1. Drechsler, Itamar, Yaron, Amir, 2011, What's Vol Got to Do with It, The Review of
Financial Studies, 24, 1-45
Volatility measures are considered to be useful tools for capturing how
perceptions of uncertainty about economic fundamentals are manifested in prices.
Derivatives markets, where volatility plays a significant role, are especially relevant for
unraveling the connections between uncertainty, the dynamics of the economy,
preferences, and prices. This article focuses on a derivatives-related quantity called the
variance premium, which is measured as the difference between the square of the
Chicago Board Options Exchange's VIX index and the conditional expectation of realized
variance.
In this paper, the authors demonstrate that the variance premium captures attitudes
toward uncertainty about economic fundamentals. The authors derive conditions under
which the variance premium predicts future stock returns. They show that the variance
premium's predictive power is strong at short horizons, measured in months, in contrast
to long-horizon predictors, such as the price-dividend ratio. The authors ultimately
develop and calibrate a generalized long-run risks model that generates a variance
premium with time variation and return predictability. This model is consistent with the
data, while simultaneously matching the levels and volatilities of the market return and
risk-free rate.
During the recent macroeconomic and financial turmoil, the VIX index has served
as the "fear gauge" for the market's concerns of surprise economic shocks. As uncertainty
increased and worries about a prolonged slowdown in growth heightened, the level and
volatility of the VIX reached unprecedented levels. This paper shows that the variance
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2. premium is useful for measuring agents' perceptions of uncertainty and the risk of
influential shocks to the economy.
The authors demonstrate that a risk aversion greater than one and a preference for
early resolution of uncertainty correctly signs the variance premium and the coefficient
from a predictive regression of returns on the variance premium. In addition, they show
that time variation in economic uncertainty is a minimal requirement for qualitatively
generating 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 and
the long-run component of cash-flows, can generate many of the quantitative features of
the variance premium while remaining consistent with observed aggregate dynamics for
dividends and consumption as well as standard asset-pricing data, such as the equity
premium and risk-free rate.
As the variance premium equals the difference between the price and expected
payoff of a trading strategy, this strategy's payoff is exactly the realized variance of
returns. The variance premium is essentially always positive as the strategy's price is
higher than its expected payoff, which suggests it provides a hedge to macroeconomic
risks. This mechanism underlies the model in this article. In the model, market
participants are willing to pay an insurance premium for an asset whose payoff is high
when return variation is large. This is the case because large return variation is a result of
big or important shocks to the economic state. Also, when investors perceive that the
danger 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 an
extension of the long-run risks model of Bansal and Yaron (2004).
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3. While the analysis shows that the LRR model captures some qualitative features
of the variance premium, they also demonstrate that it requires several important
extensions in order to quantitatively capture the large size, volatility, and high skewness
of the variance premium, and importantly, its short horizon predictive power for stock
returns.
The data series for the VIX and realized variance measures covers the period
January 1990 to March 2007. Through various calculations, they solve for the
equilibrium 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-pricing
targets. Specifically, they calibrate the model with the following objectives: finding a
specification for the long-run, volatility, and jump shocks such that the following
conditions are met:
1. The model's 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 into
a key derivatives index with a model of preferences and macroeconomic conditions. As
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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 and
derivative markets to understand the influence of uncertainty on the cross-section.
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