Vineer Bhansali

Various aspects of tail-risk hedging are explored from a behavioral perspective. We first demonstrate that a myopic approach to tail hedging that does not properly account for the value of the hedging in the full portfolio context can overlook its benefits. We also address the overpricing of deeply out-of-themoney puts in the context of a behavioral model and show that the skew can be rational and persistent within these models for a wide range of reasonable parameters. In addition, we show how in the presence of investors who prefer more skewness to less, negative expected return tail hedging can be perfectly rational, even in the presence of other investors for whom tail hedging is not optimal. Finally, we discuss how tail hedging overcomes time inconsistency in investor behavior and thus can be used as a precommitment device.

Bhansali and Davis define offensive risk management as the use of tail hedges in a portfolio as a way for investors to allocate more capital to risky assets and simultaneously reduce the risk of large investment losses. If the hedge is purchased at the right price, the portfolio with tail risk hedges may have a more attractive risk–return profile than a buy-and-hold portfolio. The authors show, in the context of the 80-year history of the Standard & Poor’s Index, that intuitive rules of thumb for monetization can be justified and that the active management of tail hedges is consistent with the cyclical behavior of the economy and the markets.

In the current deleveraging episode, the severity and simultaneous realization of low-probability events across a number of strategies has brought portfolio tail-risk hedging to the center of investors' attention. In this article, the author discusses the basic principles and implementation considerations behind portfolio tail-risk management, emphasizing the importance of viewing tail risk as the consequence of a systemic shock during which normally uncorrelated markets become correlated due to a reduction in liquidity. This approach suggests that tail risk should be measured by performing macro scenario analysis and that hedges should be picked based on their cost and joint performance in periods of stress relative to the portfolio being hedged. Since liquidity reduction is a typical consequence of systemic shocks, the author also discusses specific operational issues that come to the fore in such events.

The currency “carry trade”, in which an investor buys assets in a higher yielding currency by borrowing in a lower yielding currency, has been consistently exploited as a source of profits by investors. In this article, we discuss the effectiveness of the carry trade as prospective risk (measured by implied volatilities) in exchange rates varies. Based on simple equilibrium arguments we propose the hypothesis that the carry trade is effectively a form of short volatility trade. We also explore a simple strategy that combines carry with options and present a heuristic statistic for the measurement of the economics of the carry trade. We test the stratgy on actual historical carry and option price data and find that the hypothetical strategy allows for the presence of arbitrage opportunities between the forex option and carry markets.

The probability distribution for the relative return of a portfolio constructed from a subset n of the assets from a benchmark, consisting of N assets whose returns are multivariate normal, is completely characterized by its tracking error. However, if the benchmark asset returns are not multivariate normal then higher moments of the probability distribution for the portfolio's relative return are not related to its tracking error. We discuss the convergence of generalized tracking error measures as the size of the subset of benchmark assets increases. Assuming that the joint probability distribution for the returns of the assets is symmetric under their permutations we show that increasing n makes these generalized tracking errors small (even though n « N). For n » 1 the probability distribution for the portfolio's relative return is approximately symmetric and strongly peaked about the origin. The results of this paper generalize the conclusions of Dynkin et al (Dynkin L, Hyman J and Konstantinovsky V 2002 Sufficient Diversification in Credit Portfolios (Lehman Brothers Fixed Income Research)) to more general underlying asset distributions.

The probability distribution for the relative return of a portfolio constructed from a subset n of the assets from a benchmark, consisting of N assets whose returns are multivariate normal, is completely characterized by its tracking error. However, if the benchmark asset returns are not multivariate normal then higher moments of the probability distribution for the portfolio's relative return are not related to its tracking error. We discuss the convergence of generalized tracking error measures as the size of the subset of benchmark assets increases. Assuming that the joint probability distribution for the returns of the assets is symmetric under their permutations we show that increasing n makes these generalized tracking errors small (even though n<>1 the probability distribution for the portfolio's relative return is approximately symmetric and strongly peaked about the origin. The results of this paper generalize the conclusions of Dynkin et. al. (2002) to more general underlying asset distributions.

This article deals with the problem of optimal allocation of capital to corporate bonds in fixed income portfolios when there is the possibility of correlated defaults. Using a multivariate normal Copula function for the joint default probabilities we show that retaining the first few moments of the portfolio default loss distribution gives an extremely good approximation to the full solution of the asset allocation problem. We provide detailed results on the convergence of the moment expansion and explore how the optimal portfolio allocation depends on recovery fractions, level of diversification and investment time horizon. Numerous numerical illustrations exhibit the results for simple portfolios and utility functions.

This article deals with the problem of optimal allocation of capital to corporate bonds in fixed income portfolios when there is the possibility of correlated defaults. Under fairly general assumptions for the distribution of the total net assets of a set of firms we show that retaining the first few moments of the portfolio default loss distribution gives an extremely good approximation to the full solution of the asset allocation problem. We provide detailed results on the convergence of the moment expansion. We also provide explicit results for the inverse problem, i.e. for a given allocation to the set of risky bonds, what is the average risk premium required to make the portfolio optimal. Numerous numerical illustrations exhibit the results for realistic portfolios and utility functions.