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.     

Portfolio selection with mental accounts and delegation

Das et al. (2010) develop an elegant framework where an investor selects portfolios within mental accounts but ends up holding an aggregate portfolio on the mean-variance frontier. This investor directly allocates the wealth in each account among available assets. In practice, however, investors often delegate the task of allocating wealth among assets to portfolio managers who seek to beat certain benchmarks. Accordingly, we extend their framework to the case where the investor allocates the wealth in each account among portfolio managers. Our contribution is threefold. First, we provide an analytical characterization of the existence and composition of the optimal portfolios within accounts and the aggregate portfolio. Second, we present conditions under which such portfolios are not on the mean-variance frontier, and conditions under which they are. Third, we show that the aforementioned analytical characterization is also applicable within the framework of Das et al. and thus improves upon their numerical approach.     

Performance evaluation with high moments and disaster risk

Traditional performance evaluation measures do not account for tail events and rare disasters. To address this issue, we reinterpret the riskiness measures of Aumann and Serrano (2008) and Foster and Hart (2009) as performance indices. We derive the moment properties of these indices and their sensitivity to rare disasters and show that they are consistent with the asset pricing literature. As applications, we show that “anomalous” investment strategies such as “momentum” or investment in private equity lose much of their glamour when accounting for high moments and rare events. Furthermore, using the indices to select mutual funds results in desirable high-moment properties out of sample.     

Portfolio selection with mental accounts and background risk

Das et al. (2010) develop a model where an investor divides his or her wealth among mental accounts with motives such as retirement and bequest. Nevertheless, the investor ends up selecting portfolios within mental accounts and an aggregate portfolio that lie on the mean–variance frontier. Importantly, they assume that the investor only faces portfolio risk. In practice, however, many individuals also face background risk. Accordingly, our paper expands upon theirs by considering the case where the investor faces background risk. Our contribution is threefold. First, we provide an analytical characterization of the existence and composition of the optimal portfolios within accounts and the aggregate portfolio. Second, we show that these portfolios lie away from the mean–variance frontier under fairly general conditions. Third, we find that the composition and location of such portfolios can differ notably from those of portfolios on the mean–variance frontier.     

LEVERAGED BOND PORTFOLIO OPTIMIZATION UNDER UNCERTAINTY

This paper develops a multiperiod management model for balance sheets of bond assets and liabilities. The decision variables are the amounts to buy, sell, or hold for each bond maturity class and the amount to borrow or debt to be repurchased for each liability class. Decisions are made at the beginning of each period conditional on the revealed interest rates scenario. The investor's utility is maximized in a state-preference approach. The maturity structure of the initial holdings is an important component of the input parameters. The possible states of the world are described in terms of interest rate scenarios. The solution is subject to funds flow, inventory, liquidity, leverage, policy, and expiration constraints. The model leads to a large-scale linear programming model, with multi-indexed variables, that is solved with the Dantzig-Wolfe decomposition algorithm. A numerical application that was motivated by discussions with top management at the RepublicBank Trust Department is presented. The experiments suggest that optimal portfolios frequently have a barbell structure consisting of short and long maturities with few intermediate maturities.     

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.     

Decision-making under uncertainty – A field study of cumulative prospect theory

The presented research tests cumulative prospect theory (CPT, [Kahneman, D., Tversky, A., 1979. Prospect theory: An analysis of decision under risk. Econometrica 47, 263–291; Tversky, A., Kahneman, D., 1981. The framing of decisions and the psychology of choice. Science 211, 453–480]) in the financial market, using US stock option data. Option prices possess information about actual investors’ preferences in such a way that an exploitation of conventional option analysis, along with theoretical relationships, makes it possible to elicit investor preferences. The option data in this study serve for estimating the two essential elements of the CPT, namely, the value function and the probability weighting function. The main part of the work focuses on the functions’ simultaneous estimation under CPT original parametric specification. The shape of the estimated functions is found to be in line with theory. Comparing to results of laboratory experiments, the estimated functions are closer to linearity and loss aversion is less pronounced.     

Asymmetric dynamics of stock price continuation

This paper finds that the dynamics of stock price continuation are asymmetrical, in terms of both business cycles and past performances. During times of recession, stock returns are explained differently for past losers and winners; the level of credit quality dominates the return dynamics for extreme losers, while levels of information-based trading activity and information ambiguity contribute to winners’ medium-term returns. Such asymmetry is proposed as the source of insignificant profits achieved using conventional momentum strategies. On the other hand, in times of expansion, conventional asset pricing factors are found to affect stock returns with a dependence on the level of credit quality; this suggests that more profitable momentum strategies remain to be discovered.     

The determinants of household risky asset holdings: Australian evidence on background risk and other factors

We study the portfolio allocation decisions of Australian households using the relatively new Household, Income and Labour Dynamics in Australia (HILDA) Survey. We focus on household allocations to risky financial assets. Our empirical analysis considers a range of hypothesised determinants of these allocations. We find background risk factors posed by labor income uncertainty and health risk are important. Credit constraints and observed risk preferences play the expected role. A positive age gradient is identified for risky asset holdings and home-ownership is associated with greater risky asset holdings. A unifying theme for many of our empirical findings is the important role played by financial awareness and knowledge in determining risky asset holdings. Many non-stockholding households appear to lack the experience and financial literacy that might enable them to benefit from direct investment in stocks.     

Preferred risk habitat of individual investors

The preferred risk habitat hypothesis, introduced here, is that individual investors select stocks whose volatilities are commensurate with their risk aversion. The data, 1995–2000 holdings of over 20,000 clients at a large German broker, are consistent with the predictions of the hypothesis: the returns of stocks within each portfolio have remarkably similar volatilities, when stocks are sold they are replaced by stocks of similar volatilities, and the more risk-averse customers indeed hold less volatile stocks. Greater volatility specialization is associated with lower Sharpe ratios, primarily because more specialized investors hold fewer stocks and thereby expose themselves to more unsystematic risk.     

THE MEAN‐GINI EFFICIENT PORTFOLIO FRONTIER

A main advantage of the mean‐variance (MV) portfolio frontier is its simplicity and ease of derivation. A major shortcoming, however, lies in its familiar restrictions, such as the quadraticity of preferences or the normality of distributions. As a workable alternative to MV, we present the mean‐Gini (MG) efficient portfolio frontier. Using an optimization algorithm, we compute MG and mean‐extended Gini (MEG) efficient frontiers and compare the results with the MV frontier. MEG allows for the explicit introduction of risk aversion in building the efficient frontier. For U.S. classes of assets, MG and MEG efficient portfolios constructed using Ibbotson (2000) monthly returns appear to be more diversified than MV portfolios. When short sales are allowed, distinct investor risk aversions lead to different patterns of portfolio diversification, a result that is less obvious when short sales are foreclosed. Furthermore, we derive analytically the MG efficient portfolio frontier by restricting asset distributions. The MG frontier derivation is identical in structure to that of the MV efficient frontier derivation. The penalty paid for simplifying the search for the MG efficient frontier is the loss of some information about the distribution of assets.     

EVIDENCE ON THE COMPENSATION OF PORTFOLIO MANAGERS

We surveyed 396 portfolio managers about the structure of their compensation. Overall, more compensation packages are subjective/discretionary than objective/formula based. Firm success factors such as firm profitability have more effect on bonuses than do client success factors such as investment performance. Differences in the structure of compensation across firms, clients, job types, and manager characteristics reflect likely differences in the underlying contracting environments, especially differences in the difficulty of monitoring performance and exerting control.     

Prospect theory and trading patterns

Reference dependence, loss aversion, and risk seeking for losses together comprise the preference-based component of prospect theory that sets its value function apart from the standard risk-aversion model. Using an elasticity analysis, we show that this distinctive preference component serves to underpin negative-feedback trading propensities, but cannot manifest itself in behavior directly or holistically at the individual-choice level. We then propose and demonstrate that the market interaction between prospect-theory investors and regular CRRA investors allows this preference component to dominate in equilibrium behavior and hence helps to reestablish the intuitive link between prospect-theory preferences and negative-feedback trading patterns. In the model, the interaction also reconciles the contrarian behavior of prospect-theory investors with asymmetric volatility and short-term return reversal. The results suggest that prospect-theory preferences can lead investors to behave endogenously as contrarian noise traders in the market interaction process.     

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.     

Individual investor perceptions and behavior during the financial crisis

Combining monthly survey data with matching trading records, we examine how individual investor perceptions change and drive trading and risk-taking behavior during the 2008–2009 financial crisis. We find that investor perceptions fluctuate significantly during the crisis, with risk tolerance and risk perceptions being less volatile than return expectations. During the worst months of the crisis, investors’ return expectations and risk tolerance decrease, while their risk perceptions increase. Towards the end of the crisis, investor perceptions recover. We document substantial swings in trading and risk-taking behavior that are driven by changes in investor perceptions. Overall, individual investors continue to trade actively and do not de-risk their investment portfolios during the crisis.