Joshua V. Rosenberg

Empirical pricing kernels

This paper investigates the empirical characteristics of investor risk aversion over equity return states by estimating a time-varying pricing kernel, which we call the empirical pricing kernel (EPK). We estimate the EPK on a monthly basis from 1991 to 1995, using S&P 500 index option data and a stochastic volatility model for the S&P 500 return process. We find that the EPK exhibits counter cyclical risk aversion over S&P 500 return states. We also find that hedging performance is significantly improved when we use hedge ratios based the EPK rather than a time-invariant pricing kernel.

Stock Returns and Volatility: Pricing the Short-Run and Long-Run Components of Market Risk

We decompose the time series of equity market risk into short- and long-run volatility components. Both components have negative and highly significant prices of risk in the cross section of equity returns. A three-factor model with the market return and the two volatility components compares favorably to benchmark models. We show that the short-run component captures market skewness risk, while the long-run component captures business cycle risk. Furthermore, short-run volatility is the more important cross-sectional risk factor, even though its average risk premium is smaller than the premium of the long-run component.

The Impact of CEO Turnover on Equity Volatility

A change in executive leadership is a significant event in the life of a firm. This study investigates an important consequence of a CEO turnover: a change in equity volatility. We develop three hypotheses about how changes in CEO might affect stock price volatility, and test these hypotheses using a sample of 872 CEO turnovers over the 1979-1995 period. We find that volatility increases following a CEO turnover, even when the CEO leaves voluntarily and is replaced by someone from inside the firm. Forced turnovers increase volatility more than voluntary turnovers - a finding consistent with the view that forced departures imply a higher probability of large strategy changes. For voluntary departures, outside successions increase volatility more than inside successions. We attribute this volatility change to increased uncertainty over the successor CEOs skill in managing the firms operations. We also document a greater stock price response to earnings announcements following CEO turnover, consistent with more informative signals of value driving the increased volatility. Our findings are robust to controls for firm-specific characteristics such as firm size, changes in firm operations, and changes in volatility and performance prior to the turnover.

Nonparametric Pricing of Multivariate Contingent Claims

In this paper, I derive and implement a nonparametric, arbitrage-free technique for multivariate contingent claim (MVCC) pricing. Using results from the method of copulas, I show that the multivariate risk-neutral density can be written as a product of marginal risk-neutral densities and a risk-neutral dependence function. I then develop a pricing technique using nonparametrically estimated marginal risk-neutral densities (based on options data) and a nonparametric dependence function (based on historical return data). By using nonparametric estimation, I avoid the pricing biases that result from incorrect parametric assumptions such as lognormality. ; I apply this technique to estimate the joint risk-neutral density of euro-dollar and yen-dollar returns. I compare the nonparametric risk-neutral density with density based on a lognormal dependence function and nonparametric marginals. The nonparametric euro-yen risk-neutral density has greater volatility, skewness, and kurtosis than the density based on a lognormal dependence function. In a comparison of pricing accuracy for euro-yen futures options, I find that the nonparametric model is superior to the lognormal model.

Non-Parametric Pricing of Multivariate Contingent Claims

The Black-Scholes (BS) framework is based on the assumption that an option’s underlying asset follows a lognormal diffusion. From the beginning, however, we have known that actual returns are not lognormal. Density functions estimated from realized returns invariably exhibit fat tails and other departures from lognormality. This has led to use of more flexible parametric returns distributions, and to non-parametric estimation techniques. Pervasive smile and skew patterns in the implied volatilities from option prices indicate that the market clearly anticipates departures from lognormality. An increasing number of derivative instruments, as well as procedures for assessing risk exposure more generally, require consideration of correlations among multiple risk factors. Here, again, real world returns data show correlation behavior that is inconsistent with standard models, particularly multivariate (log)normality. The method of copulas offers a general approach to more flexible and realistic modeling of correlations. In this article, Rosenberg first explains the fundamentals of this important new technology. He then illustrates its application in pricing euro-yen options using data on euro-dollar and yen-dollar exchange rates. The individual exchange rate volatilities are obtained non-parametrically from options prices, and the empirical copula function is estimated from historical returns data. The resulting estimate of the joint density function produces a better fit than standard models to prices of traded euro-yen options, and also reveals the effects of known specific events, such as the period of market disruption in October 1998.

The Information Content of FOMC Minutes

In this paper, we analyze the information content of Federal Open Market Committee minutes from 1987-2005. We apply an objective, statistical methodology known as Latent Semantic Analysis to decompose each minutes release into its characteristic themes. We show that these themes are correlated with current and future economic conditions. Our evidence suggests that market participants can extract a complex, multifaceted signal from the minutes. In particular, Treasury yield changes around the time of the minutes release depend on the specific themes expressed, the level of monetary policy uncertainty, and the economic outlook.

The Effect of Employee Stock Options on Bank Investment Choice, Borrowing, and Capital

In this paper, we test the hypothesis that granting employee stock options motivates CEOs of banking firms to undertake riskier projects. We also investigate whether granting employee stock options reduces the banks incentive to borrow while inducing a buildup of regulatory capital. Using a sample of 549 bank-years for publicly traded banks from 1992 to 2002, we find some evidence that the banks equity volatility (total as well as residual) and asset volatility increase as CEO stock option holdings increase. In addition, it appears that granting employee stock options motivates banks to reduce their borrowing, as evidenced by lower levels of interest expense and federal funds borrowing. Furthermore, we show that banking firms that grant more options to their employees build up more capital in future years.

Testing the Volatility Term Structure Using Option Hedging Criteria

The Black-Scholes formula assumes future volatility is a constant and known parameter, but this is now well-known to be untrue. A variety of models with time-varying volatility have been introduced, but there is no consensus on which one is the best, or even on how to answer that question properly. Engle and Rosenberg propose that the appropriate test of the efficacy of a given volatility model should be how well it can hedge an options position. They consider five models: Black-Scholes (BS), a BS variant with mean-reverting implied volatility, and three forms of GARCH-based model. They test how well each one is able to hedge against changing volatility by comparing their performance in a hedge of one straddle with another. The most accurate model out of sample is the GARCH components-with-leverage model. By contrast, a delta-vega hedge based on the BS model was poor, frequently leading to higher variance for the hedge than for the unhedged position.

Price Discovery in the Foreign Currency Futures and Spot Market

One of the perennial questions in derivatives research is how the derivatives market interacts with the market for its underlying instrument. Is the underlying dominant and its associated futures market just a satellite that follows along behind? Or does trading in the futures market push prices in the underlying around, maybe even driving both markets away from equilibrium at times? In this article, the authors examine the question of cash-futures interaction in foreign currency futures. Currency futures traded at the International Monetary Market division of the Chicago Mercantile Exchange have long been quite active, although still much smaller than the cash market. The relationship between intraday exchange rate movements in cash and futures is examined during 1996 and 2006. Interestingly, in 1996, futures price changes mostly led those in the cash market; while in 2006, the direction of influence was largely reversed. The authors believe this change primarily reflects increased transparency of the cash FX market.

How do Treasury Dealers Manage their Positions

Using data on U.S. Treasury dealer positions from 1990 to 2006, we find evidence of a significant role for dealers in the intertemporal intermediation of new Treasury security supply. Dealers regularly take into inventory a large share of Treasury issuance so that dealer positions increase during auction weeks. These inventory increases are only partially offset in adjacent weeks and are not significantly hedged with futures. Dealers seem to be compensated for the risk associated with these inventory changes by means of price appreciation in the subsequent week.