Cross-hedging foreign currency risk: Empirical evidence from an error correction model

In this article, the traditional price change hedge ratio estimation method is extended by applying the theory of cointegration in the case of cross-hedging of spot exchange risk of the Belgian franc (BF), the Italian lira (IL), and the Dutch guilder (NG) with U.S. Dollar Index futures contracts. Previous studies ignore the last period's equilibrium error and short-run deviations. The findings of this study indicate that the hedge ratio estimated by the error correction method is superior to that obtained from the traditional method, as evidenced by the likelihood ratio test and out-of-sample forecasts. Hedgers will be able to control the risk of their portfolios more effectively at a lower cost.     

HEDGING WITH INTERNATIONAL STOCK INDEX FUTURES: AN INTERTEMPORAL ERROR CORRECTION MODEL

In this paper we extend the traditional price change hedge ratio estimation method by applying the theory of cointegration to hedging with stock index futures contracts for France (CAC 40), the United Kingdom (FTSE 100), Germany (DAX), and Japan (NIKKEI). Previous studies ignore the last period's equilibrium error and short-run deviations. The findings of this study indicate that the hedge ratios obtained from the error correction method are superior to those obtained from the traditional method as evidenced by the likelihood ratio test and out-of-sample forecasts. Using the procedures developed in this paper, hedgers can control the risk of their portfolios more effectively at a lower cost.     

Spot asset carry cost rates and futures hedge ratios

Since the 1970s, futures hedge ratios have traditionally been calculated ex-post via economically structure-less statistical analyses. This paper proposes an ex-ante, more efficient, computationally simpler, general “carry cost rate” hedge ratio. The proposed hedge ratio is biased, but its bias is readily mitigatable via a stationary Bias Adjustment Multiplier (BAM). The 2-part intuition for the BAM and its stationarity is as follows. First, the paper reasons that the “traditional” hedge ratio should uncover the carry cost rate and shows that it does, albeit inefficiently. Then, since both the “traditional” and “carry cost rate” hedge ratios are driven by the carry cost rate, it may be that their ratio (for implementation in the same prior periods) is stationary and useful as an ex-ante BAM for the “carry cost rate” hedge ratio; the paper tests these conjectures and finds support for both. Specifically, the paper shows that the “bias-adjusted carry cost rate” hedge ratio, defined as the average product of the ex-post BAMs from prior periods and the current ex-ante “carry cost rate” hedge ratio, has higher hedge-effectiveness than that for either the “traditional” or “naive” benchmark hedge ratios in diverse real and simulated markets.

     

TREASURY BILL FUTURES AS A HEDGING TOOL: A RISK-RETURN APPROACH

The primary purpose of this study is to measure the hedging performance of Treasury Bill Futures on a risk-return basis. A theoretical model is presented and hedging effectiveness is tested using T-Bill cash and futures data. Successful hedging depends critically upon the ability to determine the optimal hedge ratio. The results also indicate that the traditional one-to-one hedge outperforms the more sophisticated hedge ratio models; however, even here the risk-return benefits of hedging are minimal.     

Using the short-lived arbitrage model to compute minimum variance hedge ratios: application to indices,stocks and commodities

The short-lived arbitrage model has been shown to significantly improve in-sample option pricing fit relative to the Black–Scholes model. Motivated by this model, we imply both volatility and virtual interest rates to adjust minimum variance hedge ratios. Using several error metrics, we find that the hedging model significantly outperforms the traditional delta hedge and a current benchmark hedge based on the practitioner Black–Scholes model. Our applications include hedges of index options, individual stock options and commodity futures options. Hedges on gold and silver are especially sensitive to virtual interest rates.     

Multivariate GARCH hedge ratios and hedging effectiveness in Australian futures markets

We use the All Ordinaries Index and the corresponding Share Price Index futures contract written against the All Ordinaries Index to estimate optimal hedge ratios, adopting several specifications: an ordinary least squares‐based model, a vector autoregression, a vector error‐correction model and a diagonal‐vec multivariate generalized autoregressive conditional heteroscedasticity model. Hedging effectiveness is measured using a risk‐return comparison and a utility maximization method. We find that time‐varying generalized autoregressive conditional heteroscedasticity hedge ratios perform better than constant hedge ratios in terms of minimizing risks, but when return effects are also considered, the utility‐based measure prefers the ordinary least squares method in the in‐sample hedge, whilst both approaches favour the conditional time‐varying multivariate generalized autoregressive conditional heteroscedasticity hedge ratio estimates in out‐of‐sample analyses.     

A Futures Duration-Convexity Hedging Method

A duration-based hedge ratio is the conventional method to hedge against price changes of a fixed-income instrument. However, the relationship between bond prices and interest rates is nonlinear, creating a convexity effect. Moreover, term structure changes often are nonparallel in nature, which causes imperfect hedges for the duration-based hedging model. One solution to these problems is to dynamically change the duration-based hedge ratio; however, this procedure is costly and is not effective when jumps in prices occur. A superior solution is to develop a two-instrument hedge ratio that simultaneously hedges both duration and convexity effects. This paper first presents such a two-instrument hedge ratio and then we examine its effectiveness. The simulation results show that this duration-convexity hedge ratio is vastly superior to alternative hedge ratio methods for both simple and complex changes in the term structure.     

Comparing Trading Performance of the Constant and Dynamic Hedge Models: A Note

The constant and dynamic hedge models, with the presence of transaction costs are compared for the Share Price Index futures contract trading on the Sydney Futures Exchange. The optimal hedge ratio is estimated by using a dynamic, bivariate two-stage model for the return equation with a dynamic GARCH error structure for the conditional hedge ratios. When portfolio projections are compared based on their profit positions (net of transaction costs), the GARCH hedge model dominates the next best competitor in terms of trading profit.     

Comparing the Effectiveness of Traditional and Time Varying Hedge Ratios Using New Zealand and Australian Debt Futures Contracts

We apply cointegration methodology to the New Zealand and Australian 90-day, three-year and 10-year debt and futures markets. We compare traditional methods of calculating hedge ratios with those computed by using univariate and multivariate error correction models. We use out-of-sample forecasting to determine which approach is the most effective. Contrary to recent research, our results show that univariate and multivariate error correction models do not outperform more traditional methods of constructing hedges.     

Performance hypothesis testing with the Sharpe ratio: The case of hedge funds

As recent research highlights that the Sharpe ratio has a decision theoretic foundation even in the case of asymmetric or fat-tailed excess returns and thus is adequate even for the evaluation of hedge funds, this note provides the first Sharpe ratio based performance analysis of the hedge fund market. Furthermore, it addresses the important practical question whether the choice of hypothesis test used to statistically compare Sharpe ratios can influence an investor’s hedge fund selection process. Our key findings are as follows: (i) Only a small fraction of hedge funds in our large dataset can significantly outperform passive investments in corresponding hedge fund indices. (ii) Especially in the presence of autocorrelated or skewed excess returns, the traditional test of Jobson and Korkie, 1981, Memmel, 2003 tends to overstate the number of significant outperformers and thus provides potentially misleading information for investors. Decision makers are advised to use the bootstrap test of Ledoit and Wolf (2008) allowing robust and more reliable inference.     

Measuring minimum variance hedging effectiveness: Traditional vs. sophisticated models

This study investigates whether the more sophisticated GARCH based models are better minimum variance hedging strategies than the less sophisticated regression based traditional models. The findings of the study suggest that the traditional models that directly estimate the optimal hedge ratio significantly outperform the more sophisticated models that indirectly estimate the optimal hedge ratio based on timevarying variance-covariance parameters. Although, the sophisticated models seem to have more theoretical appeal, the higher estimation and misspecification errors of these models reduce their hedging effectiveness, making them inferior to the traditional models.     

The use and abuse of the hedging effectiveness measure

Ederington (1979) proposed an effectiveness measure for futures hedging. Since then, this measure has been widely adopted in the literature to compare different hedge ratios against the OLS (ordinary least squares) hedge ratio. This note attempts to demonstrate this application is inappropriate. Ederington hedging effectiveness is only useful for measuring the risk reduction effect of the OLS hedge ratio. It does not apply to other hedge ratios and therefore should not serve as a criterion to compare different hedge strategies against the OLS strategy. A strict application of this measure almost always leads to an incorrect conclusion stating that the OLS hedge ratio is the best hedging strategy.     

Determination of Optimal Hedging Strategy for Index Futures: Evidence from Turkey

This paper aims to determine optimal hedge strategy for the Istanbul Stock Exchange (ISE)-30 stock index futures in Turkey by comparing hedging performance of constant and time-varying hedge ratios under mean-variance utility criteria. We employ standard regression and bivariate GARCH frameworks to estimate constant and time-varying hedge ratios respectively. The Turkish case is particularly challenging since Turkey has one of the most volatile stock markets among emerging economies and the turnover ratio as a measure of liquidity is very high for the market. These facts can be considered to highlight the great risk and, therefore, the extra need for hedging in the Istanbul Stock Exchange (ISE). The empirical results from the study reveal that the dynamic hedge strategy outperforms the static and the traditional strategies.     

Risk measurement distortion: an improved model of return smoothing

We examine the effects of smoothed hedge fund returns on standard deviation, skewness, and kurtosis of return and on correlation of returns using a MA(2)-GARCH(1,1)-skewed-t representation instead of the traditional MA(2) model employed in the literature. We present evidence that our proposed representation is more consistent with the behavior of hedge fund returns than the traditional MA(2) representation and that the traditional method tends to overstate the degree of smoothing observed in hedge fund returns. We examine methods for correcting the distortive effects of smoothing using our representation.     

Minimum variance hedging when spot price changes are partially predictable

In many markets, changes in the spot price are partially predictable. We show that when this is the case: (1) although unbiased, traditional regression estimates of the minimum variance hedge ratio are inefficient, (2) estimates of the riskiness of both hedged and unhedged positions are biased upward, and (3) estimates of the percentage risk reduction achievable through hedging are biased downward. For natural gas cross hedges, we find that both the inefficiency and bias are substantial. We further find that incorporating the expected change in the spot price, as measured by the futures-spot price spread at the beginning of the hedge, into the regression results in a substantial increase in efficiency and reduction in the bias.     

Zur Risikoanalyse von Hedgefonds: Ein datenanalytischer Ansatz

Hedge fund returns have a number of specific features compared to traditional investments which result in problems when applying traditional methods of risk analysis (Markowitz portfolio selection theory, Sharpe Ratio, value at risk calculation based on normal returns). These problems have to be considered adequately by insurance companies when constructing internal risk models and performing risk management for hedge funds in their investment.The present paper has its focus on the departure of hedge fund returns from the normality hypothesis, especially with respect to the statistical quantities skewness and kurtosis (fat tail problem). A statistical analysis of hedge fund index returns gives evidence that the majority of hedge fund returns show substantial departures from normality. In addition, the analysis shows that hedge fund returns are adequately represented by the family of GH-distributions developed in exploratory data analysis. Following this result a risk analysis of hedge fund strategies is performed on the basis of the GH-value at risk.     

Testing for constant hedge ratios in commodity markets: a multivariate GARCH approach

We develop a new multivariate generalized ARCH (GARCH) parameterization suitable for testing the hypothesis that the optimal futures hedge ratio is constant over time, given that the joint distribution of cash and futures prices is characterized by autoregressive conditional heteroskedasticity (ARCH). The advantage of the new parameterization is that it allows for a flexible form of time-varying volatility, even under the null of a constant hedge ratio. The model is estimated using weekly corn prices. Statistical tests reject the null hypothesis of a constant hedge ratio and also reject the null that time variation in optimal hedge ratios can be explained solely by deterministic seasonality and time to maturity effects.     

Should hedge funds be cautious reporting high returns?

In a recent article, Schuster and Auer (2012) show that fund managers with a certain positive performance need to be aware of the fact that too high prospective excess returns can lower the empirical Sharpe ratio of their funds. In this note, we investigate the empirical relevance of this effect. We analyse whether hedge funds being evaluated on the basis of the Sharpe ratio negatively influence their performance by reporting too high returns. Our results show that a economically significant number of hedge funds listed in the CISDM hedge fund database has at least once reported a high return causing this effect.     

Hedge fund allocation: Evaluating parametric and nonparametric forecasts using alternative portfolio construction techniques

We propose a model for constructing Asian funds of hedge funds. We compare the accuracy of forecasts of hedge fund returns using an ordinary least squares (OLS) regression model, a nonparametric regression model, and a nonlinear nonparametric model. We backtest to assess these forecasts using three different portfolio construction processes: an “optimized” portfolio, an equally-weighted portfolio, and the Kelly criterion-based portfolio. We find that the Kelly criterion is a reasonable method for constructing a fund of hedge funds, producing better results than a basic optimization or an equally-weighted portfolio construction method. Our backtests also indicate that the nonparametric forecasts and the OLS forecasts produce similar performance at the hedge fund index level. At the individual fund level, our analysis indicates that the OLS forecasts produce higher directional accuracy than the nonparametric methods but the nonparametric methods produce more accurate forecasts than OLS. In backtests, the highest information ratio to predict hedge fund returns is obtained from a combination of the OLS regression with the Fung–Hsieh eight-factor variables as predictors using the Kelly criterion portfolio construction method. Similarly, the highest information ratio using forecasts generated from a combination of the nonparametric regression using the Fung–Hsieh eight-factor model variables is achieved using the Kelly criterion portfolio construction method. Simulations using risk-adjusted total returns indicate that the nonparametric regression model generates superior information ratios than the analogous backtest results using the OLS. However, the benefits of diversification plateau with portfolios of more than 20 hedge funds. These results generally hold with portfolio implementation lags up to 12 months.     

Does the choice of performance measure influence the evaluation of hedge funds?

The Sharpe ratio is adequate for evaluating investment funds when the returns of those funds are normally distributed and the investor intends to place all his risky assets into just one investment fund. Hedge fund returns differ significantly from a normal distribution. For this reason, other performance measures for hedge fund returns have been proposed in both the academic and practice-oriented literature. In conducting an empirical study based on return data of 2763 hedge funds, we compare the Sharpe ratio with 12 other performance measures. Despite significant deviations of hedge fund returns from a normal distribution, our comparison of the Sharpe ratio to the other performance measures results in virtually identical rank ordering across hedge funds.