<Emphasis Type="Italic">K</Emphasis>-fold cross validation performance comparisons of six naive portfolio selection rules: how naive can you be and still have successful out-of-sample portfolio performance?

Recent research reports that optimal portfolio selection models often perform worse than equal-weight naive diversification in out-of-sample testing. This paper extends this line of inquiry by comparing the out-of-sample performance of the equal-weight naive strategy to the out-of-sample performance of five alternative naive strategies, each of which derives from a simple heuristic that does not require any optimization. Out-of-sample portfolio performance is assessed by mean, standard deviation, skewness, and Sharpe ratio; k-fold cross validation is used as the out-of-sample testing mechanism. The results indicate that the proposed naive heuristic rules exhibit strong out-of-sample performance, in most cases superior to the equal-weight naive strategy. These findings are consequential for at least two reasons: first, if these simple heuristic-based rules outperform the equal-weight naive strategy, then by transitivity they can outperform the mean–variance- and shortfall-optimal portfolio rules that have been shown in the literature to be inferior to the equal-weight naive rule, which further emphasizes the out-of-sample fragility of “optimal” methods; and second, among naive diversification strategies, some appear more robust in out-of-sample testing than others, hence the proposed methods may be useful when forming mixed portfolio selection models wherein a naive strategy is combined with an optimal strategy to improve performance.     

International portfolio selection and efficiency analysis

In the risk-return tradeoff, the traditional mean-variance analysis has been widely used for studies of international portfolio efficiency and diversification. Without prior knowledge about either the parametric structure of assets' return distributions or the form of investors' preference functions, the variance may no longer serve as a suitable risk proxy. This article examines international portfolio efficiency and diversification effects through mean-variance and various distribution-free (or less restrictive) risk-return measures. We show empirically that the mean-variance model is appropriate for large or well-diversified portfolios, but may provide biased results for single assets and less diversified portfolios. While stochastic dominance stands as theoretically the most appropriate method of international portfolio selection and efficiency analysis, the lack of optimal search algorithms reduces its practical usefulness. Very little gain is obtained by using the Gini-mean-difference risk measure as compared to the semivariance measure. The semivariance measure is a powerful and convenient discriminator of risky prospects, while stochastic dominance can serve as a benchmark to justify portfolio efficiency.     

A bootstrap-based comparison of portfolio insurance strategies

This study presents a systematic comparison of portfolio insurance strategies. We implement a bootstrap-based hypothesis test to assess statistical significance of the differences in a variety of downside-oriented risk and performance measures for pairs of portfolio insurance strategies. Our comparison of different strategies considers the following distinguishing characteristics: static versus dynamic protection; initial wealth versus cumulated wealth protection; model-based versus model-free protection; and strong floor compliance versus probabilistic floor compliance. Our results indicate that the classical portfolio insurance strategies synthetic put and constant proportion portfolio insurance (CPPI) provide superior downside protection compared to a simple stop-loss trading rule and also exhibit a higher risk-adjusted performance in many cases (dependent on the applied performance measure). Analyzing recently developed strategies, neither the TIPP strategy (as an ‘improved’ CPPI strategy) nor the dynamic VaR-strategy provides significant improvements over the more traditional portfolio insurance strategies.     

The Effect of Shortfall as a Risk Measure for Portfolios with Hedge Funds

Abstract:  Current research suggests that the large downside risk in hedge fund returns disqualifies the variance as an appropriate risk measure. For example, one can easily construct portfolios with nonlinear pay-offs that have both a high Sharpe ratio and a high downside risk. This paper examines the consequences of shortfall-based risk measures in the context of portfolio optimization. In contrast to popular belief, we show that negative skewness for optimal mean-shortfall portfolios can be much greater than for mean-variance portfolios. Using empirical hedge fund return data we show that the optimal mean-shortfall portfolio substantially reduces the probability of small shortfalls at the expense of an increased extreme crash probability. We explain this by proving analytically under what conditions short-put payoffs are optimal for a mean-shortfall investor. Finally, we show that quadratic shortfall or semivariance is less prone to these problems. This suggests that the precise choice of the downside risk measure is highly relevant for optimal portfolio construction under loss averse preferences.     

OPTIMAL PORTFOLIO SELECTION WITH A SHORTFALL PROBABILITY CONSTRAINT: EVIDENCE FROM ALTERNATIVE DISTRIBUTION FUNCTIONS

We propose a new approach to optimal portfolio selection in a downside risk framework that allocates assets by maximizing expected return subject to a shortfall probability constraint, reflecting the typical desire of a risk-averse investor to limit the maximum likely loss. Our empirical results indicate that the loss-averse portfolio outperforms the widely used mean-variance approach based on the cumulative cash values, geometric mean returns, and average risk-adjusted returns. We also evaluate the relative performance of the loss-averse portfolio with normal, symmetric thin-tailed, symmetric fat-tailed, and skewed fat-tailed return distributions in terms of average return, risk, and average risk-adjusted return.     

A dynamic model of active portfolio management with benchmark orientation

This paper studies optimal dynamic portfolios for investors concerned with the performance of their portfolios relative to a benchmark. Assuming that asset returns follow a multi-linear factor model similar to the structure of Ross (1976) [Ross, S., 1976. The arbitrage theory of the capital asset pricing model. Journal of Economic Theory, 13, 342–360] and that portfolio managers adopt a mean tracking error analysis similar to that of Roll (1992) [Roll, R., 1992. A mean/variance analysis of tracking error. Journal of Portfolio Management, 18, 13–22], we develop a dynamic model of active portfolio management maximizing risk adjusted excess return over a selected benchmark. Unlike the case of constant proportional portfolios for standard utility maximization, our optimal portfolio policy is state dependent, being a function of time to investment horizon, the return on the benchmark portfolio, and the return on the investment portfolio. We define a dynamic performance measure which relates portfolio’s return to its risk sensitivity. Abnormal returns at each point in time are quantified as the difference between the realized and the model-fitted returns. Risk sensitivity is estimated through a dynamic matching that minimizes the total fitted error of portfolio returns. For illustration, we analyze eight representative mutual funds in the U.S. market and show how this model can be used in practice.     

A Note on International Portfolio Diversification with Short Selling

In this paper, the diversification benefits of using stock index futures are examined. Empirical evidence shows that traditional diversification in international equity markets does not produce a risk adjusted performance superior to the US market. An explanation for this result is that restrictions on short selling prohibit the best allocation of resources when overseas stock markets are riskier and have worse returns. However, when such restrictions are eased for short selling in index futures markets, investors are enabled to both allocate their investments more efficiently and to construct a superior portfolio.     

Using industry momentum to improve portfolio performance

Minimum-variance portfolios, which ignore the mean and focus on the (co)variances of asset returns, outperform mean–variance approaches in out-of-sample tests. Despite these promising results, minimum-variance policies fail to deliver a superior performance compared with the simple 1/N rule. In this paper, we propose a parametric portfolio policy that uses industry return momentum to improve portfolio performance. Our portfolio policies outperform a broad selection of established portfolio strategies in terms of Sharpe ratio and certainty equivalent returns. The proposed policies are particularly suitable for investors because portfolio turnover is only moderately increased compared to standard minimum-variance portfolios.     

A differential evolution copula-based approach for a multi-period cryptocurrency portfolio optimization

Recent years have seen a growing interest among investors in the new technology of blockchain and cryptocurrencies and some early investors in this new type of digital assets have made significant gains. The heuristic algorithm, differential evolution, has been advocated as a powerful tool in portfolio optimization. We propose in this study two new approaches derived from the traditional differential evolution (DE) method: the GARCH-differential evolution (GARCH-DE) and the GARCH-differential evolution t-copula (GARCH-DE-t-copula). We then contrast these two models with DE (benchmark) in single and multi-period optimizations on a portfolio consisting of five cryptoassets under the coherent risk measure CVaR constraint. Our analysis shows that the GARCH-DE-t-copula outperforms the DE and GARCH-DE approaches in both single- and multi-period frameworks. For these notoriously volatile assets, the GARCH-DE-t-copula has shown risk-control ability, hereby confirming the ability of t-copula to capture the dependence structure in the fat tail.     

REGULATORY INFLUENCES ON PORTFOLIO PERFORMANCE: SHORT SELLING AND REGULATION T

Several models are developed to examine the portfolio effect of short selling. Three things are demonstrated in this study. First, that for many assets, short selling is a useful strategy for reducing risk when constructing mean-variance efficient portfolios. Second, Regulation T can be used in combination with short selling to further improve expected portfolio performance. Third, the performance of the suggested models is superior to previously suggested allocation models. Ex ante and ex post tests are conducted to arrive at the above conclusions.     

Convex risk measures based on generalized lower deviation and their applications

Considering the implementability and the properties that a reasonable and realistic risk measure should satisfy, we propose a new class of risk measures based on generalized lower deviation with respect to a chosen benchmark. Besides convexity and monotonicity, our new risk measure can reflect the investor's degree of risk aversion as well as the fat-tail phenomenon of the loss distribution with the help of different benchmarks and weighted functions. Based on the new risk measure, we establish a realistic portfolio selection model taking market frictions into account. To examine the influence of the benchmarks and weighted functions on the optimal portfolio and its performance, we carry out a series of empirical studies in Chinese stock markets. Our in-sample and out-of-sample results show that the new risk measure and the corresponding portfolio selection model can reflect the investor's risk averse attitude and the impact of different trading constraints. Most importantly, with the new risk measure we can obtain an optimal portfolio which is more robust and superior to the optimal portfolios obtained with the traditional expected shortfall risk measures.     

A comparison of static and dynamic portfolio policies

Garleanu and Pedersen (2013) show that the optimal static portfolio policy in light of quadratic transaction costs is a weighted average of the existing portfolio and the target portfolio. In this paper, we demonstrate the importance of the robust target portfolio in the static portfolio policy that considers quadratic transaction costs. By using both empirical and simulated data, we find no evidence that the optimal dynamic portfolio policy proposed by Garleanu and Pedersen (2013) is superior to the static portfolio policy that trades towards the robust target portfolio. The robust target portfolio is achieved by either introducing time-varying covariances or restricting portfolio weights. Furthermore, the static portfolio with time-varying covariances and the short sale-constrained static portfolio are both very efficient in reducing portfolio turnover. The good performance of the static portfolio policy is robust to parameter uncertainty and trading parameters.     

Generalized DEA model of fundamental analysis and its application to portfolio optimization

Fundamental analysis is used in asset selection for equity portfolio management. In this paper, a generalized data envelopment analysis (DEA) model is developed to analyze a firm’s financial statements over time in order to determine a relative financial strength indicator (RFSI) that is predictive of firm’s stock price returns. RFSI is based on maximizing the correlation between the DEA-based score of financial strength and the stock market performance. This maximization involves a difficult binary nonlinear program that requires iterative re-configuration of parameters of financial statements as inputs and outputs. We utilize a two-step heuristic algorithm that combines random sampling and local search optimization. The proposed approach is tested with 230 firms from various US technology-industries to determine optimized RFSI indicators for stock selection. Then, those selected stocks are used within portfolio optimization models to demonstrate the usefulness of the scheme for portfolio risk management.     

Corporate Sustainability Performance and Idiosyncratic Risk: A Global Perspective

Does investing in sustainability leaders affect portfolio performance? Analyzing two mutually exclusive leading and lagging global corporate sustainability portfolios (Dow Jones) finds that (1) leading sustainability firms do not underperform the market portfolio, and (2) their lagging counterparts outperform the market portfolio and the leading portfolio. Notably, we find leading (lagging) corporate social performance (CSP) firms exhibit significantly lower (higher) idiosyncratic risk and that idiosyncratic risk might be priced by the broader global equity market. We develop an idiosyncratic risk factor and find that its inclusion significantly reduces the apparent difference in performance between leading and lagging CSP portfolios.     

The effectiveness of incorporating higher moments in portfolio strategies: evidence from the Chinese commodity futures markets

This paper examines portfolio strategies that incorporate individual and systematic higher-order moments, within a stochastic optimization framework with uncertain mean and covariance. Using weekly, daily, and 30-minute interval data on Chinese commodity futures, we show that incorporating higher moments into portfolio strategies generally leads to better performance. The systematic fourth-order moment, among all systematic moments considered, can lead to the most robust, and a relatively large, improvement in investment performance, while the contribution of individual moments to the improved performance depends on the data horizon. We also find that adding higher moments brings superior performance in more cases for 30-minute-interval data than for other low-frequency data, suggesting that our strategy most likely performs best in 30-minute-rebalancing investments.     

THE PERFORMANCE MEASUREMENT AND EVALUATION OF A CORPORATE RETIREMENT PLAN: A CASE STUDY

This paper is based on an actual study of a pooled profit-sharing plan sponsored by a Fortune 50 company from September 1978 to June 1983. The purpose of performance measurement is to identify skill at portfolio management and provide evidence indicating whether performance coincides with the investment skills claimed by the portfolio manager. The approach here is to apply the security market line analysis suggested by Fama. Characteristic lines were determined for the plan portfolio allowing the calculation for alpha, the Jensen differential performance index, beta, and R². Tests are made to determine if the investment manager was able to achieve superior performance by shifting portfolio market sensitivity in anticipation of major market moves (market-timing effect) and/or selecting undervalued securities (security-selection effect).     

Recursive risk measures under regime switching applied to portfolio selection

In this paper, we define the conditional risk measure under regime switching and derive a class of time consistent multi-period risk measures. To do so, we describe the information process with regime switching in a product space associated with the product of two filtrations. Moreover, we show how to establish the corresponding multi-stage portfolio selection models using the time consistent multi-period risk measure for medium-term or long-term investments. Take the conditional value-at-risk measure as an example, we demonstrate the resulting multi-stage portfolio selection problem can be transformed into a second-order cone programming problem. Finally, we carry out a series of empirical tests to illustrate the superior performance of the proposed random framework and the corresponding multi-stage portfolio selection model.     

Performance comparison between exchange-traded funds and closed-end country funds

The objective of this study is to compare the risk and return performance of exchange-traded funds (ETFs) available for foreign markets and closed-end country funds. We utilize 29 closed-end country funds (CEFs) for 14 countries over the sample period from April 1996 to December 2001. The performance proxies are mean returns and risk-adjusted returns. Results indicate that ETFs exhibit higher mean returns and higher Sharpe ratios than foreign closed-end funds, while CEFs exhibit negative alphas. This indicates that a passive investment strategy utilizing ETFs may be superior to an active investment strategy using CEFs. The findings reported here offer some insight on the relative advantages of each type of investment. Specifically, there may be some potential for additional types of ETFs that offer higher risk-adjusted returns than closed-end funds. Such ETFs may be able to offer higher risk-adjusted returns as part of an internationally diversified portfolio.     

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.     

A conditional asset-pricing model with the optimal orthogonal portfolio

This paper employs a conditional asset-pricing model based on the optimal orthogonal portfolio approach to construct a factor portfolio that embodies all the latent factors important for pricing a given set of test assets. The advantage of this portfolio to the anomaly related mimicking portfolios is its ability to separate out the components of average return that are not related to the return covariation. The performance of this portfolio is evaluated against several conventional factors, using both cross-sectional and time-series regression approaches, as well as the Hansen and Jagannathan (1997) distance measure. Its strong out-of-sample results indicate that our suggested methodology may have important applications in risk management, portfolio selection and performance evaluation.