Implied Risk Aversion Parameter from Option Prices

This paper estimates the representative investor's coefficient of relative risk aversion using option price data. Estimation is carried out using the method of simulated moments. Employing the following assumptions: a) agents have constant proportional risk averse preferences, b) complete markets exist, and c) asset returns are distributed lognormally, an objective function is constructed within the equivalent martingale measure framework. Unlike the case of equity markets, the implied risk aversion parameter from option prices is quite low and stays between zero and one.     

Empirical risk aversion functions-estimates and assessment of their reliability

In this paper, we examine investor's risk preferences implied by option prices. In order to derive these preferences, we specify the functional form of a pricing kernel and then shift its parameters until realized returns are best explained by the subjective probability density function, which consists of the ratio of the risk-neutral probability density function and the pricing kernel. We examine, alternatively, pricing kernels of power, exponential, and higher order polynomial forms. Using S&P 500 index options, we find surprising evidence of risk neutrality, instead of risk aversion, in both the power and exponential cases. When extending the underlying assumption on the specification of the pricing kernel to one of higher order polynomial functions, we obtain functions exhibiting ‘monotonically decreasing’ relative risk aversion (DRRA) and anomalous ‘inverted U-shaped’ relative risk aversion. We find, however, that only the DRRA function is robust to variation in sample characteristics, and is statistically significant. Finally, we also find that most of our empirical results are consistent, even when taking into account market imperfections such as illiquidity.     

Does religion matter in corporate decision making in America?

We examine how corporate culture influences firm behavior. Prior research suggests a link between individual religiosity and risk aversion. We find that this relationship also influences organizational behavior. Firms located in counties with higher levels of religiosity display lower degrees of risk exposure, as measured by variances in equity returns or returns on assets. They exhibit a lower investment rate and less growth, but generate a more positive market reaction, when they announce new investments. Finally, chief executive officers are more likely to join a firm with a similar religious environment as in their previous firm when they switch employers.     

Effects of uncertainty and risk aversion on the exposure of investment-style factor returns to real activity

How do uncertainty and risk aversion affect the behavior of investment-style factors? We argue that a significant channel through which both uncertainty and risk aversion impact aggregate risk factors is the exposure of factor returns to real activity. We analyze this issue using mixed data sampling decomposition of the sensitivity of factor returns to real activity into high- and low-frequency components. We find a positive and significant relation between uncertainty and risk aversion for the low-frequency component of the sensitivity of factor returns to economic activity. More importantly, risk aversion significantly amplifies the effects of uncertainty on real activity exposure. The quality-based factor is an important exception to these findings.     

Does liquidity drive stock market returns? The role of investor risk aversion

In this paper, we explore the relations between liquidity, stock returns, and investor risk aversion as captured by the variance risk premium (VRP). This is motivated by theoretical and empirical evidence in the literature which suggests that investor risk aversion negatively correlates with asset liquidity, and ample empirical evidence documenting liquidity risk premium. We use monthly US data from January 1999 to December 2018 and show that innovations in the VRP Granger-cause stock returns, which in turn drive liquidity. Our findings are consistent with predictions of prior theories and highlight the predictability of the VRP. They also contribute to the on-going debate on the causal relation between stock returns and liquidity. Finally, we explore the channels through which the VRP impacts liquidity and find that the VRP influences market and momentum factors, and that movements in these factors lead to changes in liquidity.

     

The Recovery Theorem

We can only estimate the distribution of stock returns, but from option prices we observe the distribution of state prices. State prices are the product of risk aversion—the pricing kernel—and the natural probability distribution. The Recovery Theorem enables us to separate these to determine the market's forecast of returns and risk aversion from state prices alone. Among other things, this allows us to recover the pricing kernel, market risk premium, and probability of a catastrophe and to construct model‐free tests of the efficient market hypothesis.     

Risk aversion in the expected and the nonexpected utility functions

If asset returns are i.i.d. over time, the preference parameter in the time additive von Neumann-Morgenstern expected utility is the risk aversion coefficient in the Epstein-Zin nonexpected utility. By distinguishing between risk aversion and intertemporal substitution, this article provides an explanation about the observed discrepancy in the empirical estimates of the risk aversion coefficient.     

Investing for the Long-run in European Real Estate

We calculate optimal portfolio choices for a long-horizon, risk-averse investor who diversifies among European stocks, bonds, real estate, and cash, when excess asset returns are predictable. Simulations are performed for scenarios involving different risk aversion levels, horizons, and statistical models capturing predictability in risk premia. Importantly, under one of the scenarios, the investor takes into account the parameter uncertainty implied by the use of estimated coefficients to characterize predictability. We find that real estate ought to play a significant role in optimal portfolio choices, with weights between 12 and 44%. Under plausible assumptions, the welfare costs of either ignoring predictability or restricting portfolio choices to traditional financial assets only are found to be in the order of 150–300 basis points per year. These results are robust to changes in the benchmarks and in the statistical framework.      

TIME VARIABILITY IN MARKET RISK AVERSION

We adopt realized covariances to estimate the coefficient of risk aversion across portfolios and through time. Our approach yields second moments that are free from measurement error and not influenced by a specified model for expected returns. Supporting the permanent income hypothesis, we find risk aversion responds to consumption-smoothing behavior. As income increases, or as the consumption-to-income ratio falls, relative risk aversion decreases. We also document variation in risk aversion across portfolios: risk aversion is highest for small and value portfolios.     

DAYLIGHT AND INVESTOR SENTIMENT: A SECOND LOOK AT TWO STOCK MARKET BEHAVIORAL ANOMALIES

Kamstra, Kramer, and Levi (2000, 2003) describe two stock market behavioral anomalies associated with changes in investor sentiment caused by daylight saving time (DST) changes and seasonal affective disorder (SAD). According to the hypothesized effects, DST changes and SAD affect asset prices by changing investors’ risk aversion. Although changes in the timing or amount of daylight are correlated with unusual stock market returns, I present evidence they do not cause those unusual returns. Instead, seasonal patterns in market‐related information during the sample period are the likely cause of the correlation between stock market returns and DST changes or SAD.     

Preferred risk habitat of individual investors

The preferred risk habitat hypothesis, introduced here, is that individual investors select stocks whose volatilities are commensurate with their risk aversion. The data, 1995–2000 holdings of over 20,000 clients at a large German broker, are consistent with the predictions of the hypothesis: the returns of stocks within each portfolio have remarkably similar volatilities, when stocks are sold they are replaced by stocks of similar volatilities, and the more risk-averse customers indeed hold less volatile stocks. Greater volatility specialization is associated with lower Sharpe ratios, primarily because more specialized investors hold fewer stocks and thereby expose themselves to more unsystematic risk.     

Consumption-based equity valuation

Using a CCAPM-based risk-adjustment model, we perform yearly valuations of a large sample of stocks listed on NYSE, AMEX, and NASDAQ over a 30-year period. The model differs from standard valuation models in the sense that it adjusts forecasted residual income for risk in the numerator rather than through a risk-adjusted cost of equity in the denominator. The risk adjustments are derived based on assumptions about the time-series properties of residual income returns and aggregate consumption rather than on historical stock returns. We compare the performance of the model with several implementations of standard valuation models, both in terms of median absolute valuation errors (MAVE) and in terms of excess returns on simple investment strategies based on the differences between model and market prices. The CCAPM-based valuation model yields a significantly lower MAVE than the best performing standard valuation model. Both types of models can identify investment strategies with subsequent excess returns. The CCAPM-based valuation model yields time-series of realized hedge returns with more and higher positive returns and fewer and less negative returns compared with the time-series of realized hedge returns based on the best performing standard valuation model for holding periods from 1 to 5 years. In a statistical test of 1-year-ahead excess return predictability based on the models’ implied pricing errors, the CCAPM-based valuation model is selected as the better model. Using the standard series of aggregate consumption and the nominal price index, a reasonable level of relative risk aversion, and calibrated growth rates in the continuing value at each valuation date, the CCAPM-based valuation model produces small risk adjustments to forecasted residual income and low continuing values. Compared with standard valuation models, it relies less on estimated parameters and speculative elements when aggregating residual earnings forecasts into a valuation.     

Loss aversion,asymmetric market comovements,and the home bias

Loss aversion has been used to explain why a high equity premium might be consistent with plausible levels of risk aversion. The intuition is that the first-order-different utility impact of wealth gains and losses leads loss-averse investors to behave similarly to investors with high risk aversion. But if so, should those agents not perceive larger gains from international diversification than standard expected-utility investors with plausible levels of risk aversion? They might not, because comovements in international stock markets are asymmetric: correlations are higher in market downturns than in upturns. This asymmetry dampens the gains from diversification relatively more for loss-averse investors. We analyze the portfolio problem of such an investor who has to choose between home and foreign equities in the presence of asymmetric comovement in returns. Perhaps surprisingly, in the context of the home bias puzzle we find that loss-averse investors behave similarly to those with standard expected-utility preferences and plausible levels of risk aversion. We argue that preference specifications that appear to perform well with respect to the equity premium puzzle should be subjected to this “test”.     

The Estimation of Systematic Risk under Differentiated Risk Aversion: A Mean-Extended Gini Approach

This paper examines a mean-Gini model of systematic risk estimation that resolves some econometric problems with mean-variance beta estimation and allows for heterogeneous risk aversion across investors. Using the mean-extended Gini (MEG) model, we estimate systematic risks for different degrees of risk aversion. MEG betas are shown to be instrumental variable estimators that provide econometric solutions to biases generated by the estimation of mean-variance (MV) betas. When security returns are not normally distributed, MEG betas are proved to differ from MV betas. We design an econometric test that assesses whether these differences are significant. As an application using daily returns, we estimate MEG and MV betas for U.S. securities.     

AN EXAMINATION OF THE SMALL-FIRM EFFECT ON THE BASIS OF SKEWNESS PREFERENCE

This paper tests the hypothesis that the small-firm effect can be explained on the basis of investor preference for positive skewness. Traditional stochastic dominance methodology is extended to consider portfolios including variable weights of investment in a riskless asset. Including a riskless asset provides the result that small-firm portfolios stochastically dominate all other portfolios. This result, which is derived on the basis of 19 years of monthly returns, indicates that the small-firm effect cannot be fully attributed to tax effects, benchmark error, or incorrect assumptions of the CAPM about investor risk aversion.     

Commodity futures hedging,risk aversion and the hedging horizon

This paper examines the impact of management preferences on optimal futures hedging strategy and associated performance. Applying an expected utility hedging objective, the optimal futures hedge ratio is determined for a range of preferences on risk aversion, hedging horizon and expected returns. Empirical results reveal substantial hedge ratio variation across distinct management preferences and are supportive of the hedging policies of real firms. Hedging performance is further shown to be strongly dependent on underlying preferences. In particular, hedgers with high risk aversion and short horizon reduce hedge portfolio risk but achieve inferior utility in comparison to those with low aversion.     

Whence GARCH? A Preference-Based Explanation for Conditional Volatility

We develop a preference-based equilibrium asset pricing modelthat explains low-frequency conditional volatility. Similarto Barberis, Huang, and Santos (2001), agents in our model careabout wealth changes, experience loss aversion, and keep a mentalscorecard that affects their level of risk aversion. A new featureof our model is that when perturbed by unexpected returns, investorsbecome temporarily more sensitive to news. Gradually investorsbecome accustomed to the new level of wealth, restoring priorlevels of risk aversion and news sensitivity. The state-dependentsensitivity to news creates the type of volatility clusteringfound in low-frequency stock returns. We find empirical supportfor our model's predictions that relate the scorecard to conditionalvolatility and skewness.     

Home bias in equity portfolios, inflation hedging, and international capital market equilibrium

We test whether the home bias in equity portfolios is causedby investors trying to hedge inflation risk. The empirical evidenceis consistent with this motive only if investors have very highlevels of risk tolerance and equity returns are negatively correlatedwith domestic inflation. We then develop a model of internationalportfolio choice and equity market equilibrium that integratesinflation risk and deadweight costs. Using this model we estimatethe levels of costs required to generate the observed home biasin portfolios consistent with different levels of risk aversion.For a level of risk aversion consistent with standard estimatesof the domestic equity market risk premium these costs are abouta few percent per annum greater than observable costs such aswithholding taxes. Thus, the home bias cannot be explained byeither inflation hedging or direct observable costs of internationalinvestment unless investors have very low levels of risk aversion.     

Time-varying risk aversion and asset prices

This paper uses a variant of the consumption-based representative agent model in Campbell and Cochrane [Campbell, J.Y., Cochrane, J.H., 1999. By force of habit: Consumption-based explanation of aggregate stock market behavior. Journal of Political Economy 107, 205–251] to study how investors’ time-varying risk aversion affects asset prices. First, we show that a countercyclical variation of risk aversion drives a procyclical conditional risk premium. Second, we show that with a small value for the volatility of the log surplus consumption ratio, a large value of risk aversion may not determine whether the equity premium and the risk-free rate puzzles can be resolved or not. Third, we show that countercyclical risk aversion may not help explain the predictability of long-horizon stock returns, the univariate mean-reversion of stock prices and the “leverage effect” in return volatility.     

Identity Theft and Consumer Payment Choice: Does Security Really Matter?

In their paper “Spectral Risk Measures: Properties and Limitations”, Dowd et al. (J Financ Serv Res 341:61–75, 2008) introduce exponential and power spectral risk measures as subclasses of spectral risk measures (SRMs) to the literature, and claim that they are subject to three serious limitations: First, for these subclasses, the spectral risk may be counterintuitively decreasing when the user’s risk aversion is increasing. Second, these subclasses, and power SRMs in particular, become completely insensitive to market volatility when the respective parameters of risk aversion tend to their lower and upper boundaries. Third, exponential SRMs exhibit constant absolute risk aversion, while constant relative risk aversion better meets the empirical evidence. Consequently, “users of spectral risk measures must be careful to select utility functions that fit the features of the particular problems they are dealing with, and should be especially careful when using power SRMs.” (p. 61). In this comment, we show that the findings of Dowd et al. (J Financ Serv Res 341:61–75, 2008) suffer from misinterpretations and wrong conclusions.