Stephen Figlewski

Estimation of the optimal futures hedge

Standard approaches to designing a futures hedge often suffer from two major problems. First, they focus only on minimizing risk, so no account is taken of the impact on expected return. Second , in estima ting the hedge ratio, no allowance is made for time variation in the distribution of cash and futures price changes. This paper describes a technique for estimating the optimal futures hedge that corrects these problems and illustrates its use in hedging Treasury bonds with T-bond futures. Copyright 1988 by MIT Press.

The Informational Effects of Restrictions on Short Sales: Some Empirical Evidence

In a world of heterogeneous investors, a competitive financial market has two major functions. First, it is the mechanism by which ownership of the existing supply of risky assets is distributed among investors. This is the role which is analyzed in detail by the standard Capital Asset Pricing Model (CAPM) and its many extensions. The second important market function is to aggregate the diverse information held by different investors into a single price. Most versions of the CAPM eliminate the information aggregation function by assuming that investors hold homogeneous beliefs with respect to the probability distribution of asset returns. Exceptions which deal with some aspects of the problem are Lintner [7], Grossman [4], Grossman and Stiglitz [5], and Figlewski [1, 3 ].

Forecasting Volatilities and Correlations with EGARCH Models

Volatility varies randomly over time, making forecasting it d@cult. Formal models for systems with timevarying volatility have been developed in recent years, and widely applied in economics and finance. Models in the Autoregressive Conditional Heteroscedasticity (ARCH) family have been particularly popular. Prior studies of ARCH-type models of securities return variances have looked at a single asset and focused on in-sample explanation of volatility movements, rather than forecasting. This article considers time variation for both volatilities and correlations among returns on broad asset classes in the US. and Japan, specijcally, equities, long-term government bonds, a n d the do l l a r lyen exchange rate. We are most concerned with out-

Modeling the Dynamics of Correlations Among Implied Volatilities

--sample forecasting performance. We fi t Exponen t i a l Genera l ized ARCH (EGARCH) models for the returns variances of weekly data from 1977 to 1990. In-sample parameter estimates are statistically signijcant and of the expected signs and magnitudes. In both regressions and directional tests of outof-sample forecasting ability, the EGARCH models seem to contain more information than historical volatility. But overall explanatory power is not great. Forecasting correlations is less successful. Only six of ten pairwise correlations show any significant ARCH efects. Although the model forecasts were less biased than the historical correlation, explanatory power in all cases is very low.

How to Lose Money in Derivatives

Implied volatility (IV) reflects both expected empirical volatility and also risk premia. Stochastic variation in either creates unhedged risk in a delta hedged options position. We develop EGARCH/DCC models for the dynamics of volatilities and correlations among daily IVs from options on twenty-eight large cap stocks. The data strongly support a general correlation structure and also a one-factor model with the VIX index as the common factor. Using IVs from stocks that are either highly correlated with the target stock’s IV or in the same industry together with the VIX can significantly improve hedging of individual IV changes.

International asset allocation with time varying risk: an analysis and implementation

This year has seen a large number o f disturbing and widely reported losses from trading in derivatives, j o m the

Modeling Financial Data Using Clustering AndTree-based Approaches

1.3 billion hit taken by Metal&esellschgt and Procter G Gamble’s

Viewing the Financial Crisis from 20,000 Feet Up

157 million loss, to many smaller but distressing losses experienced by much less sophisticated investors, including college endowment funds and munickal government pension plans. How has this happened?’ And does it mean that derivatives are so dangerously risky that a sign

The pricing of convexity risk and timedecay in options markets

cant increase in government regulation o f the industry is called for? This article discusses many of the ways j r m s can, and do, lose money in derivatives trading. A major theme is that there isjequently more than one way to think about a given derivatives-related loss, and in many cases there is less cause for public concern than an uncritical reading o f the news reports would suggest.

Option Investor Rationality Revisited: The Role of Exercise Boundary Violations

Abstract This paper investigates the problem of optimally allocating funds in an investment portfolio among major classes of U.S. and Japanese assets, given that the asset risk parameters vary over time. We devise an econometric specification in the ARCH/GARCH family to model the evolution of the returns covariance matrix and find substantial time variation in both returns variances and correlations. The fitted covariance matrices are then used to analyze optimal asset allocation portfolios. The time patterns in the portfolio weights and risk assessment make sense: They show the change in character of the U.S. Treasury bond market in 1979 and the increase in stock market risk in October 1987, for example. However, while the models capture some of the time variation in asset risk parameters, the improvement in portpolio performance is limited. We also examine investment performance under different portfolio constraints, and find that allowing international diversification makes the biggest impact, especially for a U.S. investor. Prohibiting short sales and the hedging of currency risk seem to have little impact. We find that post-sample performance of the model deteriorates relative to the fixed variance model.