Simple Variance Swaps, November, 2011 NBER Working Paper 16884 Slides The events of 2008-9 disrupted volatility derivatives markets and caused the single-name variance swap market to dry up completely; it has never recovered. This paper introduces the simple variance swap, a relative of the variance swap with more desirable properties. Simple variance swaps are robust: they can be priced and hedged even if the underlying asset's price can jump. I construct SVIX, an index based on simple variance swaps that measures market volatility. SVIX is consistently lower than VIX in the time series, which rules out the possibility that the market return and stochastic discount factor are conditionally lognormal. The SVIX series implies a lower bound on the forward-looking equity premium that peaked above 50% at the height of the credit crisis.
The Forward Premium Puzzle in a Two-Country World, November, 2011 NBER Working Paper 17564 Slides I explore the behavior of asset prices and the exchange rate in a two-country world. When the large country has bad news, the relative price of the small country's output declines. As a result, the small country's bonds are risky, and uncovered interest parity fails, with positive excess returns available to investors who borrow at the large country's interest rate and lend at the small country's interest rate.
How Much Do Financial Markets Matter? Cole-Obstfeld Revisited, November, 2010 Cole and Obstfeld (1991) asked, “How much do financial markets matter?” Emphasizing the importance of intratemporal relative price adjustment as a risk-sharing mechanism that operates even in the absence of financial asset trade, their answer was: not much. I revisit their question and find that in calibrations featuring rare disasters that generate reasonable risk premia without implausibly high risk aversion, the cost of shutting down trade in financial assets is on the order of 3 to 20 per cent of wealth.
The Lucas Orchard, June, 2011 NBER Working Paper 17563 Slides This paper investigates the behavior of asset prices in an endowment economy in which a representative agent with power utility consumes the dividends of multiple assets. The assets are Lucas trees; a collection of Lucas trees is a Lucas orchard. The model generates return correlations that vary endogenously, spiking at times of disaster. Since disasters spread across assets, the model generates large risk premia even for assets with stable fundamentals. Very small assets may comove endogenously and hence earn positive risk premia even if their fundamentals are independent of the rest of the economy. I provide conditions under which the variation in a small asset's price-dividend ratio can be attributed almost entirely to variation in its risk premium.
The Valuation of Long-Dated Assets, September, 2011 NBER Working Paper 16219 Slides The expected time- and risk-adjusted cumulative return on any asset equals one at all horizons. Nonetheless, I show that a typical asset's realized time- and risk-adjusted cumulative return tends to zero almost surely. As a corollary, the value of a typical long-dated asset is driven by extreme events: either by good news at the level of the individual asset or by bad news at the aggregate level. In the case of the aggregate market, the fact that its Sharpe ratio is higher than its volatility suggests that bad news is the relevant consideration in practice.
Publications
Consumption-Based Asset Pricing with Higher Cumulants, conditionally accepted, Review of Economic Studies NBER Working Paper 16153 Slides I extend the Epstein-Zin-lognormal consumption-based asset-pricing model to allow for general i.i.d. consumption growth. Information about the higher moments—equivalently, cumulants—of consumption growth is encoded in the cumulant-generating function. I apply the framework to economies with rare disasters, and argue that the importance of such disasters is a double-edged sword: parameters that govern the frequency and sizes of rare disasters are critically important for asset pricing, but extremely hard to calibrate. I show how to sidestep this issue by using observable asset prices to make inferences that are robust to the details of the underlying consumption process.
Disasters Implied by Equity Index Options (with David Backus and Mikhail Chernov), Journal of Finance (2011), 66:6:1969-2012 Slides We use equity index options to quantify the distribution of consumption growth disasters. The challenge lies in connecting the risk-neutral distribution of equity returns implied by options to the true distribution of consumption growth estimated from macroeconomic data. We attack the problem from three perspectives. First, we compare pricing kernels constructed from macro-finance and option-pricing models. Second, we compare option prices derived from a macro-finance model to those we observe. Third, we compare the distribution of consumption growth derived from option prices using a macro-finance model to estimates based on macroeconomic data. All three perspectives suggest that options imply smaller probabilities of extreme outcomes than have been estimated from international macroeconomic data. The third comparison yields a viable alternative calibration of the distribution of consumption growth that matches the equity premium, option prices, and the sample moments of US consumption growth.