Narrow Results

This paper provides a risk framework for fiduciaries by considering using a core-satellite approach to investing. While the article mainly covers the additional risk measurement techniques, which are needed when investing in hedge funds, its recommendations are also relevant for other investments that have default, devaluation, and/or liquidity risks associated with them. Also, while the article's focus is on quantitative techniques, we note that a fiduciary must also understand the economic basis for each investment's returns.

We study the Markowitz mean-variance portfolio selection model under three types of regularizations: single-norm regularizations on individual stocks, mixed-norm regularizations on stock groups, and composite regularizations that combine the single-norm and mixed-norm regularizations. With mixed-norm regularizations incorporated, our model can accomplish group and stock selections simultaneously. Our empirical results using both US and global equity market data show that compared to the classical mean-variance portfolio, almost all regularized portfolios have better out-of-sample risk-adjusted performance measured by Sharpe ratio. In addition, stock selection and group screening accomplished by adding ${\ell }_1$ and ${\ell }_{2,1}$ regularizations respectively can lead to decreased volatility, turnover rate, and leverage ratio. Yet there are instances in which diversifying across different groups is more favorable, depending on the grouping methods. Moreover, we find a positive correlation between portfolio turnover and leverage. Heavily leveraged portfolios also have high turnover rates and thus high transaction costs.

Traders are compensated by bonuses, in addition to their basic salary. However, little is known about how to optimally reward a trader. In this article we build a framework for the study of this problem and explore a variety of possible compensation structures.

This paper deals with the problem of determining the correct risk measure for options in a Black–Scholes (BS) framework when time is discrete. For the purposes of hedging or testing simple asset pricing relationships previous papers used the "local", i.e., the continuous-time, BS beta as the measure of option risk even over discrete time intervals. We derive a closed-form solution for option betas over discrete return periods where we distinguish between "covariance betas" and "asset pricing betas". Both types of betas involve only simple Black–Scholes option prices and are thus easy to compute. However, the theoretical properties of these discrete betas are fundamentally different from those of local betas. We also analyze the impact of the return interval on two performance measures, the Sharpe ratio and the Treynor measure. The dependence of both measures on the return interval is economically significant, especially for OTM options.

We analyze portfolio strategies which are locally optimal, meaning that they maximize the Sharpe ratio in a general continuous time jump-diffusion framework. These portfolios are characterized explicitly and compared to utility based strategies. We show that in the presence of jumps, maximizing the Sharpe ratio is generally inconsistent with maximizing expected utility, in the sense that a utility maximizing individual will not choose a strategy which has a maximal Sharpe ratio. This result will hold unless markets are incomplete or jump risk has no risk premium. In case of an incomplete market we show that the optimal portfolio of a utility maximizing individual may "accidentally" have maximal Sharpe ratio. Furthermore, if there is no risk premium for jump risk, a utility maximizing investor may select a portfolio having a maximal Sharpe ratio, if jump risk can be hedged away. We note that uncritical use of the Sharpe ratio as a performance measure in a world where asset prices exhibit jumps may lead to unreasonable investments with positive probability of ruin.

In recent years, researchers and practitioners have invested considerable effort in the development of new investment fund performance measures that account for mean, variance and the higher moments of the return distribution. To justify the application and necessity of the new performance measures in decision-making, some authors argue that the theoretical conditions required to use the Sharpe ratio are violated by high skewness and kurtosis in empirical asset return data. In this note, we highlight that high levels of skewness and kurtosis and even cross-sectional variations in skewness and kurtosis do not allow a decision-theoretic rejection of the Sharpe ratio. However, we also point out that while it is hard to discard the measure on decision-theoretic grounds, it can be challenged on technical grounds because it has several undesirable properties.

The question addressed in this paper is the performance of the optimal strategy, and the impact of partial information. The setting we consider is that of a stochastic asset price model where the trend follows an unobservable Ornstein–Uhlenbeck process. We focus on the optimal strategy with a logarithmic utility function under full or partial information. For both cases, we provide the asymptotic expectation and variance of the logarithmic return as functions of the signal-to-noise ratio and of the trend mean reversion speed. Finally, we compare the asymptotic Sharpe ratios of these strategies in order to quantify the loss of performance due to partial information.

This paper introduces a new functional optimization approach to portfolio optimization problems by treating the unknown weight vector as a function of past values instead of treating them as fixed unknown coefficients in the majority of studies. We first show that the optimal solution, in general, is not a constant function. We give the optimal conditions for a vector function to be the solution, and hence give the conditions for a plug-in solution (replacing the unknown mean and variance by certain estimates based on past values) to be optimal. After showing that the plug-in solutions are sub-optimal in general, we propose gradient-ascent algorithms to solve the functional optimization for mean–variance portfolio management with theorems for convergence provided. Simulations and empirical studies show that our approach can perform significantly better than the plug-in approach.

Bernard et al. [(2019) Optimal strategies under omega ratio, European Journal of Operational Research 275 (2), 755–767] use convex ordering arguments to determine the bounded payoff for maximizing the omega ratio. However, it appears difficult to apply such reasoning to estimate the bounded payoff for maximizing the Sharpe ratio. As a proposed solution, this paper uses a Lagrange multiplier method to derive the bounded payoff for maximizing the Sharpe ratio. In contrast to the optimal strategy in Bernard & Vanduffel [(2014) Mean–variance optimal portfolios in the presence of a benchmark with applications to fraud detection, European Journal of Operational Research 234 (2), 469–480], the optimal strategy in this paper is bounded from below. It can protect investors from substantial losses when they invest in payoffs with a maximized Sharpe ratio.

This paper uses differing objective functions under the Longstaff model (1990) to discuss the strategic choices faced by the creditor when deciding whether to grant maturity extension on a defaulted loan. The results reveal that: (1) it ensures that the return per unit of risk is higher after maturity extension than before; (2) it recognizes that the risk profile of the firm substantially affects the strategic behavior of the creditor; and (3) it demonstrates that the higher the profit sharing percentage the creditor get, the more willing it will be to extend maturity.

We examine buy and hold and a number of rebalancing strategies on a portfolio of indices that are tracked by ETFs. The indices include Barkley's treasuries and MSCI indices on emerging markets, Pacific and European markets, value funds, and growth funds. Portfolios are rebalanced using threshold schemes and compared with portfolios rebalanced using weights from different points on the Markowitz efficient frontier. We also examine portfolios that are rebalanced across monetary policy regimes. We find that portfolios rebalanced using Markowitz weights that allow for shifts in monetary policy regimes easily outperform both threshold rebalancing and buy and hold strategies.

This paper documents predictable time-variation in stock market Sharpe ratios. Predetermined financial variables are used to estimate both the conditional mean and volatility of equity returns, and these moments are combined to estimate the conditional Sharpe ratio, or the Sharpe ratio is estimated directly as a linear function of these same variables. In sample, estimated conditional Sharpe ratios show substantial time-variation that coincides with the phases of the business cycle. Generally, Sharpe ratios are low at the peak of the cycle and high at the trough. In an out-of-sample analysis, using 10-year rolling regressions, relatively naive market-timing strategies that exploit this predictability can identify periods with Sharpe ratios more than 45% larger than the full sample value. In spite of the well-known predictability of volatility and the more controversial forecastability of returns, it is the latter factor that accounts primarily for both the in-sample and out-of-sample results.

The aim of the study covers, at first, the rank comparison drawn among mutual funds at categorical and investment policy level and secondly, among the selected three families of performance measures against famous Sharpe ratio. The Spearman rank order correlation and mean rank order approach have been used for this purpose. The major findings of the study reveal that the most of the performance measures have shown a similar ranking order of mutual funds, at the investment policy level, against the standard measure i.e., Sharpe ratio. However, funds that have shown a non-normal trend, led to misspecification syndrome.

By assuming multivariate normal distribution of excess returns, we find that the sample maximum squared Sharpe ratio (MSR) has a significant upward bias. We then construct estimators for MSR based on Bayes estimation and unbiased estimation of the squared slope of the asymptote to the minimum variance frontier (ψ²). While the often used unbiased estimator may lead to unreasonable negative estimates in the case of finite sample, Bayes estimators will never produce negative values as long as the prior is bounded below by zero although it has a larger bias. We also design a mixed estimator by combining the Bayes estimator with the unbiased estimator. We show by simulation that the new mixed estimator performs as good as the unbiased estimator in terms of bias and root mean square errors and it is always positive. The mixed estimators are particularly useful in trend analysis when MSR is very low, for example, during crisis or depression time. While negative or zero estimates from unbiased estimator are not admissible, Bayes and mixed estimators can provide more information.

Over the last 20 years, investors have come to approach investment decision-making in an increasingly mechanical manner. Optimizers are filled up with historical return data and the “optimal” portfolio follows almost automatically. In this paper, we argue that such an approach can be extremely dangerous, especially when alternative investments such as hedge funds are involved. Proper hedge fund investing requires a much more elaborate approach to investment decision-making than currently in use by most investors. The available data on hedge funds should not be taken at face value, but should first be corrected for various types of biases and autocorrelation. Tools like mean–variance analysis and the Sharpe ratio that many investors have become accustomed to over the years are no longer appropriate when hedge funds are involved as they concentrate on the good part while completely skipping over the bad part of the hedge fund story. Investors also have to find a way to figure in the long lock-up and advance notice periods, which makes hedge fund investments highly illiquid. In addition, investors will have to give weight to the fact that without more insight in the way in which hedge funds generate their returns it is very hard to say something sensible about hedge funds' future longer-run performance. The tools to accomplish this formally are not all there yet, meaning that more than ever investors will have to rely on common sense and doing their homework.

The Sharpe ratio is not monotone: an investment strategy which yields a higher return may have a lower Sharpe ratio. This may lead to suboptimal investment decisions.

In this paper we present a modification of the Sharpe ratio, which is monotone with respect to second-order stochastic dominance. We study its properties and obtain a representation which allows to compute it in an efficient way.