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.     

International portfolio diversification: Is there a role for the Middle East and North Africa?

We examine the issue of possible portfolio diversification benefits into seven Middle East and North African (MENA) stock markets. We construct international portfolios in dollars and local currencies. Ex ante weights are obtained by plugging five optimization models and two risk measures into a rolling block-bootstrap methodology. This allows us to derive 48 monthly rebalanced ex post portfolio returns. We analyze the out-of-sample performance based on Sharpe and Sortino ratios and the Jobson–Korkie statistic. Our results highlight outstanding diversification benefits in the MENA region, both in dollar and local currencies. Overall, we show that these under-estimated, under-investigated markets could attract more portfolio flows in the future.     

Exploring the diversification benefits of US international equity closed-end funds

Financial Markets and Portfolio Management - I use the simulation approach of Jobson and Korkie (J Portfolio Manag 7:70–74, 1981), combined with Michaud optimization (Michaud and Michaud,...     

A LIKELIHOOD RATIO TEST OF THE ZERO-BETA CAPM IN AUSTRALIAN EQUITY RETURNS

This paper tests the zero-beta CAPM with Australian equity returns, using the multivariate approach developed by Gibbons (1982). For the period 1958 to 1987, based on its asymptotic distribution, the likelihood ratio test (LRT) statistic indicates a strong rejection of the model when an equally weighted market index is used. However, small sample adjustments to the test suggested by Jobson and Korkie (1982) and by Shanken (1985) place the validity of this conclusion in some doubt. When a value weighted market index is used for the period 1974 to 1987, the tests reveal at least moderate support for the zero-beta CAPM.     

Performance Evaluation,Portfolio Selection,and HARA Utility

Absract

The main goal of this work is the generalization of the approach of Jobson and Korkie for funds performance evaluation. Therefore, the paper considers the portfolio selection problem of an investor who faces short sales restrictions when choosing among F different investment funds and assumes the investor’s utility function to be of the HARA type. A performance measure is developed and its relationship to previously proposed measures is discussed. Particular attention is given to the special case of cubic utility implying skewness preferences. Findings are illustrated by an empirical example.     

Portfolio performance of linear SDF models: an out-of-sample assessment

We evaluate linear stochastic discount factor models using an ex-post portfolio metric: the realized out-of-sample Sharpe ratio of mean–variance portfolios backed by alternative linear factor models. Using a sample of monthly US portfolio returns spanning the period 1968–2016, we find evidence that multifactor linear models have better empirical properties than the CAPM, not only when the cross-section of expected returns is evaluated in-sample, but also when they are used to inform one-month ahead portfolio selection. When we compare portfolios associated to multifactor models with mean–variance decisions implied by the single-factor CAPM, we document statistically significant differences in Sharpe ratios of up to 10 percent. Linear multifactor models that provide the best in-sample fit also yield the highest realized Sharpe ratios.     

Global style momentum

We first document the empirical regularity of significant style-level momentum returns in international data. Then we test some Barberis and Shleifer (2003) propositions regarding style momentum. One proposition holds that Sharpe ratios from style-level momentum strategies should be at least as large as stock-level momentum Sharpe ratios. We test for style-level momentum profitability in our sample of global markets and find some evidence of larger style momentum Sharpe ratios, especially within the value-growth style. However, most of the evidence favors stock momentum. The Barberis and Shleifer (2003) model also suggests that style momentum could be time-varying. Variables that effectively condition stock momentum are much less effective with style momentum.     

Time-variation,multiple testing,and the factor zoo

Bayesians circumvent the need for significance threshold correction when multiple testing and we recommend controlling the Type-S (sign), rather than the Type-1, error rate because it yields more reliable frequency properties for inferences. Our unified Bayesian framework, with theory-informed priors, identifies two breaks (2001 and 2008) in our 1980–2018 sample period. After each break the set of characteristics changes, and only market beta is selected in all regimes. In a portfolio application, the method generates significantly larger Sharpe ratios after transaction costs than a range of benchmark methods, including the same model that uses a Type-1 (not Type-S) error framework.     

Conducting event studies with Asia-Pacific security market data

We investigate the effectiveness of several well-known parametric and non-parametric event study test statistics with security price data from the major Asia-Pacific security markets. Extensive Monte Carlo simulation experiments with actual daily security returns data reveal that the parametric test statistics are prone to misspecification with Asia-Pacific returns data. Two non-parametric tests, a rank test [Corrado and Zivney (Corrado, C.J., Zivney, T.L., 1992, The specification and power of the sign test in event study hypothesis tests using daily stock returns, Journal of Financial and Quantitative Analysis 27(3), 465-478)] and a sign test [Cowan (Cowan, A.R., 1992, Non-parametric event study tests, Review of Quantitative Finance and Accounting 1(4), 343–358)] were the best performers overall with market model excess returns computed using an equal weight index.     

Comment on “Optimal portfolio selection in a value-at-risk framework”

This comment discusses some errors in [Journal of Banking and Finance 25 (2001) 1789]. Given the portfolio rate of return is normally distributed, the following can be inferred. First, taking expected portfolio return rate as the benchmark of value-at-risk (VaR), the risk–return ratio collapses to a multiple of the Sharpe index. However, using risk-free rate as the benchmark, then above inference does not hold. Second, whether the benchmark of VaR is expected portfolio return rate or the risk-free rate, the optimal asset allocations for maximizing the risk–return ratio and Sharpe index are identical.     

Extreme volumes and expected stock returns: Evidence from China's stock market

We examine the relation between extreme trading volumes and expected returns for individual stocks traded on the Shanghai Stock Exchange and the Shenzhen Stock Exchange over the July 1994–December 2000 interval. Contrasted with the evidence obtained from the US data [J. Finance 56 (2001) 877], our results show that stocks experiencing extremely high (low) volumes are associated with low (high) subsequent returns. Moreover, this extreme volume–return relation significantly co-varies with security characteristics like past stock performance, firm size, and book-to-market values. In particular, stocks with extreme volumes are related to poorer performance if they are past winners, large firms, and glamour stocks than if they are past losers, small firms, and value stocks, respectively. These results are robust to both daily and weekly samples as well as stock exchange sub-samples. Although the liquidity premium hypothesis of Amihud and Mendelson [J. Financ. Econ. 17 (1986) 223] provides a partial explanation for the extreme volume–return relation, our results fit better the behavioral hypothesis of Baker and Stein [J. Financ. Mark. 7 (2004) 271].     

Basket trading under co-integration with the logistic mixture autoregressive model

In this paper, we propose a co-integration model with a logistic mixture auto-regressive equilibrium error (co-integrated LMAR), in which the equilibrium relationship among cumulative returns of different financial assets is modelled by a logistic mixture autoregressive time series model. The traditional autoregression (AR) based unit root test (ADF test), used in testing co-integration, cannot give a sound explanation when a time series passes the ADF test. However, its largest root in the AR polynomial is extremely close to, but less than, one, which is most likely the result of a mixture of random-walk and mean-reverting processes in the time series data. With this background, we put an LMAR model into the co-integration framework to identify baskets that have a large spread but are still well co-integrated. A sufficient condition for the stationarity of the LMAR model is given and proved using a Markovian approach. A two-step estimating procedure, combining least-squares estimation and the Expectation-Maximization (EM) algorithm, is given. The Bayesian information criterion (BIC) is used in model selection. The co-integrated LMAR model is applied to basket trading, which is a widely used tool for arbitrage. We use simulation to assess the model in basket trading strategies with the statistical arbitrage feature in equity markets. Data from several sectors of the Hong Kong Hang Seng Index are used in a simulation study on basket trading. Empirical results show that a portfolio using the co-integrated LMAR model has a higher return than portfolios selected by traditional methods. Although the volatility in the return increases, the Sharpe ratio also increases in most cases. This risk–return profile can be explained by the shorter converging period in the co-integrated LMAR model and the larger volatility in the ‘mean-reverting’ regime.     

Discrete time hedging with liquidity risk

We study a discrete time hedging and pricing problem in a market with liquidity costs. Using Leland’s discrete time replication scheme [Leland, H.E., 1985. Journal of Finance, 1283–1301], we consider a discrete time version of the Black–Scholes model and a delta hedging strategy. We derive a partial differential equation for the option price in the presence of liquidity costs and develop a modified option hedging strategy which depends on the size of the parameter for liquidity risk. We also discuss an analytic method of solving the pricing equation using a series solution.     

Improvement in finite sample properties of the Hansen–Jagannathan distance test

Jagannathan and Wang [Jagannthan, R., and Wang, Z., “The conditional CAPM and the cross-section of expected returns.” Journal of Finance, 51 (1996), 3–53] derive the asymptotic distribution of the Hansen–Jagannathan distance (HJ-distance) proposed by Hansen and Jagannathan [Hansen, L.P., and Jagannathan, R., Assessing specific errors in stochastic discount factor models." Journal of Finance, 52 (1997), 557–590], and develop a specification test of asset pricing models based on the HJ-distance. While the HJ-distance has several desirable properties, Ahn and Gadarowski [Ahn, S.C., and Gadarowski, C., “Small sample properties of the GMM specification test based on the Hansen–Jagannathan distance.” Journal of Empirical Finance, 11 (2004), 109–132] find that the specification test based on the HJ-distance overrejects correct models too severely in commonly used sample size to provide a valid test. This paper proposes to improve the finite sample properties of the HJ-distance test by applying the shrinkage method [Ledoit, O., and Wolf, M., “Improved estimation of the covariance matrix of stock returns with an application to portfolio selection.” Journal of Empirical Finance, 10 (2003), 603–621] to compute its weighting matrix. The proposed method improves the finite sample performance of the HJ-distance test significantly.     

Market symmetry in time-changed Brownian models

In this paper we examine which Brownian subordination with drift exhibits the symmetry property introduced by Fajardo and Mordecki [2006. Quantitative Finance 6, 219–227]. We find that when the subordination results in a Lévy process, a necessary and sufficient condition for the symmetry to hold is that the drift must be equal to-1/2. Also, we derive explicit conditions to test whether the NIG, CGMY and Meixner processes are symmetric or not. Finally, we perform some tests with real financial data.     

Beyond Sharpe ratio: Optimal asset allocation using different performance ratios

As the assumption of normality in return distributions is relaxed, classic Sharpe ratio and its descendants become questionable tools for constructing optimal portfolios. In order to overcome the problem, asymmetrical parameter-dependent performance ratios have been recently proposed in the literature. The aim of this note is to develop an integrated decision aid system for asset allocation based on a toolkit of eleven performance ratios. A multi-period portfolio optimization up covering a fixed horizon is set up: at first, bootstrapping of asset return distributions is assessed to recover all ratios calculations; at second, optimal rebalanced-weights are achieved; at third, optimal final wealth is simulated for each ratios. Eventually, we make a robustness test on the best performance ratios. Empirical simulations confirm the weakness in forecasting of Sharpe ratio, whereas asymmetrical parameter-dependent ratios, such as the Generalized Rachev, Sortino–Satchell and Farinelli–Tibiletti ratios show satisfactorily robustness.     

Do Property‐Casualty Insurance Underwriting Margins Have Unit Roots?

A growing literature analyzes determinants of insurance prices using time series data on insurer underwriting margins. If the variables analyzed are stationary, conventional regression models may be appropriately used to test hypotheses. Based on pretests for a unit root, several studies have instead used co‐integration analysis to analyze the long‐run relationship between purportedly nonstationary underwriting margins and macroeconomic variables. We apply a battery of unit root tests to investigate whether underwriting margins are stationary under different assumptions concerning deterministic components in the data generating process (DGP). When linear and/or quadratic trends are included in the assumed DGPs, the tests reject the null hypothesis of a unit root for loss ratios, expense ratios, combined ratios, and economic loss ratios from 1953 through 1998 for many of the individual lines examined and for all lines combined. Consistent with prior work on whether macroeconomic variables have unit roots, a simulation of test power for underwriting margins during the sample period demonstrates that nonrejections of the null hypothesis of a unit root could easily reflect low power. The overall findings suggest that conventional regression methods can be used appropriately to analyze underwriting margins after controlling for deterministic influences and transforming any nonstationary regressors.     

Long-term international diversification of equities

Equity investors exhibit home bias although they can reduce risk with diversified global portfolios. We studied 118 years of data for 21 developed markets to investigate international diversification benefits for long-horizon equity investors. Investing equal proportions in all the markets would have increased Sharpe ratios only for investors in countries with low domestic ratios. Optimal global portfolios would have significantly increased Sharpe ratios for investors in all the countries. Allocating equal proportions to five optimal countries would have provided most of the maximum potential benefits of international diversification. Investors in countries with lower domestic Sharpe ratios would have benefited more from international diversification, primarily through risk reduction.     

Testing the unbiasedness hypothesis in the forward foreign exchange market: A specification analysis

This paper evaluates two popular regression methods of testing the unbiasedness hypothesis in the forward foreign exchange market. For the 30-day Canada/United States forward foreign exchange market, the evidence overwhelmingly indicates that it is inappropriate to treat the structure of the systematic and stochastic components of the test relations as constant over time. Hence, conclusions inferred from parameter significance testing based upon full-sample estimation can be very misleading. Accordingly, we argue for a specification analysis of the test relations, and more explicit modelling of market fundamentals.     

Portfolio performance evaluation with generalized Sharpe ratios: Beyond the mean and variance

This paper presents a theoretically sound portfolio performance measure that takes into account higher moments of distribution. This measure is motivated by a study of the investor’s preferences to higher moments of distribution within Expected Utility Theory and an approximation analysis of the optimal capital allocation problem. We show that this performance measure justifies the notion of the Generalized Sharpe Ratio (GSR) introduced by Hodges (1998). We present two methods of practical estimation of the GSR: nonparametric and parametric. For the implementation of the parametric method we derive a closed-form solution for the GSR where the higher moments are calibrated to the normal inverse Gaussian distribution. We illustrate how the GSR can mitigate the shortcomings of the Sharpe ratio in resolution of Sharpe ratio paradoxes and reveal the real performance of portfolios with manipulated Sharpe ratios. We also demonstrate the use of this measure in the performance evaluation of hedge funds.