about investor behavior (i.e., investor

choice), under normal circumstances, toward assets with various levels of risk. A

positive and marginally diminishing relationship between risk and return exists.

This study is about investor behavior related to their response (not choice) to risk.

We present an argument and supporting evidence that investors’return response

to risk is increasing with the level of risk. Thus, investor behavior is subject to

change and the level of risk is a determinant of such change. We also explain the

negative time‐series correlation between risk and return.

JEL CLASSIFICATION

G12, G14, G41

KEYWORDS

investor behavior, risk aversion, risk response

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INTRODUCTION

There is no doubt that investors seek higher compensation for higher risk. On a cross section of investment choices, the

correlation of risk and return is positive in early evidence (e.g., Sharpe, 1965). More recently, the evidence is mixed for

cross‐section analysis, as well as for time‐series analysis. Lundblad (2007) provides a review of the risk‐retur n tradeoff and

provide evidence of positive correlation using about 200 years of data. Similarly, Harrison and Zhang (1999) show a posi-

tive risk‐return correlation in the long term and blame model misspecification for the negative evidence provided in the lit-

erature. While there is an abundance of evidence in the literature to show how the risk‐return tradeoff is positive and

statistically significant (e.g., Bali, 2008; French, William Schwert, & Stambaugh, 1987), there are also numer ous studies

showing that the relationship is either negative or statistically insignificant. For instance, Eraker and Wu (2017), similar to

early evidence by Glosten, Jagannathan, and Runkle (1993), shows that price response to increases in volatility is negative.

Based on a recent sample (2006–2013), this evidence is in direct disagreement with earlier positive risk‐return tradeoff evi-

dence in the literature.

In terms of bonds, there is no doubt about this positive and statistically significant tradeoff. Investors decide across

bonds, knowing all possible future payments and associated risks. While stock investors have the same risk ‐return tradeoff,

they cannot possibly know all future payments with certainty. Ex‐ante, investors choose stocks based on their possible (pre-

dicted or expected) future risk‐return schemes. Ex‐post, investors realize the risk and returns as they materialize. Thus, any

evidence about a positive and statistically significant risk‐return tradeoff, ex‐post, is evidence of the investors’success in

prediction.

Within a spectrum of investment choices, investors have the opportunity to choose according to their risk‐return prefer-

ences with rational behavior. Bond prices are present values of all future expected payments. If risk increases, investors will

decrease (by paying less) bond prices to a matching bond yield. While the overall yield will be positive and commensurate

to the risk involved, daily changes in prices, in response to risk, can be negative or positive. This is also the case for

Received: 5 February 2018

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Accepted: 16 March 2018

DOI: 10.1002/rfe.1032

Rev Financ Econ. 2019;37:197–215. wileyonlinelibrary.com/journal/rfe © 2019 University of New Orleans

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stocks. If stock prices are present values for all future expected payments, much like bonds, then the same yield theory

would apply to stocks. As risk increases, investors would decrease stock prices to a matching yield. While the overall risk -

return tradeoff stays positive for the cross section of stocks, ex-ante, daily returns would have a negative correlation with

daily changes in risk on a time-series analysis. In this study, we provide evidence that the correlatio n between daily returns

and expected risk (implied volatility) is statistically significant and negative for major U.S. equity indexes, international

equity ETFs, and a few select stocks.

Ang, Hodrick, Xing, and Zhang (2006) evaluate the risk and return relationship for all individual stocks that are traded

on AMEX, NASDAQ and NYSE. They conclude that “…stocks with high past exposure to innovations in aggregate mar-

ket volatility earn low future average returns”(p. 296). They also find that “stocks with high idiosyncratic volatility have

abysmally low average returns”(p. 296). Both conclusions of Ang et al. (2006) are based on individual stocks’sensitivitie s

to the changes in risk (market or idiosyncratic). In fact, they provide evidence of negative risk‐return correlations, ex‐post.

Our argument is different than that of Ang et al. (2006). We argue that the return response to changes in risk is immediate

(contemporaneous), similar to bonds. Stock prices will oscillate until they reach their true price. The oscillation of price will

be in response to changes in risk. The resulting ex‐post return to risk ratio can be positive or negative. In this respect, our

study is similar to Bali and Engle (2010), in which the risk and return relationship is tested wi th an intertemporal capital

asset pricing model. Their analysis is based on dynamic conditional correlations between individual stocks and portfolios of

equities with the overall market. They report, “The average relative risk aversion is estimated to be positive , highly signifi-

cant…”; they also report a “…significantly negative relation between expected return and volatility risk ”(p. 389). The main

difference between our study and Bali and Engle (2010) is the definition of risk. In our study, we focus on the return of a

security (index, ETF and stock) and its own implied volatility index. Since we are basing our theory on bond yield s, the

return response to securities’own expected risk is the foundation of our discussion. Bali and Engle (2010) focus on the

return response of individual stocks and portfolios to market risk, both in terms of expected conditional covariance and in

terms of implied volatilities.

Our main purpose is the change in investors’price response to changes in risk. Similar to the habit formation arguments

in the literature (i.e., Campbell & Cochrane, 1999; Constantinides, 1990; Otrok, Ravikumar, & Whiteman, 2002), we argue

that investors’risk‐return behavior changes when risk is above the “usual”level. It is established that investors do, in fact,

overreact to events (e.g., Byun, Lim, & Yun, 2016; De Bondt & Thaler, 1985). It is also evident that investors’risk aver-

sion changes based on habits and overall risk levels. In fact, Guiso, Sapienza, and Zingales (2013) show that investor risk

aversion increased after the 2008 financial crisis. This specific evidence shows the effect of fear (fear of a financial crash)

on further choices made by investors. Interestingly, behavioral sciences offers evidence of this effect with respect to behav-

ior for health risks. Brewer, Weinstein, Cuite, and Herrington (2004) argue that individuals’perception of higher risk leads

them to seek protection (i.e., vaccinations). This evidence is supported by Holt and Laury (2002), who show that the pay‐

out has a direct impact on the risk choices of individuals.

Based on the behavioral evidence that individuals change their behavior with respect to the level of risk (or perception

of the level of risk), we argue that investors should be expected to change their response to risk when faced with fear.

Implied volatility indexes for the equity markets (i.e., VIX) are considered to be the fear gauge. A long‐run average of the

VIX would create a feeling of normality (almost like habit formation). Levels of risk above this long‐run average would

leave investors feeling vulnerable (i.e., in fear). When in fear, investors are expected to react less rationally, more quickly

and perhaps in exaggeration. We therefore argue that investor price response to increases in risk would be higher for fear

periods. In other words, incremental price response to incremental change in the level of risk would be expected to be

higher. Given the negative time‐series return response to changes in risk, we would expect this negative response to be

even greater for days when VIX is above its long‐run average. Our evidence supports this theory. Equities have a com-

pletely different risk‐return tradeoff cross‐sectionally for high‐risk days and low‐risk days. They also have a significantly

lower negative return response to changes in risk for high‐risk days compared to low‐risk days.

The implications for our study are numerous. First, we argue that the risk-return tradeoff is different for ex-ante and

ex-post.Ex‐ante, the relationship must be positive, assuming rational investors. However, ex‐post, only the investors who

can predict correctly will achieve the desired risk‐return relationship. Studies that show such results, ex‐post, are, in effect,

testaments to investors’long‐term success in predicting investment choices. Second, while holdi ng period risk-return trade-

off is positive (ex-ante), stocks’price response to changes in risk is expected to be negatively correlated, much like bonds.

This yield theory for stocks would explain the conflicting and mixed results in the literature. While the complexity of

econometric models and the size of the samples may seem to prevail in the literature, from an investor behavior perspec-

tive, a stock is just another investment choice, similar to a bond. Its net yield is (and needs to be) compared to all other

investment alternatives. Uncertain future payouts for stocks do not change the basic investor instinct to seek a higher return

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