### Christian Skov Jensen

Christian Skov Jensen

Assistant Professor of Finance, Bocconi University

Email: christian.jensen [at] unibocconi.it

### Research papers

Research papers

**The Ex Ante Physical Distributions of Individual Stock Returns****, **September 2020, **New paper**

I present a method for deriving the entire physical return distributions of individual stocks directly from option prices. The method is theoretically nested in an equilibrium model, obeys the law-of-one-price, and can be implemented in real-time in a forward-looking manner. The method performs well out-of-sample in predicting ex-post distributions of individual stock returns. The physical stock distributions and the co-moments with the market are important for risk-management decisions, portfolio allocation, and can help understand the cross-section of returns. A tradeable long-short portfolio that buys (sells) low (high) co-skewness stocks yields a monthly five-factor alpha of 0.61% (t-stat 3.25). The equity risk factors: value, profitability, investments, momentum, and betting-against-beta can all be used to hedge co-skewness risk.

**Higher-Moment Risk****,** with Niels Joachim Gormsen, February 2020

We use a new method to estimate ex ante higher-order moments of stock market returns from option prices. Even and odd higher order moments are strongly negatively correlated, creating periods where the return distribution is riskier because it is more left-skewed and fat tailed. The higher-moment risk increases in good times when variance is lower and prices are higher. This time variation is inconsistent with disaster-based models where disaster risk, and thus higher-moment risk, peaks in bad times. The variation in higher-moment risk also has important implications for investors as it causes the probability of a three-sigma loss on the market portfolio to vary from 0.7% to 1.9% percent over the sample, peaking in calm periods such as just before the onset of the financial crisis.

**Conditional Risk in Global Stock Returns**, with Niels Joachim Gormsen, January 2020

We estimate the premium associated with time-varying market betas without using rolling betas or instruments. Instead, we use a new conditional-risk factor, which is a market timing strategy defined as the unexpected return on the market times the ex ante price of risk. The factor is a powerful tool for documenting a global effect of conditional risk on stock returns: across 23 developed countries, all major equity risk factors load on our conditional-risk factor with the right sign, meaning their alpha can partly be explained by the time variation in their market betas. The conditional-risk factor explains 50% more alpha than traditional methods that use rolling betas to capture conditional risk.

**Short Sale Costs Predict Volatility**, with Mads Vestergaard Jensen, November 2018

As a new test of models of differences of opinions, we study how shorting markets interact with equity volatility. We identify positive (negative) demand shifts for shorting of stocks by simultaneous increases (decreases) in short-sale costs and short interest. Consistent with an increase in differences of opinions, a positive (negative) demand shift, on average, predicts a volatility that is 2.8 (3.9) percentage points higher (lower) over the next quarter. Event studies show that average volatilities of stocks hit by supply or demand shifts are higher than for other stocks, and volatilities peak around the time of shifts. We also find that future volatility increases with both increases and the level of short-sale costs and short interest.

**Generalized Recovery**, with David Lando and Lasse Heje Pedersen, **Journal of Financial Economics***, 133 (1), 154-174, 2019. *[code and data]

We characterize when physical probabilities, marginal utilities, and the discount rate can be recovered from observed state prices for several future time periods. We make no assumptions of the probability distribution, thus generalizing the time-homogeneous stationary model of Ross (2015). Recovery is feasible when the number of maturities with observable prices is higher than the number of states of the economy (or the number of parameters characterizing the pricing kernel). When recovery is feasible, our model allows a closed-form linearized solution. We implement our model empirically, testing the predictive power of the recovered expected return and other recovered statistics.