Empirical evidence shows that the implied volatility smiles for index options are significantly steeper than those for individual options. We propose a model setup where we start from the joint dynamics of the stocks and where the index value is a weighted sum of individual stock prices. Then the differences between the index smile and the smiles for individual stocks are entirely determined by the dependence structure among the stocks. We illustrate our idea in a jump-diffusion framework where both the diffusion and the jumps are decomposed into common and idiosyncratic components. Empirical data for options on the German stock index DAX and on Deutsche Bank are used to show that the model can explain the stylized facts on implied volatility smiles.

Managed portfolios that exploit positive first-order autocorrelation in monthly excess returns of equity factor portfolios produce large gains in Sharpe ratios. We document this finding for factor portfolios formed on the broad market, size, value, momentum, investment, profitability, and volatility. The value-added induced by factor management via short-term momentum is a robust empirical phenomenon that survives transaction costs and carries over to multi-factor portfolios. The novel strategy established in this work compares favorably to well-known timing strategies that employ e.g. factor volatility or factor valuation. For the majority of factors, our strategies appear successful especially in recessions and times of crisis.

Tests for the existence and the sign of the volatility risk premium are often based on expected option hedging errors. When the hedge is performed under the ideal conditions of continuous trading and correct model specification, the sign of the premium is the same as the sign of the mean hedging error for a large class of models. We show that discrete trading and model misspecification may cause the standard test to yield unreliable results. In particular, ignoring jump risk premia can lead to incorrect conclusions. We also show that delta-gamma hedges do not increase the reliability of the test.

We consider a Lucas-type exchange economy with two heterogeneous stocks (trees) and a representative investor with constant relative risk aversion. The dividend process for one stock follows a geometric Brownian motion with constant and known parameters. The expected dividend growth rate for the other tree is stochastic and in general unobservable, although there may be a signal from which the investor can learn about its current value. We find that the equilibrium quantities in our model significantly depend on the information structure and on the level of risk aversion. While an observable stochastic drift mainly makes the economy more risky, a latent expected growth rate process with learning significantly changes the equilibrium price-dividend ratios, price reactions to dividend and drift innovations, expected returns, volatilities, correlations, and differences between the stocks. These effects are the more pronounced the more risk averse the representative investor.

We consider an asset allocation problem in a continuous-time model with stochastic volatility and jumps in both the asset price and its volatility. First, we derive the optimal portfolio for an investor with constant relative risk aversion. The demand for jump risk includes a hedging component, which is not present in models without volatility jumps. We further show that the introduction of derivative contracts can have substantial economic value. We also analyze the distribution of terminal wealth for an investor who uses the wrong model, either by ignoring volatility jumps or by falsely including such jumps, or who is subject to estimation risk. Whenever a model different from the true one is used, the terminal wealth distribution exhibits fatter tails and (in some cases) significant default risk.

We study the effects of market incompleteness on speculation, investor survival, and asset pricing moments when investors disagree about the likelihood of jumps and have recursive preferences. We consider two models. In a model with jumps in aggregate consumption, incompleteness barely matters because the consumption claim resembles an insurance product against jump risk and effectively reproduces approximate spanning. In a long-run risk model with jumps in the long-run growth rate, market incompleteness affects speculation and investor survival. Jump and diffusive risks are more balanced regarding their importance, and therefore the consumption claim cannot reproduce approximate spanning.

We introduce implied volatility duration (IVD) as a new measure for the timing of uncertainty resolution, with a high IVD corresponding to late resolution. Portfolio sorts on a large cross-section of stocks indicate that investors demand, on average, more than 5% return per year as a compensation for a late resolution of uncertainty. In a general equilibrium model, we show that “late” stocks can only have higher expected returns than “early” stocks if the investor exhibits a preference for early resolution of uncertainty. Our empirical analysis thus provides a purely market-based assessment of the timing preferences of the marginal investor.

Directed links in cash flow networks affect the cross-section of risk premia through three channels. In a tractable consumption-based equilibrium asset pricing model, we obtain closed-form solutions that disentangle these channels for arbitrary directed networks. First, shocks that can propagate through the economy command a higher market price of risk. Second, shock-receiving assets earn an extra premium since their valuation ratios drop upon shocks in connected assets. Third, a hedge effect pushes risk premia down: when a shock propagates through the economy, an asset that is unconnected becomes relatively more attractive and its valuation ratio increases.

In this paper, we consider conditional measures of lead-lag relations between aggregate growth and industry-level cash flow growth in the United States. Our results show that firms in leading industries pay an average annualized return 3.6 higher than that of firms in lagging industries. Using both time-series and cross-sectional tests, we estimate an annual pure timing premium ranging from 1.2 to 1.7. This finding can be rationalized in a model in which (a) agents price growth news shocks, and (b) leading industries provide valuable resolution of uncertainty about the growth prospects of lagging industries.