Model-free hedge ratios and scale-invariant models

A price process is scale-invariant if and only if the returns distribution is independent of the price measurement scale. We show that most stochastic processes used for pricing options on financial assets have this property and that many models not previously recognised as scale-invariant are indeed so. We also prove that price hedge ratios for a wide class of contingent claims under a wide class of pricing models are model-free. In particular, previous results on model-free price hedge ratios of vanilla options based on scale-invariant models are extended to any contingent claim with homogeneous pay-off, including complex, path-dependent options. However, model-free hedge ratios only have the minimum variance property in scale-invariant stochastic volatility models when price–volatility correlation is zero. In other stochastic volatility models and in scale-invariant local volatility models, model-free hedge ratios are not minimum variance ratios and our empirical results demonstrate that they are less efficient than minimum variance hedge ratios.     

International portfolio selection with exchange rate risk: A behavioural portfolio theory perspective

This paper analyzes international portfolio selection with exchange rate risk based on behavioural portfolio theory (BPT). We characterize the conditions under which the BPT problem with a single foreign market has an optimal solution, and show that the optimal portfolio contains the traditional mean–variance efficient portfolio without consideration of exchange rate risk, and an uncorrelated component constructed to hedge against exchange rate risk. We illustrate that the optimal portfolio must be mean–variance efficient with exchange rate risk, while the same is not true from the perspective of local investors unless certain conditions are satisfied. We further establish that international portfolio selection in the BPT with multiple foreign markets consists of two sequential decisions. Investors first select the optimal BPT portfolio in each market, overlooking covariances among markets, and then allocate funds across markets according to a specific rule to achieve mean–variance efficiency or to minimize the loss in efficiency.     

Reading the smile: the message conveyed by methods which infer risk neutral densities

In this study we compare the quality and information content of risk neutral densities obtained by various methods. We consider a non-parametric method based on a mixture of log–normal densities, the semi-parametric ones based on an Hermite approximation or based on an Edgeworth expansion, the parametric approach of Malz which assumes a jump-diffusion for the underlying process, and Heston's approach assuming a stochastic volatility model. We apply those models on FF/DM exchange rate options for two dates. Models differ when important news hits the market (here anticipated elections). The non-parametric model provides a good fit to options prices but is unable to provide as much information about market participants expectations than the jump-diffusion model.     

A semi-parametric approach to risk management

Abstract

The benchmark theory of mathematical finance is the Black–Scholes–Merton (BSM) theory, based on Brownian motion as the driving noise process for stock prices. Here the distributions of financial returns of the stocks in a portfolio are multivariate normal. Risk management based on BSM underestimates tails. Hence estimation of tail behaviour is often based on extreme value theory (EVT). Here we discuss a semi-parametric replacement for the multivariate normal involving normal variance–mean mixtures. This allows a more accurate modelling of tails, together with various degrees of tail dependence, while (unlike EVT) the whole return distribution can be modelled. We use a parametric component, incorporating the mean vector μ and covariance matrix Σ, and a non-parametric component, which we can think of as a density on [0,∞), modelling the shape (in particular the tail decay) of the distribution. We work mainly within the family of elliptically contoured distributions, focusing particularly on normal variance mixtures with self-decomposable mixing distributions. We discuss efficient methods to estimate the parametric and non-parametric components of our model and provide an algorithm for simulating from such a model. We fit our model to several financial data series. Finally, we calculate value at risk (VaR) quantities for several portfolios and compare these VaRs to those obtained from simple multivariate normal and parametric mixture models.     

An analysis of portfolio selection with background risk

This paper investigates the impact of background risk on an investor’s portfolio choice in a mean–variance framework, and analyzes the properties of efficient portfolios as well as the investor’s hedging behaviour in the presence of background risk. Our model implies that the efficient portfolio with background risk can be separated into two independent components: the traditional mean–variance efficient portfolio, and a self-financing component constructed to hedge against background risk. Our analysis also shows that the presence of background risk shifts the efficient frontier of financial assets to the right with no changes in its shape. Moreover, both the composition of the hedge portfolio and the location of the efficient frontier are greatly affected by a number of background risk factors, including the proportion of background assets in total wealth and the correlation between background risk and financial risk.     

Detecting structural breaks and identifying risk factors in hedge fund returns: A Bayesian approach

Extending previous work on asset-based style factor models, this paper proposes a model that allows for the presence of structural breaks in hedge fund return series. We consider a Bayesian approach to detecting structural breaks occurring at unknown times and identifying relevant risk factors to explain the monthly return variation. Exact and efficient Bayesian inference for the unknown number and positions of the breaks is performed by using filtering recursions similar to those of the forward–backward algorithm. Existing methods of testing for structural breaks are also used for comparison. We investigate the presence of structural breaks in several hedge fund indices; our results are consistent with market events and episodes that caused substantial volatility in hedge fund returns during the last decade.     

Generalized parameter functions for option pricing

We extend the benchmark nonlinear deterministic volatility regression functions of Dumas et al. (1998) to provide a semi-parametric method where an enhancement of the implied parameter values is used in the parametric option pricing models. Besides volatility, skewness and kurtosis of the asset return distribution can also be enhanced. Empirical results, using closing prices of the S&P 500 index call options (in one day ahead out-of-sample pricing tests), strongly support our method that compares favorably with a model that admits stochastic volatility and random jumps. Moreover, it is found to be superior in various robustness tests. Our semi-parametric approach is an effective remedy to the curse of dimensionality presented in nonparametric estimation and its main advantage is that it delivers theoretically consistent option prices and hedging parameters. The economic significance of the approach is tested in terms of hedging, where the evaluation and estimation loss functions are aligned.     

Conditional Value-at-Risk,spectral risk measures and (non-)diversification in portfolio selection problems – A comparison with mean–variance analysis

We study portfolio selection under Conditional Value-at-Risk and, as its natural extension, spectral risk measures, and compare it with traditional mean–variance analysis. Unlike the previous literature that considers an investor’s mean-spectral risk preferences for the choice of optimal portfolios only implicitly, we explicitly model these preferences in the form of a so-called spectral utility function. Within this more general framework, spectral risk measures tend towards corner solutions. If a risk free asset exists, diversification is never optimal. Similarly, without a risk free asset, only limited diversification is obtained. The reason is that spectral risk measures are based on a regulatory concept of diversification that differs fundamentally from the reward-risk tradeoff underlying the mean–variance framework.     

Maximum likelihood estimation of stochastic volatility models

We develop and implement a method for maximum likelihood estimation in closed-form of stochastic volatility models. Using Monte Carlo simulations, we compare a full likelihood procedure, where an option price is inverted into the unobservable volatility state, to an approximate likelihood procedure where the volatility state is replaced by proxies based on the implied volatility of a short-dated at-the-money option. The approximation results in a small loss of accuracy relative to the standard errors due to sampling noise. We apply this method to market prices of index options for several stochastic volatility models, and compare the characteristics of the estimated models. The evidence for a general CEV model, which nests both the affine Heston model and a GARCH model, suggests that the elasticity of variance of volatility lies between that assumed by the two nested models.     

Beyond the Sharpe ratio: An application of the Aumann–Serrano index to performance measurement

We propose a performance measure that generalizes the Sharpe ratio. The new performance measure is monotone with respect to stochastic dominance and consistently accounts for mean, variance and higher moments of the return distribution. It is equivalent to the Sharpe ratio if returns are normally distributed. Moreover, the two performance measures are asymptotically equivalent as the underlying distributions converge to the normal distribution. We suggest a parametric and a non-parametric estimator for the new performance measure and provide an empirical illustration using mutual funds and hedge funds data.     

Do hedge funds' exposures to risk factors predict their future returns?

This paper investigates hedge funds' exposures to various financial and macroeconomic risk factors through alternative measures of factor betas and examines their performance in predicting the cross-sectional variation in hedge fund returns. Both parametric and non-parametric tests indicate a significantly positive (negative) link between default premium beta (inflation beta) and future hedge fund returns. The results are robust across different subsample periods and states of the economy, and after controlling for market, size, book-to-market, and momentum factors as well as the trend-following factors in stocks, short-term interest rates, currencies, bonds, and commodities. The paper also provides macro-level and micro-level explanations of our findings.     

Static hedging and pricing American options

This paper utilizes the static hedge portfolio (SHP) approach of Derman et al. [Derman, E., Ergener, D., Kani, I., 1995. Static options replication. Journal of Derivatives 2, 78–95] and Carr et al. [Carr, P., Ellis, K., Gupta, V., 1998. Static hedging of exotic options. Journal of Finance 53, 1165–1190] to price and hedge American options under the Black-Scholes (1973) model and the constant elasticity of variance (CEV) model of Cox [Cox, J., 1975. Notes on option pricing I: Constant elasticity of variance diffusion. Working Paper, Stanford University]. The static hedge portfolio of an American option is formulated by applying the value-matching and smooth-pasting conditions on the early exercise boundary. The results indicate that the numerical efficiency of our static hedge portfolio approach is comparable to some recent advanced numerical methods such as Broadie and Detemple [Broadie, M., Detemple, J., 1996. American option valuation: New bounds, approximations, and a comparison of existing methods. Review of Financial Studies 9, 1211–1250] binomial Black-Scholes method with Richardson extrapolation (BBSR). The accuracy of the SHP method for the calculation of deltas and gammas is especially notable. Moreover, when the stock price changes, the recalculation of the prices and hedge ratios of the American options under the SHP method is quick because there is no need to solve the static hedge portfolio again. Finally, our static hedging approach also provides an intuitive derivation of the early exercise boundary near expiration.     

An empirical analysis of marginal conditional stochastic dominance

Stochastic dominance is a more general approach to expected utility maximization than the widely accepted mean–variance analysis. However, when applied to portfolios of assets, stochastic dominance rules become too complicated for meaningful empirical analysis, and, thus, its practical relevance has been difficult to establish. This paper develops a framework based on the concept of Marginal Conditional Stochastic Dominance (MCSD), introduced by Shalit and Yitzhaki (1994), to test for the first time the relationship between second order stochastic dominance (SSD) and stock returns. We find evidence that MCSD is a significant determinant of stock returns. Our results are robust with respect to the most popular pricing models.     

A Bayesian approach to detecting nonlinear risk exposures in hedge fund strategies

This paper proposes a model that allows for nonlinear risk exposures of hedge funds to various risk factors. We introduce a flexible threshold regression model and develop a Bayesian approach for model selection and estimation of the thresholds and their unknown number. In particular, we present a computationally flexible Markov chain Monte Carlo stochastic search algorithm which identifies relevant risk factors and/or threshold values. Our analysis of several hedge fund returns reveals that different strategies exhibit nonlinear relations to different risk factors, and that the proposed threshold regression model improves our ability to evaluate hedge fund performance.     

An advanced perspective on the predictability in hedge fund returns

This paper advances the research on the predictability in hedge fund returns, using a broad set of risk factors within a variety of different prediction models. Accounting for the fact that returns are non-normally distributed, heteroscedastic and time-varying in their exposure to pervasive economic risk factors, we advocate a non-parametric backward elimination regression approach. The interdependencies between the monthly changes of envisaged risk factors and the subsequent hedge fund returns remain remarkably stable in terms of the observed direction of impact. Thus, taking into account the specific characteristics of this asset class, we find strong evidence of its return predictability.     

Hedge fund pricing and model uncertainty

This article uses Bayesian model averaging to study model uncertainty in hedge fund pricing. We show how to incorporate heteroscedasticity, thus, we develop a framework that jointly accounts for model uncertainty and heteroscedasticity. Relevant risk factors are identified and compared with those selected through standard model selection techniques. The analysis reveals that a model selection strategy that accounts for model uncertainty in hedge fund pricing regressions can be superior in estimation/inference. We explore potential impacts of our approach by analysing individual funds and show that they can be economically important.     

Using industry momentum to improve portfolio performance

Minimum-variance portfolios, which ignore the mean and focus on the (co)variances of asset returns, outperform mean–variance approaches in out-of-sample tests. Despite these promising results, minimum-variance policies fail to deliver a superior performance compared with the simple 1/N rule. In this paper, we propose a parametric portfolio policy that uses industry return momentum to improve portfolio performance. Our portfolio policies outperform a broad selection of established portfolio strategies in terms of Sharpe ratio and certainty equivalent returns. The proposed policies are particularly suitable for investors because portfolio turnover is only moderately increased compared to standard minimum-variance portfolios.     

An analysis of commodity markets: What gain for investors?

In this paper we study whether the commodity futures market predicts the commodity spot market. Using historical daily data on four commodities—oil, gold, platinum, and silver—we find that they do. We then show how investors can use this information on the futures market to devise trading strategies and make profits. In particular, dynamic trading strategies based on a mean–variance investor framework produce somewhat different results compared with those based on technical trading rules. Dynamic trading strategies suggest that all commodities are profitable and profits are dependent on structural breaks. The most recent global financial crisis marked a period in which commodity profits were the weakest.     

Hedging with Two Futures Contracts: Simplicity Pays

We propose to use two futures contracts in hedging an agricultural commodity commitment to solve either the standard delta hedge or the roll‐over issue. Most current literature on dual‐hedge strategies is based on a structured model to reduce roll‐over risk and is somehow difficult to apply for agricultural futures contracts. Instead, we propose to apply a regression based model and a naive rules of thumb for dual‐hedges which are applicable for agricultural commodities. The naive dual strategy stems from the fact that in a large sample of agricultural commodities, De Ville, Dhaene and Sercu (2008) find that GARCH‐based hedges do not perform as well as OLS‐based ones and that we can avoid estimation error with such a simple rule. Our semi‐naive hedge ratios are driven from two conditions: omitting exposure to spot price and minimising the variance of the unexpected basis effects on the portfolio values. We find that, generally, (i) rebalancing helps; (ii) the two‐contract hedging rules do better than the one‐contract counterparts, even for standard delta hedges without rolling‐over; (iii) simplicity pays: the naive rules are the best one–for corn and wheat within the two‐contract group, the semi‐naive rule systematically beats the others and GARCH performs worse than OLS for either one‐contract or two‐contract hedges and for soybeans the traditional naive rule performs nearly as well as OLS. These conclusions are based on the tests on unconditional variance ( Diebold and Mariano, 1995 ) and those on conditional risk ( Giacomini and White, 2006 ).     

Hedging with futures: Efficacy of GARCH correlation models to European electricity markets

European electricity markets have been subject to a broad deregulation process in the last few decades. We analyse hedging policies implemented through different hedge ratios estimation. More specifically we compare naïve, ordinary least squares, and GARCH conditional variance and correlations models to test if GARCH models lead to higher variance reduction in a context of high time varying volatility as the case of electricity markets. Our results show that the choice of the hedge ratio estimation model is central on determining the effectiveness of futures hedging to reduce the portfolio volatility.