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.     

Momentum strategies based on reward–risk stock selection criteria

In this paper, we analyze momentum strategies that are based on reward–risk stock selection criteria in contrast to ordinary momentum strategies based on a cumulative return criterion. Reward–risk stock selection criteria include the standard Sharpe ratio with variance as a risk measure, and alternative reward–risk ratios with the expected shortfall as a risk measure. We investigate momentum strategies using 517 stocks in the S&P 500 universe in the period 1996–2003. Although the cumulative return criterion provides the highest average monthly momentum profits of 1.3% compared to the monthly profit of 0.86% for the best alternative criterion, the alternative ratios provide better risk-adjusted returns measured on an independent risk-adjusted performance measure. We also provide evidence on unique distributional properties of extreme momentum portfolios analyzed within the framework of general non-normal stable Paretian distributions. Specifically, for every stock selection criterion, loser portfolios have the lowest tail index and tail index of winner portfolios is lower than that of middle deciles. The lower tail index is associated with a lower mean strategy. The lowest tail index is obtained for the cumulative return strategy. Given our data-set, these findings indicate that the cumulative return strategy obtains higher profits with the acceptance of higher tail risk, while strategies based on reward–risk criteria obtain better risk-adjusted performance with the acceptance of the lower tail risk.     

Momentum strategies in commodity futures markets

The article tests for the presence of short-term continuation and long-term reversal in commodity futures prices. While contrarian strategies do not work, the article identifies 13 profitable momentum strategies that generate 9.38% average return a year. A closer analysis of the constituents of the long–short portfolios reveals that the momentum strategies buy backwardated contracts and sell contangoed contracts. The correlation between the momentum returns and the returns of traditional asset classes is also found to be low, making the commodity-based relative-strength portfolios excellent candidates for inclusion in well-diversified portfolios.     

The coskewness puzzle

We propose a novel approach to testing non-linear stochastic discount factor (SDF) specifications that arise in rational representative investor models. Our approach does not require overly-restrictive assumptions about the shape of investors’ preferences, typically imposed by the extant literature, and is based instead on restrictions that rule out “good deals”, i.e., arbitrage opportunities as well as unduly large Sharpe ratios. We apply this framework to test the empirical admissibility of 3 and 4-moment versions of the CAPM. We find that, while coskewness and cokurtosis risk help price a number of stock strategies and portfolios, including static strategies based on a fine industry-level diversification, momentum strategies and portfolios managed on the basis of available information, the CAPM and its 3 and 4-moment versions cannot provide an exhaustive account of observed asset returns.     

Style investing,comovement and return predictability

Barberis and Shleifer (2003) argue that style investing generates momentum and reversals in style and individual asset returns, as well as comovement between individual assets and their styles. Consistent with these predictions, in some specifications, past style returns help explain future stock returns after controlling for size, book-to-market and past stock returns. We also use comovement to identify style investing and assess its impact on momentum. High comovement momentum portfolios have significantly higher future returns than low comovement momentum portfolios. Overall, our results suggest that style investing plays a role in the predictability of asset returns.     

New strategies and a new paradigm for Shariah-compliant portfolio optimization

In this paper we analyze the effects of different strategies to construct Shariah compatible financial portfolios. The difference between conventional and current Shariah portfolio management is the application of sector screens and financial screens by which the asset universe is reduced. Yet, here different schools of scholars define different screening rules leading to significant differences with respect to compliance, but also with respect to performance. After analyzing this discrepancy we propose several new strategies to apply the inconsistent rule systems and a new paradigm for defining Shariah-compliance. Under this new paradigm compliance is attributed to the portfolio and not to the individual assets of the universe. We report results of an empirical study analyzing the potentials of these strategies and of the paradigm. We can show that under the proposed concepts Shariah-compliant portfolios can be realized which have return and risk profiles comparable to the conventional non-constrained portfolios.     

Macroeconomic risks and characteristic-based factor models

We show that book-to-market, size, and momentum capture cross-sectional variation in exposures to a broad set of macroeconomic factors identified in the prior literature as potentially important for pricing equities. The factors considered include innovations in economic growth expectations, inflation, the aggregate survival probability, the term structure of interest rates, and the exchange rate. Factor mimicking portfolios constructed on the basis of book-to-market, size, and momentum therefore, serve as proxy composite macroeconomic risk factors. Conditional and unconditional cross-sectional asset pricing tests indicate that most of the macroeconomic factors considered are priced. The performance of an asset pricing model based on the macroeconomic factors is comparable to the performance of the Fama and French (1993) model. However, the momentum factor is found to contain incremental information for asset pricing.     

Mitigating Estimation Risk in Asset Allocation: Diagonal Models Versus 1/N Diversification

Recent literature suggests that optimal asset‐allocation models struggle to consistently outperform the 1/N naïve diversification strategy, which highlights estimation‐risk concerns. We propose a dichotomous classification of asset‐allocation models based on which elements of the inverse covariance matrix that a model uses: diagonal only versus full matrix. We argue that parsimonious diagonal‐only strategies, which use limited information such as volatility or idiosyncratic volatility, are likely to offer a good tradeoff between incorporating limited information while mitigating estimation risk. Evaluating five sets of portfolios over 1926–2012, we find that 1/N is generally not optimal when compared with these diagonal strategies.     

Characteristic-based mean-variance portfolio choice

We study empirical mean-variance optimization when the portfolio weights are restricted to be direct functions of underlying stock characteristics such as value and momentum. The closed-form solution to the portfolio weights estimator shows that the portfolio problem in this case reduces to a mean-variance analysis of assets with returns given by single-characteristic strategies (e.g., momentum or value). In an empirical application to international stock return indexes, we show that the direct approach to estimating portfolio weights clearly beats a naive regression-based approach that models the conditional mean. However, a portfolio based on equal weights of the single-characteristic strategies performs about as well, and sometimes better, than the direct estimation approach, highlighting again the difficulties in beating the equal-weighted case in mean-variance analysis. The empirical results also highlight the potential for ‘stock-picking’ in international indexes using characteristics such as value and momentum with the characteristic-based portfolios obtaining Sharpe ratios approximately three times larger than the world market.     

Do ETFs provide effective international diversification?

Global investments have been a hot issue for years. Investors can diversify risks and obtain benefits from foreign markets by investing directly in the foreign security market or indirectly in Exchange-Trade Funds (ETFs). Because direct investments are not always feasible, we investigate whether indirect investments can replace direct investments. We create different regional optimal portfolios containing ETFs and ensure optimal asset portfolio allocation. In addition to mean-variance approach, the Sharpe index, we also adopt the Campbell et al. (2001) method to have the efficient frontier under control risks, the Value at Risk. We apply both normal and non-normal distributions for comparisons and find that different assumptions of return distributions affect the results of efficient frontier. The results show that international diversification is a reasonable strategy. In addition, when comparing ETFs and target market index portfolios, ETFs have higher Sharpe measures than target market indices especially in the emerging markets. However, there are no significant performance differences between direct and indirect methods even if we use different performance measures. We also find that the diversification benefits are the same before and after the Subprime crisis. We conclude that it is effective for investors to use indirect methods to create internationally diversified portfolios.     

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.     

Predicting European Takeover Targets

This article extends the Palepu (1986) acquisition likelihood model by incorporating measures of a technical nature, e.g. momentum, trading volume as well as a measure of market sentiment. We use the proposed model to predict takeover targets in a large sample of European and cross‐border merger and acquisition deals and validate its performance on an in‐ and out‐of‐sample basis. The robustness of the proposed model is investigated across several dimensions. In addition we explore the ability of the model to form the basis of successful takeover timing investment strategies. The results of our empirical analysis suggest that the proposed model predicts European takeover targets with relatively high accuracy and is able to determine portfolios that earn significant returns which are not explained by conventional risk factors.     

Risk adjustment and momentum sources

We show that the conventional procedure of risk adjustment by running full-sample time-series Fama-French three-factor regressions is not appropriate for momentum portfolios because the procedure fails to allow for the systematic dynamics of momentum portfolio factor loadings. We propose a simple procedure to adjust risks associated with the Fama-French three factors for momentum portfolios. Using our proposed method, the Fama-French three factors can explain approximately 40% of momentum profits generated by individual stocks and nearly all of momentum returns from style 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.     

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.     

Residual momentum

Conventional momentum strategies exhibit substantial time-varying exposures to the Fama and French factors. We show that these exposures can be reduced by ranking stocks on residual stock returns instead of total returns. As a consequence, residual momentum earns risk-adjusted profits that are about twice as large as those associated with total return momentum; is more consistent over time; and less concentrated in the extremes of the cross-section of stocks. Our results are inconsistent with the notion that the momentum phenomenon can be attributed to a priced risk factor or market microstructure effects.     

Regime switching based portfolio selection for pension funds

This paper shows how a mean variance criterion can be applied to a multi period setting in order to obtain efficient portfolios in an asset and liability context. The optimization model allows for rebalancing activities, transaction costs, stochastic volatilities for both assets and liabilities. Furthermore, a general framework for the projection of pension fund liabilities as well as for the generation of asset returns is given. In a further step the dynamics of the liability maturity structure is modeled as customized index, whose volatility and correlation with asset returns become integral components of the applied regime switching approach. The numerical results illustrate the diversification of the assets and its risk return pattern in dependency of the liability dynamics.     

International portfolio diversification: Currency,industry and country effects revisited

We examine the relative importance of country, industry, world market and currency risk factors for international stock returns. Our approach focuses on testing the mean-variance efficiency of the various factor portfolios. An unconditional analysis does not show significant differences between country, industry and world portfolios, nor any role for currency risk factors. However, when we allow expected returns, volatilities and correlations to vary over time, we find that equity returns are mainly driven by global industry and currency risk factors. We propose a novel test to evaluate the relative benefits of alternative investment strategies and find that including currencies is critical to take full advantage of the diversification benefits afforded by international markets.     

An alternative measure of the “world market portfolio”: Determinants, efficiency, and information content

The world market portfolio plays an important role in international asset pricing, but is unobservable in practice. We first propose a framework for constructing a market proxy that corresponds to the “market portfolio” of financial theory. We then construct this proxy, analyze its determinants and test its efficiency and explanatory power over the period 1975-2007 with respect to the return generating processes of a broad asset universe. We show that its major determinants are traded assets and that it is not efficient. However, it is significant for explaining individual asset returns over an asset universe that includes stocks, bonds, money markets and commodities. The explanatory information is incremental to what is available in traded asset prices and the significance of this information is robust with respect to diversified portfolios generated by factor analysis and to characteristic-sorted portfolios as well as to various model specifications, including the single-index model, the Fama-French (1992) three factor model for stocks, and various specifications of multi-index models hedged and unhedged for foreign currency risk.