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When options are traded, one can use their prices and price changes to draw inference about the set of risk factors and their risk premia. We analyze tests for the existence and the sign of the market prices of jump risk that are based on option hedging errors. We derive a closed-form solution for the option hedging error and its expectation in a stochastic jump model under continuous trading and correct model specification. Jump risk is structurally different from, e.g., stochastic volatility: there is one market price of risk for each jump size (and not just \emph{the} market price of jump risk). Thus, the expected hedging error cannot identify the exact structure of the compensation for jump risk. Furthermore, we derive closed form solutions for the expected option hedging error under discrete trading and model mis-specification. Compared to the ideal case, the sign of the expected hedging error can change, so that empirical tests based on simplifying assumptions about trading frequency and the model may lead to incorrect conclusions.
It has been documented that vertical customer-supplier links between industries are the basis for strong cross-sectional stock return predictability (Menzly and Ozbas (2010)). We show that robust predictability also arises from horizontal links between industries, i.e., from the fact that industries are competitors or offer products, which are substitutes for each other. These horizontally linked industries exhibit positively correlated fundamentals. The signal derived from this type of connectedness is the basis for significant alpha in sorted portfolio strategies, and informed investors take the related information into account when they form their portfolios. We thus provide evidence of return predictability based on a new type of economic links between industries not captured in previous studies.
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 about seven percent 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.
We show that time-varying volatility of volatility is a significant risk factor which affects the cross-section and the time-series of index and VIX option returns, beyond volatility risk itself. Volatility and volatility-of-volatility measures, identified model-free from the option price data as the VIX and VVIX indices, respectively, are only weakly related to each other. Delta-hedged index and VIX option returns are negative on average, and are more negative for strategies which are more exposed to volatility and volatility-of-volatility risks. Volatility and volatility of volatility significantly and negatively predict future delta-hedged option payoffs. The evidence is consistent with a no-arbitrage model featuring time-varying market volatility and volatility-of-volatility factors, both of which have negative market price of risk.
Predictability and the cross-section of expected returns: a challenge for asset pricing models
(2020)
Many modern macro finance models imply that excess returns on arbitrary assets are predictable via the price-dividend ratio and the variance risk premium of the aggregate stock market. We propose a simple empirical test for the ability of such a model to explain the cross-section of expected returns by sorting stocks based on the sensitivity of expected returns to these quantities. Models with only one uncertainty-related state variable, like the habit model or the long-run risks model, cannot pass this test. However, even extensions with more state variables mostly fail. We derive criteria models have to satisfy to produce expected return patterns in line with the data and discuss various examples.
We analyze the equilibrium in a two-tree (sector) economy with two regimes. The output of each tree is driven by a jump-diffusion process, and a downward jump in one sector of the economy can (but need not) trigger a shift to a regime where the likelihood of future jumps is generally higher. Furthermore, the true regime is unobservable, so that the representative Epstein-Zin investor has to extract the probability of being in a certain regime from the data. These two channels help us to match the stylized facts of countercyclical and excessive return volatilities and correlations between sectors. Moreover, the model reproduces the predictability of stock returns in the data without generating consumption growth predictability. The uncertainty about the state also reduces the slope of the term structure of equity. We document that heterogeneity between the two sectors with respect to shock propagation risk can lead to highly persistent aggregate price-dividend ratios. Finally, the possibility of jumps in one sector triggering higher overall jump probabilities boosts jump risk premia while uncertainty about the regime is the reason for sizeable diffusive risk premia.
The term 'financialization' describes the phenomenon that commodity contracts are traded for purely financial reasons and not for motives rooted in the real economy. Recently, financialization has been made responsible for causing adverse welfare effects especially for low-income and low-wealth agents, who have to spend a large share of their income for commodity consumption and cannot participate in financial markets. In this paper we study the effect of financial speculation on commodity prices in a heterogeneous agent production economy with an agricultural and an industrial producer, a financial speculator, and a commodity consumer. While access to financial markets is always beneficial for the participating agents, since it allows them to reduce their consumption volatility, it has a decisive effect with respect to overall welfare effects who can trade with whom (but not so much what types of instruments can be traded).
In a parsimonious regime switching model, we find strong evidence that expected consumption growth varies over time. Adding inflation as a second variable, we uncover two states in which expected consumption growth is low, one with high and one with negative expected inflation. Embedded in a general equilibrium asset pricing model with learning, these dynamics replicate the observed time variation in stock return volatilities and stock- bond return correlations. They also provide an alternative derivation for a measure of time-varying disaster risk suggested by Wachter (2013), implying that both the disaster and the long-run risk paradigm can be extended towards explaining movements in the stock-bond correlation.
This paper deals with the superhedging of derivatives and with the corresponding price bounds. A static superhedge results in trivial and fully nonparametric price bounds, which can be tightened if there exists a cheaper superhedge in the class of dynamic trading strategies. We focus on European path-independent claims and show under which conditions such an improvement is possible. For a stochastic volatility model with unbounded volatility, we show that a static superhedge is always optimal, and that, additionally, there may be infinitely many dynamic superhedges with the same initial capital. The trivial price bounds are thus the tightest ones. In a model with stochastic jumps or non-negative stochastic interest rates either a static or a dynamic superhedge is optimal. Finally, in a model with unbounded short rates, only a static superhedge is possible.
Managed portfolios that exploit positive first-order autocorrelation in monthly excess returns of equity factor portfolios produce large alphas and gains in Sharpe ratios. We document this finding for factor portfolios formed on the broad market, size, value, momentum, investment, prof- itability, 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.
The leading premium
(2022)
In this paper, we consider conditional measures of lead-lag relationships between aggregate growth and industry-level cash-flow growth in the US. 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.
When estimating misspecified linear factor models for the cross-section of expected returns using GMM, the explanatory power of these models can be spuriously high when the estimated factor means are allowed to deviate substantially from the sample averages. In fact, by shifting the weights on the moment conditions, any level of cross-sectional fit can be attained. The mathematically correct global minimum of the GMM objective function can be obtained at a parameter vector that is far from the true parameters of the data-generating process. This property is not restricted to small samples, but rather holds in population. It is a feature of the GMM estimation design and applies to both strong and weak factors, as well as to all types of test assets.
Standard applications of the consumption-based asset pricing model assume that goods and services within the nondurable consumption bundle are substitutes. We estimate substitution elasticities between different consumption bundles and show that households cannot substitute energy consumption by consumption of other nondurables. As a consequence, energy consumption affects the pricing function as a separate factor. Variation in energy consumption betas explains a large part of the premia related to value, investment, and operating profitability. For example, value stocks are typically more energy-intensive than growth stocks and thus riskier, since they suffer more from the oil supply shocks that also affect households.