Working Papers

Selected Working  Papers and Papers Under Review

Implied equity risk premium in an horizon dependent economy: The role of risk neutral conditional leverage (with Hugues Langlois), This draft, 8/2023. (update coming soon!)

Abstract: In a one-period economy, Martin (2017) and Chabi-Yo and Loudis (2020) derive bounds for the equity risk premium that use options of the same maturity as the horizon at which the premium is measured. In contrast, we provide an expression and an empirical methodology to measure the premium at a given horizon in a multi-period economy using options of multiple maturities. The premium depends on risk-neutral leverage effects and the expected future risk-neutral market variance and skewness, which contribute to increasing the premium at short horizons. Our measure outperforms in terms of prediction accuracy and portfolio allocation performance. The term structure of expected excess holding period returns is flatter on average and dramatically more negative during market turmoil than those implied by previous measures. 

Maxing Out Entropy: A Conditioning Approach  (with Yan Liu) (update coming soon!)

Abstract:  We show how conditioning information can be optimally incorporated to bound the entropy of the pricing kernel, complementing the well-known Sharpe ratio bound for the L2-space. Similar to Sharpe ratio, our solution is interpretable as generalized Sharpe ratios in the entropy space and strikes a balance in exploiting physical return predictability and hedging risk-neutral higher order moments. We apply our approach to recently proposed return predictors and document the unique information provided by the variance risk premium (VRP) and VIX options.

  Distorting Arrow-Debreu Securities: New Entropy Restrictions Implied by the Option Cross Section  (with  Yan  Liu ) This draft, 05/2022

Abstract: Replacing equity return (as in the equity risk premium) with returns on an arbitrary contingent claim, we obtain a new class of economic risk premiums to impose upon candidate models. These risk premiums reflect the distance between the physical and risk-neutral moments for asset returns, can be estimated in a model-free fashion from the option cross section, and provide sharp information in distinguishing alternative models. Confronting leading macro-finance models with our risk premiums, we uncover a wide dispersion in performance across candidate models. Our evidence points to the importance of incorporating persistent stochastic volatilities and/or higher moments in fundamentals to reconcile with the option data, as exemplified by Bansal and Yaron (2004) and Bekaert and Engstrom (2017). This draft 05/2022.

 A Factor Model for Stock Returns Based on Option Prices  (with Turan Bali and Scott Murray), This draft, 05/2022

Abstract:  Option prices reflect investors' assessment of future risk and risk premia, and therefore contain information about expected stock returns. We show theoretically that expected stock returns are a function of the difference between risk-neutral and physical variance, and the stock borrow fee. Based on this theory, we construct an empirical factor model that includes factors formed by sorting stocks on option-based variables. We find that the model has a higher tangent portfolio Sharpe ratio than extant factor models and outperforms such models at explaining the performance of portfolios formed by sorting on many option-based and traditional asset pricing variables. 

  What Is the Conditional Autocorrelation on the Stock Market? 

Abstract: We derive lower and upper bounds on the conditional market autocorrelation index at various investment horizons without using the precise form of the utility function. The bounds are derived in terms of option prices and can be computed at daily frequency for any given horizon. The bounds incorporate all the information contained in the entire distribution of returns. We use options on the S&P 500 index to quantify the bounds and document that asset prices imply a negative upper bound on the market conditional autocorrelation index. The upper bound on the market conditional autocorrelation index is highly volatile, skewed, and exhibits fat tails. It varies from -28% to -3% and takes extremely negative values during crisis or recession periods while being close to zero during normal times. On average, the upper bound on the market conditional autocorrelation index is -14%. We also document that periods of extremely negative market conditional autocorrelation index coincide with periods of a high Sharpe ratio, and we show that leading asset pricing models cannot reproduce both the negative market conditional autocorrelation index and the negative average market conditional autocorrelation index implied by asset prices

 The Real-Time Distribution of Stochastic Discount Factors ,  This draft, 08/2018                                      

Abstract: I use option prices to infer real-time distributions of stochastic discount factors. The distribution of the discount factor is characterized by its moments. The moments are estimated, from daily S&P 500 index option data, in real time, without relying on past observations. These moments are forward-looking and significantly predict the market excess return. A cross-sectional analysis shows that SDF moments are priced in the cross-section of returns. The theory suggests that the SDF variance (kurtosis) is positively priced in the cross-section of returns while the SDF skewness is negatively priced in the cross section of returns. Estimates of the price of risks associated with the moments of the SDF are economically and statistically significant after controlling for a comprehensible set of economic variables.

 An Inquiry into the Nature and Sources of Variation in the Expected Excess Return of a Long-Term Bond 

Latest draft: 07/2015 (with Gurdip Bakshi and Xiaohui Gao).