Optimal delegated portfolio management with background risk

Most investors delegate the management of a fraction of their wealth to portfolio managers who are given the task of beating a benchmark. However, in an influential paper [Roll, R., 1992. A mean/variance analysis of tracking error. Journal of Portfolio Management 18, 13–22] shows that the objective functions commonly used by these managers lead to the selection of portfolios that are suboptimal from the perspective of investors. In this paper, we provide an explanation for the use of these objective functions based on the effect of background risk on investors’ optimal portfolios. Our main contribution is to provide conditions under which investors can optimally delegate the management of their wealth to portfolio managers.     

Active portfolio management with benchmarking: A frontier based on alpha

Active portfolio management often involves the objective of selecting a portfolio with minimum tracking error variance (TEV) for some expected gain in return over a benchmark. However, Roll (1992) shows that such portfolios are generally suboptimal because they do not belong to the mean-variance frontier and are thus overly risky. Our paper proposes an appealing method to lessen this suboptimality that involves the objective of selecting a portfolio from the set of portfolios that have minimum TEV for various levels of ex-ante alpha, which we refer to as the alpha-TEV frontier. Since practitioners commonly use ex-post alpha to assess the performance of managers, the use of this frontier aligns the objectives of managers with how their performance is evaluated. Furthermore, sensible choices of ex-ante alpha lead to the selection of portfolios that are less risky (in variance terms) than the portfolios that active managers would otherwise select.     

The efficiency of Greek public pension fund portfolios

Greek public pension funds can invest up to 23% into risky assets and are not allowed to invest outside Greece. This paper seeks to investigate the costs of investment constraints on pension fund portfolios. In particular we try to quantify the losses that portfolios suffer due to under-diversification and sub-optimal asset allocation. We find that the high concentration of Greek equity portfolios imposes a substantial return and utility loss which is further increased when the lack of international diversification is taken into account. Restricting the weight of equities to 23% of the total portfolio, leads to sub-optimal asset allocation that costs as much as 2% (3%) per annum compared to a balanced domestic (global) benchmark.     

International diversification strategies: Revisited from the risk perspective

Following Roll [Roll, R., 1992. Industrial structure and comparative behaviour of international stock market indices. Journal of Finance 47, 3–42] and Heston and Rouwenhorst [Heston, S.L., Rouwenhorst, G.K., 1994. Does industrial structure explain the benefits of international diversification. Journal of Financial Economics 36, 3–27], researchers have decomposed stock returns into country and industry components. Evidence suggests that industry components have become more important in recent years, but the reasons for this are unclear. Existing research concentrated mainly on stock returns in industrial countries. In this paper we consider instead the decomposition of stock risks within emerging equity markets. We provide a rationale for this procedure and its relationship to return decompositions. The results provide new firm-specific evidence on the debate over country and industry components, their stability over time, and the implications for portfolio 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.     

Real investment and risk dynamics

We ask to what extent the negative relation between investment and average stock returns is driven by risk. We show that: (i) the average return spread between low and high asset growth and investment portfolios is largely accounted for by their spread in systematic risk, as measured by the loadings on the Chen, Roll, and Ross (1986) factors; (ii) as predicted by q-theory and real options models, systematic risk falls during large investment periods; (iii) the returns of factors formed on the investment-to-assets, asset growth, and investment growth all forecast aggregate economic activities. Our evidence suggests that risk plays an important role in explaining the investment-return relation.     

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.     

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.     

Beyond Sharpe ratio: Optimal asset allocation using different performance ratios

As the assumption of normality in return distributions is relaxed, classic Sharpe ratio and its descendants become questionable tools for constructing optimal portfolios. In order to overcome the problem, asymmetrical parameter-dependent performance ratios have been recently proposed in the literature. The aim of this note is to develop an integrated decision aid system for asset allocation based on a toolkit of eleven performance ratios. A multi-period portfolio optimization up covering a fixed horizon is set up: at first, bootstrapping of asset return distributions is assessed to recover all ratios calculations; at second, optimal rebalanced-weights are achieved; at third, optimal final wealth is simulated for each ratios. Eventually, we make a robustness test on the best performance ratios. Empirical simulations confirm the weakness in forecasting of Sharpe ratio, whereas asymmetrical parameter-dependent ratios, such as the Generalized Rachev, Sortino–Satchell and Farinelli–Tibiletti ratios show satisfactorily robustness.     

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.     

Australian evidence on the implementation of the size and value premia

This study investigates whether passive investment managers can exploit the size and value premia without incurring prohibitive transaction costs or being exposed to substantial tracking error risk. Returns on the value premium are shown to be pervasive across size groups, while the size premium is nonlinear and driven by microcaps. The value premium cannot be explained by the capital asset pricing model; however, returns on value portfolios do covary across monetary regimes. The substantial turnover required to achieve annual rebalancing and the relative illiquidity of Australian small‐cap firms means that investing in a portfolio of large‐cap value firms appears to be the best way for passive fund managers to exploit the Fama and French (1993) premia.     

Nonlinear mean reversion in stock prices

This paper provides new evidence on the time-series predictability of stock market returns by introducing a test of nonlinear mean reversion. The performance of extreme daily returns is evaluated in terms of their power to predict short- and long-horizon returns on various stock market indices and size portfolios. The paper shows that the speed of mean reversion is significantly higher during the large falls of the market. The parameter estimates indicate a negative and significant relation between the monthly portfolio returns and the extreme daily returns observed over the past one to eight months. Specifically, in a quarter in which the minimum daily return is −2% the expected excess return is 37 basis points higher than in a month in which the minimum return is only −1%. This result holds for the value-weighted and equal-weighted stock market indices and for each of the size decile portfolios. The findings are also robust to different sample periods, different indices, and investment horizons.     

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.     

Investment shocks and the commodity basis spread

I identify a “slope” factor in the cross section of commodity futures returns: high-basis commodity futures have higher loadings on this factor than low-basis commodity futures. Combined with a level factor (an index of commodity futures), this slope factor explains most of the average excess returns of commodity futures portfolios sorted by basis. More importantly, I find that this factor is significantly correlated with investment shocks, which represent the technological progress in producing new capital. I investigate a competitive dynamic equilibrium model of commodity production to endogenize this correlation. The model reproduces the cross-sectional futures returns and many asset pricing tests.     

Idiosyncratic risk and the cross-section of expected stock returns

Theories such as Merton [1987. A simple model of capital market equilibrium with incomplete information. Journal of Finance 42, 483–510] predict a positive relation between idiosyncratic risk and expected return when investors do not diversify their portfolio. Ang, Hodrick, Xing, and Zhang [2006. The cross-section of volatility and expected returns. Journal of Finance 61, 259–299], however, find that monthly stock returns are negatively related to the one-month lagged idiosyncratic volatilities. I show that idiosyncratic volatilities are time-varying and thus, their findings should not be used to imply the relation between idiosyncratic risk and expected return. Using the exponential GARCH models to estimate expected idiosyncratic volatilities, I find a significantly positive relation between the estimated conditional idiosyncratic volatilities and expected returns. Further evidence suggests that Ang et al.'s findings are largely explained by the return reversal of a subset of small stocks with high idiosyncratic volatilities.     

Limited participation and the closed-end fund discount

In this paper, we present economic forces that affect the closed-end fund share price using a simple two-period model with limited participation. We characterize three economic forces: management fee, principal-agent problem effect and diversification benefit effect. The role of the management fee is consistent with recent studies by Ross [Ross S., 2002. Neoclassical finance, alternative finance and the closed end fund puzzle. European Financial Management 8, 129–137, Ross, S., 2002. A neoclassical look at behavioral finance: closed end funds. The Princeton lectures in finance III] and findings of various empirical studies [e.g., Kumar, R., Noronha, G.M., 1992. A re-examination of the relationship between closed-end fund discounts and expenses. Journal of Financial Research 15(2) Summer, 139–147; Russel, P.S., 2005. Closed-end fund pricing: The puzzle, the explanations, and some new evidence, Journal of Business and Economic Studies 11(1), 34–49; Gemmill, G., Thomas, D.C., 2002. Noise trading, costly arbitrage, and asset prices: Evidence from closed end funds. Journal of Finance 57(6), 2571–2594]. The model’s principal-agent problem effect is consistent with empirical findings by Brickley et al. [Brickley, James, Steven Manaster, Schallheim, James, 1991. The tax-timing option and the discounts on closed-end investment companies. Journal of Business 64, 287–312] of positive relation between the fund discount and the average variance of the constituent assets in the fund portfolio. In addition, it provides a theoretical framework for empirical studies, which examine the role of agency costs [Barclay, Michael J., Clifford G. Holderness, Jeffrey Pontiff, 1993. Private benefits from block ownership and discounts on closed-end funds. Journal of Financial Economics 33, 263–291] and compensation contracts [Coles, J., Suay, J., Woodbury, D., 2000. Fund advisor compensation in closed-end funds. Journal of Finance 55 (3), 1385–1414; Deli, Daniel N., 2002. Mutual fund advisory contracts: An empirical Investigation. Journal of Finance 57(1), 109–133] on the behavior of fund managers and fund discounts. The model’s diversification benefit effect supports the result in [Bonser-Neal C., Brauer,G., Neal, R.., Wheatley, S., 1990. International investment restrictions and closed-end country fund prices. Journal of Finance 45, 523–547] that announcement of financial market liberalization is associated with a decrease in the fund premium. It also supports the findings of [Kumar, R., Noronha, G.M., 1992. A re-examination of the relationship between closed-end fund discounts and expenses. Journal of Financial Research 15(2) Summer, 139–147; Chay, J.B., Trzcinka, Charles A., 1999. Managerial performance and the cross-sectional pricing of closed-end funds. Journal of Financial Economics 52, 379–408] of a positive relation between current premium and the risk-adjusted return over the following year.     

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.     

Size matters: Optimal calibration of shrinkage estimators for portfolio selection

We carry out a comprehensive investigation of shrinkage estimators for asset allocation, and we find that size matters—the shrinkage intensity plays a significant role in the performance of the resulting estimated optimal portfolios. We study both portfolios computed from shrinkage estimators of the moments of asset returns (shrinkage moments), as well as shrinkage portfolios obtained by shrinking the portfolio weights directly. We make several contributions in this field. First, we propose two novel calibration criteria for the vector of means and the inverse covariance matrix. Second, for the covariance matrix we propose a novel calibration criterion that takes the condition number optimally into account. Third, for shrinkage portfolios we study two novel calibration criteria. Fourth, we propose a simple multivariate smoothed bootstrap approach to construct the optimal shrinkage intensity. Finally, we carry out an extensive out-of-sample analysis with simulated and empirical datasets, and we characterize the performance of the different shrinkage estimators for portfolio selection.     

Optimal asset allocation for a large number of investment opportunities

This paper introduces a stock‐picking algorithm that can be used to perform an optimal asset allocation for a large number of investment opportunities. The allocation scheme is based upon the idea of causal risk. Instead of referring to the volatility of the assets time series, the stock‐picking algorithm determines the risk exposure of the portfolio by concerning the non‐forecastability of the assets. The underlying expected return forecasts are based on time‐delay recurrent error correction neural networks, which utilize the last model error as an auxiliary input to evaluate their own misspecification. We demonstrate the profitability of our stock‐picking approach by constructing portfolios from 68 different assets of the German stock market. It turns out that our approach is superior to a preset benchmark portfolio. Copyright © 2005 John Wiley & Sons, Ltd.     

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.