Market pricing of executive stock options and implied risk preferences

When managers get to trade in options received as compensation, their trading prices reveal several aspects of subjective option pricing and risk preferences. Two subjective pricing models are fitted to show that executive stock option prices incorporate a subjective discount. It depends positively on implied volatility and negatively on option moneyness. Further, risk preferences are estimated using the semiparametric model of Aït-Sahalia and Lo (2000). The results suggest that relative risk aversion is just above 1 for a certain stock price range. This level of risk aversion is low but reasonable, and it may be explained by the typical manager being wealthy and having low marginal utility. Related to risk aversion, it is found that marginal rate of substitution increases considerably in states with low stock prices.     

A dynamic equilibrium model for U-shaped pricing kernels

This paper proposes a dynamic equilibrium model that can provide a unified explanation for the stylized facts observed in stock index markets such as the fat tails of the risk-neutral return distribution relative to the physical distribution, negative expected returns on deep OTM call options and negative realized variance risk premiums. In particular, we focus on the U-shaped pricing kernel against the stock index return, which is closely related to the negative call returns. We assume that the stock index return follows a time-changed Lévy process and that a representative investor has power utility over the aggregate consumption that forms a linear regression of the stock index return and its stochastic activity rate. This model offers a macroeconomic interpretation of the stylized facts from the perspective of the sensitivity of the activity rate and stock index return on aggregate consumption as well as the investor’s risk aversion.     

Time Variation in the Covariance between Stock Returns and Consumption Growth

The conditional covariance between aggregate stock returns and aggregate consumption growth varies substantially over time. When stock market wealth is high relative to consumption, both the conditional covariance and correlation are high. This pattern is consistent with the “composition effect,” where agents' consumption growth is more closely tied to stock returns when stock wealth is a larger share of total wealth. This variation can be used to test asset‐pricing models in which the price of consumption risk varies. After accounting for variations in this price, the relation between expected excess stock returns and the conditional covariance is negative.     

The dividend-price ratio and expectations of future dividends and discount factors

A dividend-ratio model is introduced here that makes the logof the dividend-price ratio on a stock linear in optimally forecastfuture one-period real discount rates and future one-periodgrowth rates of real dividends. If ex post discount rates areobservable, this model can be tested by using vector autoregressivemethods. Four versions of the linearized model, differing inthe measure of discount rates, are tested for U.S. time series1871-1986 and 1926-1986: a version that imposes constant realdiscount rates, and versions that measure discount rates fromreal interest rate data, aggregate real consumption data, andreturn variance data. The results yield a metric to judge therelative importance of real dividend growth, measured real discountrates, and unexplained factors in determining the dividend-priceratio.     

Asset pricing under quantile utility maximization

“Focus on the downside, and the upside will take care of itself” is a famous quote among professional investors. By considering an agent who follows this advice, we reproduce the first and second moments of stock returns, risk-free rate and consumption growth. The agent's behavior toward risk is analogous to a relative risk aversion of about 3 under expected utility, the elasticity of intertemporal substitution is about 0.5 and the time discount factor is below 1. In particular, the proposed model separates time and risk preferences in an innovative way.     

An Empirical Investigation of the Campbell-Cochrane Habit Utility Model

Abstract:  This paper tests whether the Campbell and Cochrane (1999) habit utility model generates a valid stochastic discount factor for the 25 Fama-French size/book-to-market and size/momentum sorted portfolios. Campbell and Cochrane (1999) derive a consumption based habit utility asset pricing model and calibrate it to aggregate US stock market data. However, they do not test whether their model is consistent with a larger cross section of asset returns. We test their model using the methodology of Hansen and Jagannathan (1991) and Burnside (1994) . In contrast to previous studies, we find that for reasonable parameter values, the model's stochastic discount factor is inside the Hansen-Jagannathan bounds and therefore satisfies the necessary conditions for a valid stochastic discount factor. We trace the difference between our results and previous studies to the method used to estimate the model's parameters and the parameter values themselves.     

Preference heterogeneity and asset prices: An exact solution

We introduce a general equilibrium model of a multi-agent, pure-exchange economy and find a set of conditions that enable us to obtain explicit closed-form solutions to the equilibrium interest rate, stock price, risk premium and stock market volatility when investors have heterogenous risk aversions. Because the market is dynamically complete, full risk sharing obtains and a representative agent can be constructed, though the risk aversion of this agent fluctuates over time with the state of the economy, as the relative wealth distribution of the individual investors changes. We show that preference heterogeneity can cause asset prices to be significantly more volatile than the underlying dividends and that it can lead to leverage-like effects in volatility, in the sense that volatility increases after stock-market declines.     

Why Is Long‐Horizon Equity Less Risky? A Duration‐Based Explanation of the Value Premium

We propose a dynamic risk‐based model that captures the value premium. Firms are modeled as long‐lived assets distinguished by the timing of cash flows. The stochastic discount factor is specified so that shocks to aggregate dividends are priced, but shocks to the discount rate are not. The model implies that growth firms covary more with the discount rate than do value firms, which covary more with cash flows. When calibrated to explain aggregate stock market behavior, the model accounts for the observed value premium, the high Sharpe ratios on value firms, and the poor performance of the CAPM.     

Time‐Varying Risk–Return Trade‐off in the Stock Market

We uncover a strong comovement of the stock market risk–return trade‐off with the consumption–wealth ratio (CAY). The finding reflects time‐varying investment opportunities rather than countercyclical aggregate relative risk aversion. Specifically, the partial risk–return trade‐off is positive and constant when we control for CAY as a proxy for investment opportunities. Moreover, conditional market variance scaled by CAY is negatively priced in the cross‐section of stock returns. Our results are consistent with a limited stock market participation model, in which shareholders require an illiquidity premium that increases with CAY, in addition to the risk premium that is proportional to conditional market variance.     

Portfolio Choice and Life Insurance: The CRRA Case

We solve a portfolio choice problem that includes life insurance and labor income under constant relative risk aversion (CRRA) preferences. We focus on the correlation between the dynamics of human capital and financial capital and model the utility of the family as opposed to separating consumption and bequest. We simplify the underlying Hamilton–Jacobi–Bellman equation using a similarity reduction technique that leads to an efficient numerical solution. Households for whom shocks to human capital are negatively correlated with shocks to financial capital should own more life insurance with greater equity/stock exposure. Life insurance hedges human capital and is insensitive to the family's risk aversion, consistent with practitioner guidance.     

An Empirical Examination of the Price-Dividend Relation with Dividend Management

Some recent empirical evidence suggests that stock prices are not properly modeled as the present discounted value of expected dividends. In this paper, we estimate a present value model of stock price that is capable of explaining the observed long-term trends in stock prices. The model recognizes that firm managers control cash dividend payments. The model estimates indicate that stock price movements may be explained by managerial behavior.     

The term structures of equity and interest rates

This paper proposes a dynamic risk-based model capable of jointly explaining the term structure of interest rates, returns on the aggregate market, and the risk and return characteristics of value and growth stocks. Both the term structure of interest rates and returns on value and growth stocks convey information about how the representative investor values cash flows of different maturities. We model how the representative investor perceives risks of these cash flows by specifying a parsimonious stochastic discount factor for the economy. Shocks to dividend growth, the real interest rate, and expected inflation are priced, but shocks to the price of risk are not. Given reasonable assumptions for dividends and inflation, we show that the model can simultaneously account for the behavior of aggregate stock returns, an upward-sloping yield curve, the failure of the expectations hypothesis, and the poor performance of the capital asset pricing model.     

Technology prospects and the cross-section of stock returns

In an economy with time-varying investment opportunities, the changes in technology prospects affect aggregate consumption and individual firm's future dividends, and lead to systematic technology risk. We construct a technology factor to track the changes in technology prospects measured by U.S. patent shocks, and find that this factor explains the growth of aggregate consumption, helps to price important stock portfolios, and carries significant risk premium. Our empirical results suggest the existence of technology risk in the cross-section of stock returns.     

Stock performance by utility indifference pricing and the Sharpe ratio

We compare stock performance based on utility indifference pricing and the Sharpe ratio assuming that stock returns follow the class of discrete normal mixture distributions. The utility indifference price with an exponential utility function satisfies several desirable properties that a suitable value measure should satisfy. For utility indifference pricing, we employ the inner rate of risk aversion proposed by Miyahara [Evaluation of the scale risk. RIMS Kokyuroku, No. 1886, Financial Modeling and Analysis (2013/11/20-2013/11/22), 181–188, 2014], which is the degree of risk aversion that makes the utility indifference price with the exponential utility function zero in order to evaluate stock performance. Using a selection of U.S. stocks, the results show that the evaluation of stock performance based on the inner rate of risk aversion is more relevant for risk-averse investors than that based on the Sharpe ratio, which represents performance by the first two moments.     

Non-addictive Habit Formation and the Equity Premium Puzzle

I analyse a model in a simple representative-agent economy with one risky and one riskless asset, populated by habit forming consumer-investors. These consumer-investors exhibit non-addictive habit formation in the sense that the current consumption rate of the consumer-investors can fall below their past habit-forming consumption rate. I endogenise the real riskless rate of return in this representative-agent economy and find that the equity premium puzzle is resolved for plausible values of the coefficient of relative risk aversion, the discount rate, and the intensity of non-addictive habit formation. These values have been validated in previous empirical or survey-based studies. Non-addictive habit-formation studied here complements and extends current research on habit-forming preferences. Given a constant investment opportunity set, the real riskless rate in the economy increases with relative risk aversion of the consumer and decreases as the habit-formation intensity increases. Extensions with time-varying investment opportunity sets could explain the low risk-free rate and the relatively large variability of the market return over the variability of the risk-free rate through time.     

Risk Attitude and Housing Wealth Effect

This paper examines whether the housing wealth effect—the consumption change induced by house price appreciation is dependent upon households’ attitudes toward risk. A simple theoretical model is introduced to highlight a negative relationship between the wealth effect and risk aversion. The paper empirically tests for this negative relationship, using data from the U.S. Consumer Expenditure Survey. The investigation involves two steps. In the first step, we make use of households’ demographics and their risky and liquid asset holdings to estimate risk aversion. The Heckman correction model is applied to address the issue of limited stock market participation. For the second step, we construct pseudo panel data through grouping households by their birth years and their predicted values of risk aversion, and then, we estimate the responses of households’ consumption changes to house price fluctuations by risk-attitude group. Consistent with the prediction of the theoretical model, the estimation results suggest a significant negative relationship between the housing wealth effect and households’ risk attitudes. Households, who are less risk averse, experience greater consumption changes in response to house price appreciation.     

Asymmetric Effects of Interest Rate Changes on Stock Prices

This study examines the stock price adjustment process around announcements of changes in the federal funds rate target in the 1990s using an asymmetric autoregressive exponential GARCH model (ASAR‐EGARCH). We find that target change announcements convey new information to the stock market. Risk aversion increases before the announcement of a rate change, and especially before the announcement of a joint target and discount rate change. The volatility estimates suggest that such joint rate changes send a clearer signal to the stock market about monetary policy objectives relative to unilateral target changes. Our findings are consistent with overreaction in the wake of bad news (rate hikes), and point to a shift in volatility from before to after the rate change announcement since the adoption of the immediate disclosure policy of the Federal Open Market Committee in February 1994.     

On the rationality of Korea's stock market: was the recent Korean financial crisis due to fundamental factors?

This paper examines whether the recent financial crisis in Korea was due to fundamental factors. To address this issue, we identify various components of Korea's stock market prices (KOSPI) and examine their responses to different types of shocks. Given the stationary behavior of KOSPI dividends, we relate stock price directly to earnings by deriving and using a log-linear model of the spread between price and earnings with a time-varying discount factor. Therefore, stock-price movements are explained by earnings (numerator component), time-varying discount factors (denominator component), and non-fundamental factors. Although we find evidence of substantial non-fundamental components in Korea's stock market prices, the sudden decline in Korea's stock market prices during the 1997 financial crisis was primarily due to fundamental components, in particular, the numerator component (e.g. earnings) combined with the denominator component (i.e. time-varying discount factor) rather than non-fundamental factors.     

Habit-based asset pricing with limited participation consumption

We calibrate and estimate a consumption-based asset pricing model with habit formation using limited participation consumption data. Based on survey data of a representative sample of American households, we distinguish between assetholder and non-assetholder consumption, as well as the standard aggregate consumption series commonly used in the CCAPM literature. We show that assetholder consumption outperforms non-assetholder and aggregate consumption data in explaining bond returns, bond yields, and the volatility of bond yields. We further show that the high volatility of assetholder consumption enables the model to explain the equity premium puzzle and the risk-free rate puzzle simultaneously for a reasonable value of relative risk aversion.     

An Extended Set of Risk Neutral Valuation Relationships for the Pricing of Contingent Claims

This article establishes an extended set of risk neutral valuation relationships (RNVR's), assuming a representative agent who has an extended power utility function, of the HARA class of utility functions. The utility function of the representative agent displays either increasing, constant or decreasing proportional risk aversion. Aggregate consumption and the random payoff of the underlying asset are bivariate three-parameter lognormal distributed. As an application of the RNVR's, closed-form solutions for the price of a call written on a stock are derived. These include an extra parameter, the threshold parameter, not contained in the Black-Scholes formula.