Systematic Risk and Empirical Research

We show here that risky asset returns generating processes stated in terms of factors which include both accounting and non-accounting based measures of risk (e.g. book to market ratios) imply, under fairly standard regularity conditions, that the Sharpe-Lintner-Black asset pricing model beta is a 'sufficient' statistic in the sense that it captures all important attributes of the returns generating process in a single number. We then derive the parametric relationship between betas based on inefficient index portfolios and betas based on the market or tangency portfolio. We demonstrate that the relationship between risky asset expected returns and betas computed on the basis of inefficient index portfolios is both consistent with the predictions of the Capital Asset Pricing Model and the multi-factor asset pricing models of Fama and French (1992, 1993, 1995 and 1996). The 'trick' is to realise that inefficient index portfolios are composed of the market portfolio and a collection of inefficient but self financing 'kernel' or 'arbitrage' portfolios. It then follows that there is a perfect linear cross sectional relationship between risky asset expected returns, betas based on inefficient index portfolios and the arbitrage portfolios. Hence, if we happen to stumble across variables that span the same subspace as the vectors representing the arbitrage portfolios, it is easy to create the illusion that risky asset expected returns depend on variables other than 'beta'.     

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.     

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.     

Deciphering robust portfolios

Robust portfolio optimization has been developed to resolve the high sensitivity to inputs of the Markowitz mean–variance model. Although much effort has been put into forming robust portfolios, there have not been many attempts to analyze the characteristics of portfolios formed from robust optimization. We investigate the behavior of robust portfolios by analytically describing how robustness leads to higher dependency on factor movements. Focusing on the robust formulation with an ellipsoidal uncertainty set for expected returns, we show that as the robustness of a portfolio increases, its optimal weights approach the portfolio with variance that is maximally explained by factors.     

Options Trading and the CAPM

This article studies equilibrium asset pricing when agents facenonnegative wealth constraints. In the presence of these constraintsit is shown that options on the market portfolio are nonredundantsecurities and the economy's pricing kernel is a function ofboth the market portfolio and the nonredundant options. Thisimplies that the options should be useful for explaining riskyasset returns. To test the theory, a model is derived in whichthe expected excess return on any risky asset is linearly related(via a collection of betas) to the expected excess return onthe market portfolio and to the expected excess returns on thenonredundant options. The empirical results indicate that thereturns on traded index options are relevant for explainingthe returns on risky asset portfolios.     

INTERNATIONAL DIVERSIFICATION OF EQUITIES AND FIXED-INCOME SECURITIES

Portfolio selection models have been applied principally to common stocks traded in the United States and in foreign stock markets. This study examines the efficient set of portfolios selected from a choice set that includes returns derived from domestic and international corporate bond and government bond indices as well as domestic and international stock indices. To assess the benefits of international multi-asset diversification, the authors examine the following issues: (1) the extent to which international and domestic fixed-income securities are included in efficient portfolios; (2) the effect on efficient set composition of using the Sharpe portfolio selection model as compared to the Markowitz portfolio selection model; (3) the sensitivity of efficient set characteristics produced from a single-index based portfolio selection model to alternative world market indices; and (4) the correspondence between expected and realized portfolio risk and return for the different portfolio selection models.     

On the distribution and estimation of trading costs

This paper investigates the uncertainty about the trading costs associated with a given portfolio strategy. I derive accurate approximations of the ex ante probability distributions of proportional trading costs and portfolio turnover under the conventional assumption of normal asset returns. Based on these approximations, I express the expected trading costs as a function of asset and portfolio characteristics. All else equal, the expected trading costs increase with: i) the deviations of the expected asset returns from the expected portfolio return, ii) the assets' volatility and iii) the portfolio volatility. At the same time, they decrease with the covariance between the assets and the portfolio. Furthermore, I propose novel estimators of the expected turnover and trading costs and show that they offer small bias and low variance, even when the sample size is small. Finally, I incorporate my results into a portfolio selection framework to produce portfolios with low levels of risk and trading costs. Several experiments with real and simulated data confirm the practical value of the results.     

Trading Volume: Implications of an Intertemporal Capital Asset Pricing Model

We derive an intertemporal asset pricing model and explore its implications for trading volume and asset returns. We show that investors trade in only two portfolios: the market portfolio, and a hedging portfolio that is used to hedge the risk of changing market conditions. We empirically identify the hedging portfolio using weekly volume and returns data for U.S. stocks, and then test two of its properties implied by the theory: Its return should be an additional risk factor in explaining the cross section of asset returns, and should also be the best predictor of future market returns.     

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.     

Household portfolio optimization with XTFs? An empirical study using the SHS-base

XTFs are plain-vanilla Exchange Traded Funds (ETFs) which replicate a broad, internationally diversified market index. We question, if XTFs can optimize the performance of households’ portfolios when taking multiple relevant asset classes into account, not only stocks. As opposed to most existing studies, we apply representative household portfolio data to estimate households’ portfolios. Households’ portfolios in our sample show similar compositions and can be grouped into one of three stylized portfolio compositions which exhibit asset class concentrations on cash/savings, mutual funds and individual stocks. For each stylized portfolio, we first investigate if an easily investable 60/40 stock/bond XTF portfolio which is risk-adjusted (including (de-)leverage costs) to the risk of the stylized portfolios, achieves higher returns than the stylized portfolios. This is the case for all stylized portfolios, even those with concentrations on cash/savings or mutual funds. Second, we examine risk/return-changes when replacing the entire risky assets of the stylized portfolios with the 60/40 stock/bond XTF portfolio including transaction costs. This leads to return enhancements in all stylized portfolios and particularly in the portfolio with high stock concentrations to risk reductions. Overall, we find that XTFs are generally suitable to optimize the performance of households’ portfolios under consideration of multiple relevant asset classes.     

Optimal commodity asset allocation with a coherent market risk modeling

This paper fills a fundamental gap in commodity price risk management and optimal portfolio selection literatures by contributing a thorough reflection on trading risk modeling with a dynamic asset allocation process and under the supposition of illiquid and adverse market settings. This paper analyzes, from a portfolio managers' perspective, the performance of liquidity adjusted risk modeling in obtaining efficient and coherent investable commodity portfolios under normal and adverse market conditions. As such, the author argues that liquidity risk associated with the uncertainty of liquidating multiple commodity assets over given holding periods is a key factor in formalizing and measuring overall trading risk and is thus an important component to model, particularly in the wake of the repercussions of the recent 2008 financial crisis. To this end, this article proposes a practical technique for the quantification of liquidity trading risk for large portfolios that consist of multiple commodity assets and whereby the holding periods are adjusted according to the specific needs of each trading portfolio. Specifically, the paper proposes a robust technique to commodity optimal portfolio selection, in a liquidity-adjusted value-at-risk (L-VaR) framework, and particularly from the perspective of large portfolios that have both long and short positions or portfolios that consist of merely pure long trading positions. Moreover, in this paper, the author develops a portfolio selection model and an optimization-algorithm which allocates commodity assets by minimizing the L-VaR subject to applying credible operational and financial constraints based on fundamental asset management considerations. The empirical optimization results indicate that this alternate L-VaR technique can be regarded as a robust portfolio management tool and can have many uses and applications in real-world asset management practices and predominantly for fund managers with large commodity portfolios.     

Mean–variance and mean–semivariance portfolio selection: a multivariate nonparametric approach

While univariate nonparametric estimation methods have been developed for estimating returns in mean-downside risk portfolio optimization, the problem of handling possible cross-correlations in a vector of asset returns has not been addressed in portfolio selection. We present a novel multivariate nonparametric portfolio optimization procedure using kernel-based estimators of the conditional mean and the conditional median. The method accounts for the covariance structure information from the full set of returns. We also provide two computational algorithms to implement the estimators. Via the analysis of 24 French stock market returns, we evaluate the in-sample and out-of-sample performance of both portfolio selection algorithms against optimal portfolios selected by classical and univariate nonparametric methods for three highly different time periods and different levels of expected return. By allowing for cross-correlations among returns, our results suggest that the proposed multivariate nonparametric method is a useful extension of standard univariate nonparametric portfolio selection approaches.     

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.     

The Causal Effect of Limits to Arbitrage on Asset Pricing Anomalies

We examine the causal effect of limits to arbitrage on 11 well-known asset pricing anomalies using the pilot program of Regulation SHO, which relaxed short-sale constraints for a quasi-random set of pilot stocks, as a natural experiment. We find that the anomalies became weaker on portfolios constructed with pilot stocks during the pilot period. The pilot program reduced the combined anomaly long–short portfolio returns by 72 basis points per month, a difference that survives risk adjustment with standard factor models. The effect comes only from the short legs of the anomaly portfolios.     

Spectral risk measures and portfolio selection

This paper deals with risk measurement and portfolio optimization under risk constraints. Firstly we give an overview of risk assessment from the viewpoint of risk theory, focusing on moment-based, distortion and spectral risk measures. We subsequently apply these ideas to an asset management framework using a database of hedge funds returns chosen for their non-Gaussian features. We deal with the problem of portfolio optimization under risk constraints and lead a comparative analysis of efficient portfolios. We show some robustness of optimal portfolios with respect to the choice of risk measure. Unsurprisingly, risk measures that emphasize large losses lead to slightly more diversified portfolios. However, risk measures that account primarily for worst case scenarios overweight funds with smaller tails which mitigates the relevance of diversification.     

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.     

Asset allocation and portfolio performance: Evidence from university endowment funds

We use university endowment funds to study the relationship between asset allocation decisions and performance in multiple asset class portfolios. Although endowments differ substantially in asset class composition, policy portfolio returns and volatilities are remarkably similar across the sample. The risk-adjusted performance of the average endowment is negligible, but actively managed funds generate significantly larger alphas than passive ones. This is consistent with endowment managers exploiting their security selection abilities by over-weighting asset classes in which they have superior skills. Contrary to both theory and prevailing beliefs, asset allocation is not related to portfolio returns in the cross-section but does indirectly influence performance.     

Art as an investment: risk, return and portfolio diversification in major painting markets

The present paper examines risk, return and the prospects for portfolio diversification among major painting and financial markets over the period 1976–2001. The art markets examined are Contemporary Masters, French Impressionists, Modern European, 19th Century European, Old Masters, Surrealists, 20th Century English and Modern US paintings. The financial markets comprise US Treasury bills, corporate and government bonds and small and large company stocks. In common with the published literature in this area, the present study finds that the returns on paintings are much lower and the risks much higher than conventional investment markets. Moreover, while low correlations of returns suggest that opportunities for portfolio diversification in art works alone and in conjunction with equity markets exist, the construction of Markowitz mean‐variance efficient portfolios indicates that no diversification gains are provided by art in financial asset portfolios. However, diversification benefits in portfolios comprised solely of art works are possible, with Contemporary Masters, 19th Century European, Old Masters and 20th Century English paintings dominating the efficient frontier during the period in question.     

A relaxation algorithm for building undominated portfolios

Stochastic dominance methods which have been developed in recent years are generally more valid than mean-variance (EV) and higher moment methods for selecting a portfolio from a given finite set of possible portfolios. One of the limitations of these methods is the lack of procedures for building portfolios from a given set of securities and the probability distribution of their returns. Markowitz has developed an algorithm based on the restriction method in linear programming to build undominated portfolios. In this paper a more efficient method based on the relaxation method of linear programming is developed and tested for efficiency. Computational results justify its use as a practical tool for portfolio building.     

A multivariate model of strategic asset allocation

We develop an approximate solution method for the optimal consumption and portfolio choice problem of an infinitely long-lived investor with Epstein–Zin utility who faces a set of asset returns described by a vector autoregression in returns and state variables. Empirical estimates in long-run annual and post-war quarterly U.S. data suggest that the predictability of stock returns greatly increases the optimal demand for stocks. The role of nominal bonds in long-term portfolios depends on the importance of real interest rate risk relative to other sources of risk. Long-term inflation-indexed bonds greatly increase the utility of conservative investors.