Parameter uncertainty in portfolio selection: Shrinking the inverse covariance matrix

The estimation of the inverse covariance matrix plays a crucial role in optimal portfolio choice. We propose a new estimation framework that focuses on enhancing portfolio performance. The framework applies the statistical methodology of shrinkage directly to the inverse covariance matrix using two non-parametric methods. The first minimises the out-of-sample portfolio variance while the second aims to increase out-of-sample risk-adjusted returns. We apply the resulting estimators to compute the minimum variance portfolio weights and obtain a set of new portfolio strategies. These strategies have an intuitive form which allows us to extend our framework to account for short-sale constraints, transaction costs and singular covariance matrices. A comparative empirical analysis against several strategies from the literature shows that the new strategies often offer higher risk-adjusted returns and lower levels of risk.     

Portfolio selection with limited downside risk

A safety-first investor maximizes expected return subject to a downside risk constraint. Arzac and Bawa [Arzac, E.R., Bawa, V.S., 1977. Portfolio choice and equilibrium in capital markets with safety-first investors. Journal of Financial Economics 4, 277–288.] use the Value at Risk as the downside risk measure. The paper by Gourieroux, Laurent and Scaillet estimates the optimal safety-first portfolio by a kernel-based method, we exploit the fact that returns are fat-tailed, and propose a semi-parametric method for modeling tail events. We also analyze a portfolio containing the two stocks used by Gourieroux et al. and discuss the merits of the safety-first approach.     

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.     

Picking funds with confidence

We present a new approach to selecting actively managed mutual funds that uses both portfolio holdings and fund return information to eliminate funds with predicted inferior performance through a sequence of pairwise fund comparisons. Our methodology determines both the number of skilled funds and their identities, and locates funds with substantially higher risk-adjusted returns than those identified by conventional alpha-ranking methods. We find strong evidence of time-series variation in both the number of funds identified as superior using our approach, as well as in their performance across different economic states.     

Some consequences of banks' LDC loans: A note

The realized returns on LDC loans made prior to 1980 and hypothetically sold at (below par) secondary market prices in either 1986, when a secondary market first began, or, say, in 1989 are moderately positive. The realized risk-adjusted returns to investors on a portfolio of large LDC lending bank stocks are unmistakenly lower than the return on a broad market index, though they are not significantly so. Similarly, although the difference is not statistically significant, the average realized return on LDC lending banks' stocks is well below that of a portfolio of non-LDC lending banks. The article concludes that while shareholders suffered economic losses as a result of LDC lending activity, these losses were not quantitatively large.     

Hedge fund portfolio construction: A comparison of static and dynamic approaches

This article studies the impact of modeling time-varying covariances/correlations of hedge fund returns in terms of hedge fund portfolio construction and risk measurement. We use a variety of static and dynamic covariance/correlation prediction models and compare the optimized portfolios’ out-of-sample performance. We find that dynamic covariance/correlation models construct portfolios with lower risk and higher out-of-sample risk-adjusted realized return. The tail-risk of the constructed portfolios is also lower. Using a mean-conditional-value-at-risk framework we show that dynamic covariance/correlation models are also successful in constructing portfolios with minimum tail-risk.     

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.     

SYMMETRIC VERSUS ASYMMETRIC CONDITIONAL COVARIANCE FORECASTS: DOES IT PAY TO SWITCH?

Volatilities and correlations for equity markets rise more after negative returns shocks than after positive shocks. Allowing for these asymmetries in covariance forecasts decreases mean‐variance portfolio risk and improves investor welfare. We compute optimal weights for international equity portfolios using predictions from asymmetric covariance forecasting models and a spectrum of expected returns. Investors who are moderately risk averse, have longer rebalancing horizons, and hold U.S. equities benefit most and may be willing to pay around 100 basis points annually to switch from symmetric to asymmetric forecasts. Accounting for asymmetry in both variances and correlations significantly lowers realized portfolio risk.     

Risks and rewards for momentum and reversal portfolios

Rational asset pricing implies a positive relation between the expected risk-adjusted return and the volatility of a factor-mimicking portfolio. The relation for the momentum portfolio is weak after its return is adjusted for the risks associated with the market return, the size factor, and the book-to-market factor. However, the relation is significantly positive and captures most of the average return on the momentum portfolio after the return is adjusted for the market return and the risk associated with the short-term reversal portfolio return. The result supports the hypothesis that there is a common factor underlying both momentum and short-term reversal. The dynamics of the factor loadings and the correlation structure of the underlying factors have important implications for the risk prices associated with the factor-mimicking portfolios and the risk–return trade-off for momentum and reversal portfolios.     

Who gains and who loses on stock markets? Risk preferences and timing matter

This paper uses an agent-based multi-asset model to examine the effect of risk preferences and optimal rebalancing frequency on performance measures while tracking profit and risk-adjusted return. We focus on the evolution of portfolios managed by heterogeneous mean-variance optimizers with a quadratic utility function under different market conditions. We show that patient and risk-averse agents are able to outperform aggressive risk-takers in the long-run. Our findings also suggest that the trading frequency determined by the optimal tolerance for the deviation from portfolio targets should be derived from a tradeoff between rebalancing benefits and rebalancing costs. In a relatively calm market, the absolute range of 6% to 8% and the complete-way back rebalancing technique outperforms others. During particular turbulent periods, however, none of the existing rebalancing techniques improves tax-adjusted profits and risk-adjusted returns simultaneously.     

Commercial Real Estate Return Performance: A Cross-Country Analysis

This paper investigates the return performance of publicly traded real estate companies. The analysis spans the 1984–1999 time period and includes return data on over 600 companies in 28 countries. The return data reveal a substantial amount of variation in mean real estate returns and standard deviations across countries. Moreover, standard Treynor ratios, which scale country excess returns by the estimated beta on the world wealth portfolio, also reveal substantial variation across countries in excess real estate returns per unit of systematic risk. However, when we estimate Jensens alphas using both single and multifactor specifications, we detect little evidence of abnormal, risk-adjusted returns at the country level. We do, however, find evidence of a strong world-wide factor in international real estate returns. Furthermore, even after controlling for the effects of world-wide systematic risk, an orthogonalized country-specific factor is highly significant. This suggests that real estate securities may provide international diversification opportunities.     

Loss aversion,asymmetric market comovements,and the home bias

Loss aversion has been used to explain why a high equity premium might be consistent with plausible levels of risk aversion. The intuition is that the first-order-different utility impact of wealth gains and losses leads loss-averse investors to behave similarly to investors with high risk aversion. But if so, should those agents not perceive larger gains from international diversification than standard expected-utility investors with plausible levels of risk aversion? They might not, because comovements in international stock markets are asymmetric: correlations are higher in market downturns than in upturns. This asymmetry dampens the gains from diversification relatively more for loss-averse investors. We analyze the portfolio problem of such an investor who has to choose between home and foreign equities in the presence of asymmetric comovement in returns. Perhaps surprisingly, in the context of the home bias puzzle we find that loss-averse investors behave similarly to those with standard expected-utility preferences and plausible levels of risk aversion. We argue that preference specifications that appear to perform well with respect to the equity premium puzzle should be subjected to this “test”.     

The price of shelter - Downside risk reduction with precious metals

Investor aversion to extreme losses may motivate them to seek out investments perceived to function as a safe haven during times of crisis. In this study, we consider the potential for precious metals to mitigate downside risk when combined with equities, and evaluate the impact on portfolio risk-adjusted returns. Each of gold, silver and platinum are found to contribute to downside risk reduction at short horizons, but diversification into silver and platinum may result in increased long horizon portfolio risk. The price of sheltering an equity portfolio from downside risk is a relative reduction in portfolio risk-adjusted returns. Variance and kurtosis properties of precious metals are identified as marginal contributors to downside risk reduction. Futures markets on precious metals are also shown to present an interesting and viable diversification alternative to physical metals.     

Time-varying risk The case of the American computer industry

A bivariate GARCH-in-mean model for individual stock returns and the market portfolio is designed to model volatility and to test the conditional Capital Asset Pricing Model versus the conditional Residual Risk Model. We find that a univariate model of volatility for individual stock returns is misspecified. A joint modelling of the market return and the individual stock return shows that a major force driving the conditional variances of individual stocks is the history contained in the market return variance. We find that a conditional residual risk model, where the variance of the individual stock return is used to explain expected returns, is preferred to a conditional CAPM. We propose a partial ordering of securities according to their market risk using first and second order dominance criteria.     

Disentangling the role of variance and covariance information in portfolio selection problems

The covariation among financial asset returns is often a key ingredient used in the construction of optimal portfolios. Estimating covariances from data, however, is challenging due to the potential influence of estimation error, specially in high-dimensional problems, which can impact negatively the performance of the resulting portfolios. We address this question by putting forward a simple approach to disentangle the role of variance and covariance information in the case of mean-variance efficient portfolios. Specifically, mean-variance portfolios can be represented as a two-fund rule: one fund is a fully invested portfolio that depends on diagonal covariance elements, whereas the other is a long-short, self financed portfolio associated with the presence of non-zero off-diagonal covariance elements. We characterize the contribution of each of these two components to the overall performance in terms of out-of-sample returns, risk, risk-adjusted returns and turnover. Finally, we provide an empirical illustration of the proposed portfolio decomposition using both simulated and real market data.     

Are good-news firms riskier than bad-news firms?

This paper examines the relative risk of good-news firms, i.e., those with high standardized unexpected earnings (SUE), and bad-news (low SUE) firms using a stochastic discount factor approach. We find that a stochastic discount factor constructed from a set of basis assets helps explain post-earnings-announcement drift (PEAD). The risk exposures on the pricing kernel increase monotonically from the lowest to highest SUE sorted portfolios. Specifically, good-news firms always have higher risk exposures than bad-news firms in both 10 SUE sorted portfolios and 25 size and SUE sorted portfolios. However, the estimated expected risk premium is too small to explain the observed magnitude of returns on the PEAD strategy. Our risk adjustment can explain only about one-fourth of the total magnitude of the average realized return to the PEAD strategy. As a result, the average risk-adjusted returns of earnings momentum strategies are mostly positive and significant. Overall, our results support the view that at least some portion of the returns to the earnings momentum strategies examined represent compensation for bearing increased risk.     

The Conditional CAPM and the Cross-Section of Expected Returns

Most empirical studies of the static CAPM assume that betas remain constant over time and that the return on the value-weighted portfolio of all stocks is a proxy for the return on aggregate wealth. The general consensus is that the static CAPM is unable to explain satisfactorily the cross-section of average returns on stocks. We assume that the CAPM holds in a conditional sense, i.e., betas and the market risk premium vary over time. We include the return on human capital when measuring the return on aggregate wealth. Our specification performs well in explaining the cross-section of average returns.     

Covariance complexity and rates of return on assets

This paper considers the estimation of the expected rate of return on a set of risky assets. The approach to estimation focuses on the covariance matrix for the returns. The structure in the covariance matrix determines shared information which is useful in estimating the mean return for each asset. An empirical Bayes estimator is developed using the covariance structure of the returns distribution. The estimator is an improvement on the maximum likelihood and Bayes–Stein estimators in terms of mean squared error. The effect of reduced estimation error on accumulated wealth is analyzed for the portfolio choice model with constant relative risk aversion utility.     

Climate change news sensitivity and mutual fund performance

In the presence of rising concern about climate change that potentially affects risk and return of investors' portfolio companies, active investors might have dispersed climate change risk exposures. We compute mutual fund covariance with market-wide climate change news index and find that high (positive) climate news beta funds outperform low (negative) climate news beta funds by 0.24% per month on a risk-adjusted basis. High climate news beta funds tilt their holdings toward stocks with high potential to hedge against climate change news risk. In the cross section, such stocks yield higher excess returns, which are driven by greater pricing pressure and superior financial performance over our sample period.     

Dynamic hedge fund portfolio construction: A semi-parametric approach

In this article, we evaluate alternative optimization frameworks for constructing portfolios of hedge funds. We compare the standard mean–variance optimization model with models based on CVaR, CDaR and Omega, for both conservative and aggressive hedge fund investment strategies. In order to implement the CVaR, CDaR and Omega optimization models, we propose a semi-parametric methodology, which is based on extreme value theory, copula and Monte Carlo simulation. We compare the semi-parametric approach with the standard, non-parametric approach, used to compute CVaR, CDaR and Omega, and the benchmark parametric approach, based on both static and dynamic mean–variance optimization. We report two main findings. The first is that the CVaR, CDaR and Omega models offer a significant improvement in terms of risk-adjusted portfolio performance over the parametric mean–variance model. The second is that semi-parametric estimation of the CVaR, CDaR and Omega models offers a very substantial improvement over non-parametric estimation. Our results are robust to the choice of target return, risk limit and estimation sample size.