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Vol article


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Vol article

  1. 1. Drechsler, Itamar, Yaron, Amir, 2011, Whats Vol Got to Do with It, The Review ofFinancial Studies, 24, 1-45 Volatility measures are considered to be useful tools for capturing howperceptions of uncertainty about economic fundamentals are manifested in prices.Derivatives markets, where volatility plays a significant role, are especially relevant forunraveling the connections between uncertainty, the dynamics of the economy,preferences, and prices. This article focuses on a derivatives-related quantity called thevariance premium, which is measured as the difference between the square of theChicago Board Options Exchanges VIX index and the conditional expectation of realizedvariance. In this paper, the authors demonstrate that the variance premium captures attitudestoward uncertainty about economic fundamentals. The authors derive conditions underwhich the variance premium predicts future stock returns. They show that the variancepremiums predictive power is strong at short horizons, measured in months, in contrastto long-horizon predictors, such as the price-dividend ratio. The authors ultimatelydevelop and calibrate a generalized long-run risks model that generates a variancepremium with time variation and return predictability. This model is consistent with thedata, while simultaneously matching the levels and volatilities of the market return andrisk-free rate. During the recent macroeconomic and financial turmoil, the VIX index has servedas the "fear gauge" for the markets concerns of surprise economic shocks. As uncertaintyincreased and worries about a prolonged slowdown in growth heightened, the level andvolatility of the VIX reached unprecedented levels. This paper shows that the variance 1
  2. 2. premium is useful for measuring agents perceptions of uncertainty and the risk ofinfluential shocks to the economy. The authors demonstrate that a risk aversion greater than one and a preference forearly resolution of uncertainty correctly signs the variance premium and the coefficientfrom a predictive regression of returns on the variance premium. In addition, they showthat time variation in economic uncertainty is a minimal requirement for qualitativelygenerating a positive, time-varying variance premium that predicts excess stock returns.Finally, they show that an extended long-run risks model, with jumps in uncertainty andthe long-run component of cash-flows, can generate many of the quantitative features ofthe variance premium while remaining consistent with observed aggregate dynamics fordividends and consumption as well as standard asset-pricing data, such as the equitypremium and risk-free rate. As the variance premium equals the difference between the price and expectedpayoff of a trading strategy, this strategys payoff is exactly the realized variance ofreturns. The variance premium is essentially always positive as the strategys price ishigher than its expected payoff, which suggests it provides a hedge to macroeconomicrisks. This mechanism underlies the model in this article. In the model, marketparticipants are willing to pay an insurance premium for an asset whose payoff is highwhen return variation is large. This is the case because large return variation is a result ofbig or important shocks to the economic state. Also, when investors perceive that thedanger of big shocks to the state of the economy is high, the hedging premium increases,resulting in a large variance premium. The authors model this mechanism in anextension of the long-run risks model of Bansal and Yaron (2004). 2
  3. 3. While the analysis shows that the LRR model captures some qualitative featuresof the variance premium, they also demonstrate that it requires several importantextensions in order to quantitatively capture the large size, volatility, and high skewnessof the variance premium, and importantly, its short horizon predictive power for stockreturns. The data series for the VIX and realized variance measures covers the periodJanuary 1990 to March 2007. Through various calculations, they solve for theequilibrium price process of the model economy. In order to study the variance premium,equity risk premium, and their relationship, they also solve for the market return. The authors confront the model with a broad set of cash-flow and asset-pricingtargets. Specifically, they calibrate the model with the following objectives: finding aspecification for the long-run, volatility, and jump shocks such that the followingconditions are met: 1. The models consumption and dividend growth statistics are consistent with salient features of the consumption and dividends data 2. The model generates consistent unconditional moments of asset prices, such as the equity premium and the risk-free rate 3. The model generates a large and volatile variance premium and features of its return predictability 4. The model is consistent with consumption and return predictability by the price- dividend ratio. A main contribution of this article is to quantitatively link information priced intoa key derivatives index with a model of preferences and macroeconomic conditions. As 3
  4. 4. per the authors, the evidence in this paper suggests that derivative markets and high-frequency measures of variation should be very useful at identifying these risk factors.Further, interesting implications could therefore arise from jointly using cash-flows andderivative markets to understand the influence of uncertainty on the cross-section. 4