Asset–liability modelling and pension schemes: the application of robust optimization to USS

This paper uses a novel numerical optimization technique – robust optimization – that is well suited to solving the asset–liability management (ALM) problem for pension schemes. It requires the estimation of fewer stochastic parameters, reduces estimation risk and adopts a prudent approach to asset allocation. This study is the first to apply it to a real-world pension scheme, and the first ALM model of a pension scheme to maximize the Sharpe ratio. We disaggregate pension liabilities into three components – active members, deferred members and pensioners, and transform the optimal asset allocation into the scheme's projected contribution rate. The robust optimization model is extended to include liabilities and used to derive optimal investment policies for the Universities Superannuation Scheme (USS), benchmarked against the Sharpe and Tint, Bayes–Stein and Black–Litterman models as well as the actual USS investment decisions. Over a 144-month out-of-sample period, robust optimization is superior to the four benchmarks across 20 performance criteria and has a remarkably stable asset allocation – essentially fix-mix. These conclusions are supported by six robustness checks.     

Jumping over a low hurdle: personal pension fund performance

This paper provides a comprehensive analysis of the annual and of the long-term performance of personal pension funds relative to their Primary Prospectus Benchmarks (PPBs) and T-bills. The study covers 9659 personal pension funds from across all 30 ABI investment sectors that operated in the UK in the 1980–2009 period. Of these, 4531 pension funds are compared against their PPBs. The performance measured by ordinary excess returns over the UK T-bills and over PPBs, as well as the Sharpe ratio, Sharpe ratio adjusted for skewness and kurtosis, Sortino ratio in relation to the UK T-bills and PPBs, and the Modigliani–Modigliani measure are calculated for arithmetic, geometric and log returns. We find convincing evidence that pension funds lack challenging long-term performance targets. We argue that the existing PPBs are easy to outperform given that funds are allowed to diversify in assets not included in their PPBs. We discuss policy implications of our findings.     

Investing in equity mutual funds

We construct optimal portfolios of equity funds by combining historical returns on funds and passive indexes with prior views about asset pricing and skill. By including both benchmark and nonbenchmark indexes, we distinguish pricing-model inaccuracy from managerial skill. Modest confidence in a pricing model helps construct portfolios with high Sharpe ratios. Investing in active mutual funds can be optimal even for investors who believe managers cannot outperform passive indexes. Optimal portfolios exclude hot-hand funds even for investors who believe momentum is priced. Our large universe of funds offers no close substitutes for the Fama-French and momentum benchmarks.     

Drivers of differences in performance of ESG-focused funds relative to their underlying benchmarks

Several studies have examined whether environmental, social, and governance (ESG) focused funds outperform their benchmarks. While these studies vary in their methods and scope, their findings indicate that, at a minimum, these funds do not underperform their benchmarks on a risk-adjusted basis. This study is designed to further contribute to this body of research by analyzing the performance of the Jantzi Social Index (JSI) relative to its underlying benchmark, the TSX 60, and to gain insight into the possible factors that drive their performance differences. Our findings indicate that JSI's performance differential is driven (primarily) by the higher weight that JSI attaches to companies with higher net ESG scores and not (necessarily) by its superior asset-selection ability. As the regulators globally move toward making ESG disclosure mandatory, these findings become particularly relevant.     

Benchmark Invariancy,Seasonality and APM-Free Portfolio Performance Measures

The Jobson-Korkie (1981) Z score and the positive period weighting (PPW) score of Grinblatt and Titman (1989) are applied to various benchmarks of market and mimicking portfolios to study the benchmark invariancy problem. Significantly different portfolio performance inferences are found for a sample of 146 equity mutual funds depending on the mean-variance efficiency of the portfolio benchmarks (mimicking portfolios versus market indices). Portfolio performance inferences are affected significantly by the number of factors, nonsynchronous trading adjustment, and the sizes of the firms used for factor extraction. The returns of the portfolio benchmarks exhibit significant monthly seasonalities, which, in turn, significantly influence mutual fund performance inferences.     

UK equity mutual fund alphas make a comeback

In this study, we re-visit the performance of 887 active UK equity mutual funds using a new approach proposed by Angelidis, Giamouridis, and Tessaromatis. The authors argue that mutual funds stock selection is driven by the benchmark index, so if the benchmark generates alpha, there will be a bias in interpretation of manager's stock-picking ability. In their model, the alpha of a fund is adjusted by the benchmark's alpha. By applying this method, we eliminate bias inflicted by the persistently negative alphas of FTSE 100 Index in the period 1992–2013. We find that adjusted Fama–French and Carhat alphas of UK equity mutual funds are higher than those implied by the standard three- and four-factor models and are overall positive, contrary to most of the existing literature on UK fund performance. This result is consistent across funds' investment styles and robust to the use of FTSE Small Cap as benchmark for a sub-sample of small cap funds.     

Performance evaluation and self-designated benchmark indexes in the mutual fund industry

Almost one-third of actively managed, diversified U.S. equity mutual funds specify a size and value/growth benchmark index in the fund prospectus that does not match the fund's actual style. Nevertheless, these “mismatched” benchmarks matter to fund investors. Performance relative to the specified benchmark is a significant determinant of a fund's subsequent cash inflows, even controlling for performance measures that better capture the fund's style. These incremental flows appear unlikely to be rational responses to abnormal returns. The evidence is consistent with the notion that mismatched self-designated benchmarks result from strategic fund behavior driven by the incentive to improve flows.     

Benchmarking benchmarks: measuring characteristic selectivity using portfolio holdings data

This study proposes methodological adjustments to the widely adopted performance benchmarking methodology of Daniel et al. (1997 ) as a means of improving the precision of alpha measurement for active equity fund managers. We achieve this by considering the monthly updating of characteristic benchmarks and to ensure neutrality to the Standard & Poor's/Australian Stock Exchange 300 index. Applying this benchmark to a representative sample of active Australian equity funds and simulated passive portfolios that mimic fund manager‐style characteristics, we find statistically different and lower tracking error compared with using the standard characteristic benchmark methodology. We also find evidence that the modified benchmark statistically infers an alpha closer to zero compared with the standard benchmark methodology. Our findings suggest that improved specifications of characteristic benchmarks represent better methods in quantifying fund manager skill.     

Performance persistence of closed-end funds

Studies of performance persistence of closed-end funds (CEFs) use two measures of persistence; autocorrelation and rank correlation of performance. The autocorrelation measure offers limited information because it cannot separate persistence relative to the market and to the industry. The rank correlation measure is generally applied to two periods, disregarding multi-period persistence. We investigate performance persistence of CEFs in terms of both market price return and net asset value return using contingency tables and multiple regression models. Jensen’s alpha and the Sharpe ratio are used as measures of risk-adjusted performance. We test three hypotheses: (i) CEFs performing better than the industry median will do so persistently, (ii) CEFs outperform the market persistently; and (iii) performance persistence can be partly explained by dividend yield. The findings are fivefold. First, the number of persistent years varies with the models used to calculate risk-adjusted performance. Second, with 4-index unconditional beta fixed variance model, CEFs persistently beat their industry for six out of 10 years in terms of both market price return and net asset value return. Third, with a 4-index unconditional beta fixed variance model, we find performance persistence relative to market for 6 and 7 years, out of the 10 years considered, in terms of market price return and net asset value return, respectively. Fourth, the disaggregate sample tests show that performance of municipal bond funds is more persistent than equity funds and taxable bond funds. Fifth, dividend patterns can partially explain persistence with liquidity as control.     

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.     

Risk Reduction and Mean-Variance Analysis: An Empirical Investigation

Abstract:  I examine the performance of global minimum variance (GMV) and minimum tracking error variance (TEV) portfolios in UK stock returns using different models of the covariance matrix. I find that both GMV and TEV portfolios deliver portfolio risk reduction benefits in terms of significantly lower volatility and tracking error volatility relative to passive benchmarks for every model of the covariance matrix used. However, the GMV (TEV) portfolios do not provide significantly superior Sharpe (1966) (adjusted Sharpe) performance relative to passive benchmarks except for the restricted GMV portfolios. I find that a number of alternative covariance matrix models can improve the performance of the restricted TEV portfolio formed using the sample covariance matrix but not the restricted GMV portfolio. I also find that simpler covariance matrix models perform as well as the more sophisticated models.     

The Role of the Auditor in Modern Society: An Exploratory Essay

This paper examines competing proprietary and political cost arguments for incentives facing managers of different types of Australian and UK pension fund, to voluntarily disclose pension liability information in annual reports sent to their participants. For Australian defined benefit pension funds, the disclosure reveals the fund's actuarial surplus or deficit, which conveys information to participants about the pension fund's ability to generate future cash flows. Tests are conducted on the voluntary reporting practices of a sample of 119 Australian and 100 UK pension funds, using variables which prior research suggests affects their financial valuation and performance. The empirical results support predictions that managerial discretionary disclosure carries proprietary cost implications for Australian defined benefit pension funds, as proxied by their investment risk and funding ratio, and political cost implications for Australian defined contribution and UK defined benefit pension funds, as proxied by their size.     

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.     

Benchmarking the performance of recommended allocations to equities,bonds, and cash by international investment houses

We conduct performance tests of the recommended asset allocations made by a panel of international investment houses (the “Houses”) from 1982 through 2005. We compare the returns and Sharpe Ratios from the recommended-weight portfolio against those of several benchmark portfolios and to a set of 10,000 returns and Sharpe Ratios from randomly shuffled-weight and shuffled-weight change portfolios. We find that the Houses generally fail to outperform the benchmarks. The shuffled-weight change benchmark exhibits a robust “style-preserving” property in that the average portfolio standard deviation is nearly equal to the portfolio standard deviation from the actual recommended weights.     

Unveiling the embedded coherence in divergent performance rankings

This paper focuses on analyzing functional relationships among performance measures, centered on the adjusted differential risk premium between the asset and the benchmark and on Sharpe-1994 ratio. First, we develop a risk normalization procedure for variance and Aumann–Serrano riskiness which turns contradictory rankings into coherent ones, and combines the effects of correlation and outliers into the analysis. On this basis, we deduce functional connections among performance measures, arriving at a new indicator which expresses performance as the addition of three effects due to Sharpe ratio, correlation and outliers. We show it is a strictly increasing function of Homm–Pigorsch ratio.     

Active fund management: Global asset allocation funds

We examine the value of active fund management of global asset allocation funds. We use unique daily data and a modified Sharpe's [Sharpe, W., 1992. Asset allocation: management style and performance measurement. Journal of Portfolio Management 18, 7–19] Return-Based Style Analysis method to create a three-index model. We introduce an alternative method derived from Sharpe to calculate attribution returns that measure active fund management performance. Our results suggest that a sample of global asset allocation funds add value for investors. To determine the estimation ability of our model and the implications for estimated asset allocation decisions, we report historical and cross-sectional root mean square errors, which give positive indications of reliability.     

PORTFOLIO OPTIMIZATION UNDER TRACKING ERROR AND WEIGHTS CONSTRAINTS

The performance of active portfolio managers who must comply with a weights constraint is often assessed against a benchmark. The weights constraint is common as the funds are committed by their own prospectus to a minimum (or maximum) portfolio concentration. We characterize the optimal asset allocation and analyze the implications of the weights constraint on the manager's performance and on the relevance of the information ratio. We obtain that because of the weights constraint, at the optimum, the information ratio often decreases when the manager is free to deviate more from the benchmark.     

Persistent performance in the mutual fund market: Tests with funds and investment advisers

Recent studies of mutual funds have concluded that there is some evidence of superior performance. We test for the existence of superior performance and its persistence with mutual funds and mutual fund investment advisers on a data set of monthly returns from 1979 to 1989 for 1,387 mutual funds grouped by 243 advisers. We find no evidence of superior performance or its persistence but we do find significant evidence of persistence of inferior performance. Consistent with previous studies our findings depend on the benchmark chosen, with multiple benchmarks producing a larger degree of inferior performance.     

Persistent Doubt: An Examination of Hedge Fund Performance

We examine whether performance persistence is suspicious. Top quintile portfolios formed on the Sharpe ratio, alpha, and information ratio persistently outperform similarly constructed mediocre third quintile portfolios throughout our sample period, but performance is more modest and less persistent when portfolios are formed on the excess manipulation‐proof performance measure (EMPPM). By selecting funds formed on ranking by Sharpe and information ratios, investors also select funds that have persistently doubtful performance according to the doubt ratio. In contrast, portfolios formed on alphas and especially the EMPPM have much less excess and persistent doubt.     

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.