Cedric Okou

Downside Variance Risk Premium

We propose a new decomposition of the variance risk premium in terms of upside and downside variance risk premia. The difference between upside and downside variance risk premia is a measure of skewness risk premium. We establish that the downside variance risk premium is the main component of the variance risk premium, and that the skewness risk premium is a priced factor with significant prediction power for aggregate excess returns. Our empirical investigation highlights the positive and significant link between the downside variance risk premium and the equity premium, as well as a positive and significant relation between the skewness risk premium and the equity premium. Finally, we document the fact that the skewness risk premium fills the time gap between one quarter ahead predictability, delivered by the variance risk premium as a short term predictor of excess returns and traditional long term predictors such as price-dividend or price-earning ratios. Our resul ts are supported by a simple equilibrium consumption-based asset pricing model.

An Extension of the Consumption-Based CAPM Model

We extend the Consumption-based CAPM (C-CAPM) model to representative agents with different risk attitudes. We first use the concept of expectation dependence and show that for a risk averse representative agent, it is the first-degree expectation dependence (FED) rather than the covariance that determines C-CAPM’s riskiness. We extend the assumption of risk aversion to prudence and propose the measure of second-degree expectation dependence (SED) to obtain the values of asset price and equity premium. These theoretical results are linked to the equity premium puzzle. Using the same dataset as in Campbell (2003), the estimated measures of relative risk aversion from FED and SED approximations are much lower than those obtained in the original study and correspond to the theoretical values often discussed in the literature. The theoretical model is then generalized to higher-degree risk changes and higher-order risk averse representative agents.

Disentangling Continuous Volatility from Jumps in Long-Run Risk–Return Relationships

Realized variance can be broken down into a continuous volatility and a jump components. We show that these two components have very different degrees of power of prediction on future long-term excess stock market returns. Namely, continuous volatility is a key driver of medium to long-term risk–return relationships. In contrast, jumps do not predict future medium or long-term excess returns. We use inference methods that are robust to persistent predictors in a multi-horizon setup. Specifically, we use a rescaled Student-t to test for significant risk–return relationship and simulate its exact behavior under the null in the case of multiple regressors with different levels of persistence. We also perform tests of equality of the risk–return relationship at multiple horizons. We do not find evidence against a proportional relationship between long-term continuous volatility and future returns.

Horizon effect in the term structure of long-run risk-return trade-offs

The horizon effect in the long-run predictive relationship between market excess return and historical market variance is investigated. To this end, the asymptotic multivariate distribution of the term structure of risk-return trade-offs is derived, accounting for short- and long-memory in the market variance dynamics. A rescaled Wald statistic is used to test whether the term structure of risk-return trade-offs is flat, that is, the risk-return slope coefficients are equal across horizons. When the regression model includes an intercept, the premise of a flat term structure of risk-return relationships is rejected. In contrast, there is no significant statistical evidence against the equality of slope coefficients from constrained risk-return regressions estimated at different horizons. A smoothed cross-horizon estimate is then proposed for the trade-off intensity at the market level. The findings underscore the importance of economically motivated restrictions to improve the estimation of intertemporal asset pricing models.

Can Higher-Order Risks Explain the Credit Spread Puzzle?

We tweak the conventional Merton model to account for the asymmetric properties of assets returns and investors asymmetric behavior toward the upside potential of gain versus the downside risk of loss. Using an asymmetric split normal distribution, we capture empirical asymmetries in the underlying return distribution, while we conserve the attractiveness of delivering closed-form pricing formulas that collapse to the basic Merton model in the symmetric Gaussian case. The asymmetric specification outperforms the symmetric one in matching high levels of historical credit spreads. We then link the residual (non-default-model-implied) spread to two illiquidity risk factors. The first factor is extracted from several measures of idiosyncratic illiquidity variables and the second factor is a systematic factor obtained from a general index common to all studied bonds. Our model explains 70% of the BBB-AAA spread and more than 72% of BBB and AAA credit spreads relative to the on-the-run Treasury rates.

Good Volatility, Bad Volatility and Option Pricing

Advances in variance analysis permit the splitting of the total quadratic variation of a jump-diffusion process into upside and downside components. Recent studies establish that this decomposition enhances volatility predictions and highlight the upside/downside variance spread as a driver of the asymmetry in stock price distributions. To appraise the economic gain of this decomposition, we design a new and flexible option pricing model in which the underlying asset price exhibits distinct upside and downside semivariance dynamics driven by the model-free proxies of the variances. The new model outperforms common benchmarks, especially the alternative that splits the quadratic variation into diffusive and jump components.

Affine Term Structure of Risk-Neutral Moments Models

This paper provides a novel methodology for estimating option pricing models based on risk-neutral moments. We synthesize the distribution extracted from a panel of option prices and exploit linear relationships between risk-neutral cumulants and latent factors within the continuous time affine stochastic volatility framework. We find that fitting the Andersen, Fusari, and Todorov (2015b) option valuation model to risk-neutral moments captures the bulk of the information in option prices. Our estimation strategy is effective, easy to implement, and robust, as it allows for a direct linear filtering of the latent factors and a quasi-maximum likelihood estimation of model parameters. From a practical perspective, employing risk-neutral moments instead of option prices also helps circumvent several sources of numerical errors and substantially lessens the computational burden inherent in working with a large panel of option contracts.

An Extension of the Consuption-Based CAPM Model

This paper exploits the concept of expectation dependence to propose an alternative representation of the consumption-based capital asset pricing model (C-CAPM). While the first-degree expectation dependence (FED) drives the C-CAPMs riskiness for a risk-averse investor, the second-degree expectation dependence (SED) is required to account for the downside risk faced by a prudent investor. Theoretical and empirical assessments reveal that the expectation dependence-based C-CAPM can realistically match equity premia, risk-free rates, and variance risk premia. The consumption SED risk emerges as a fundamental source of uncertainty driving asset prices.