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.     

On correlations and inferences about mean-variance efficiency

A framework is presented for investigating the mean-variance efficiency of an unobservable portfolio based on its correlation with a proxy portfolio. A sensitivity analysis derives the highest correlation between the proxy and a portfolio that reverses the inference of a test of SHarpe-Lintner tangency. For example, the maximum correlation between the value-weighted NYSE-AMEX portfolio and a portfolio inferred tangent ranges from 0.76 to 0.48. We also test whether the correlation between the proxy and the tangent portfolio exceeds a given level. This hypothesis is often rejected for the NYSE-AMEX proxy at a correlation of 0.7.     

Exact distribution-free tests of mean-variance efficiency

This paper develops exact distribution-free tests of unconditional mean-variance efficiency. These new tests allow for unknown forms of non-normalities, conditional heteroskedasticity, and other non-linear temporal dependencies among the absolute values of the error terms in the asset pricing model. Exactness here rests on the assumption that the joint temporal error density is symmetric around zero. This still leaves open the possibility of return distribution asymmetry via coskewness with the benchmark portfolio. A simulation study shows that the new tests have very good power relative to that of many commonly used tests. The inference procedures developed are further illustrated by tests of the mean-variance efficiency of a market index using a 42-year sample of monthly returns on ten U.S. equity portfolios.     

On the nature of mean-variance spanning

Asset spanning tests are very useful tools for the determination of which asset classes belong to an investor's portfolio. There are numerous applications of such tools in the finance literature. What is not so obvious is the proper decision an investor should make if the extra asset classes are spanned by some existing assets. Should the investor make a conscious decision not to invest in them as they add no value? Should the investor invest in them anyway as they do no harm? This study provides an analytical solution to the puzzle and also offers an economic rationale.     

Stochastic regularization for the mean-variance allocation scheme

Despite being based on sound principles, the original Markovitz portfolio allocation theory cannot produce sound allocations, and restrictions or modifications need to be imposed from outside the theory in order to obtain meaningful portfolios. This is unsatisfactory, and the reasons for this failure are discussed, in particular, the unavoidable small eigenvalues of the covariance. Within the original principles of risk minimization and return maximization, several modifications of the original theory are introduced. First, the strategic and tactical time horizons are separated. A base long-term allocation is chosen at the strategic time horizon, while the portfolio is optimized at the tactical time horizon using information from the price histories. Second, the tactical portfolio is financed by the strategic one, and a funding operator is introduced. The corresponding optimal allocation (without constraints) has one free parameter fixing the leverage. Third, the transaction costs are taken into account. This includes the current re-allocation cost, but crucially the expected costs of the next reallocation. This last term depends on the sensitivity of the allocation with respect to the covariance, and the expectation introduces another dependency on the (inverse) covariance. The new term regularizes the original minimization problem by modifying the lower part of the spectrum of the covariance, leading to meaningful portfolios. Without constraints, the final Lagrangian can be minimized analytically, with a solution that has a structure similar to the original Markovitz solution, but with the inverse covariance regularized by the expected transaction costs.     

Testing for mean-variance spanning: a survey

In this paper, we present a survey on the various approaches that can be used to test whether the mean-variance frontier of a set of assets spans or intersects the frontier of a larger set of assets. We analyze the restrictions on the return distribution that are needed to have mean-variance spanning or intersection. The paper explores the duality between mean-variance frontiers and volatility bounds, analyzes regression-based test procedures for spanning and intersection, and shows how these regression-based tests are related to tests for mean-variance efficiency, performance measurement, optimal portfolio choice and specification error bounds.     

Portfolio revision under mean-variance and mean-CVaR with transaction costs

The portfolio revision process usually begins with a portfolio of assets rather than cash. As a result, some assets must be liquidated to permit investment in other assets, incurring transaction costs that should be directly integrated into the portfolio optimization problem. This paper discusses and analyzes the impact of transaction costs on the optimal portfolio under mean-variance and mean-conditional value-at-risk strategies. In addition, we present some analytical solutions and empirical evidence for some special situations to understand the impact of transaction costs on the portfolio revision process.     

Dynamic programming and mean-variance hedging with partial execution risk

In this paper I consider a hedging problem in an illiquid market where there is a risk that the hedger’s order to buy or sell the underlying asset may be executed only partially. In this setting, I find a mean-variance optimal hedging strategy by the dynamic programming method. The solution contains a new endogenous state variable representing the current position in the underlying. The exogenous coefficients in the solution are given by recursive formulas which can be calculated efficiently in Markov models. I illustrate effects of the partial execution risk in several examples.      

Performance evaluation inflation and compression

We provide a behavioral account of subjective performance evaluation inflation (i.e., leniency bias) and compression (i.e., centrality bias). When a manager observes noisy signals of employee performance and the manager strives to produce accurate ratings but feels worse about unfavorable errors than about favorable errors, the manager’s selfishly optimal ratings will be biased upwards. Both the uncertainty about performance and the asymmetry in the manager’s utility are necessary conditions for performance evaluation inflation. Moreover, the extent of the bias is increasing in the variance of the performance signal and in the asymmetry in aversion to unfair ratings. Uncertainty about performance also leads to compressed ratings. These results suggest that performance appraisals based on well-defined unambiguous criteria will have less bias. Additionally, we demonstrate that employer and employee can account for biased performance evaluations when they agree to a contract, and thus, to the extent leniency bias and centrality bias persist, these biases hurt employee performance and lower firm productivity.     

A mean-variance framework for analyzing reserve requirements and monetary control

This paper analyzes an ‘almost’ contemporaneous reserve accounting system (ACRA) in which reserve computation and maintenance periods only partially overlap. As a result, banks acquire knowledge of their required reserve obligations prior to the settling period when such reserve requirements become legally binding. Our analysis suggests that the money stock behaves similarly under both ACRA and purely contemporaneous reserve accounting systems as long as banks are risk averse. When banks no longer exhibit risk aversion, the ACRA money stock tends to mimic the behavior of the money stock under a lagged reserve accounting system.     

On statistical inference on the mean-variance efficient set

A proof of the asymptotic distribution of the estimated mean-variance frontier is given. A Bayesian prediction interval is derived for the capital asset pricing model. Numerical illustrations show that the prediction intervals for the CAPM are smaller than those for the constant mean model, if the fit of the CAPM is better than that of the constant mean model.     

Buy-and-hold mean-variance portfolios with a random exit strategy

We show how buy-and-hold investors can move from horizon uncertainty to profit opportunity. The analysis is conducted under a risk-averse framework rather than the standard Markowitz formulation in the case of i.i.d. asset processes. We make this practical achievement by considering a threshold stopping rule as the strategy to determine when to exit the market. The resulting investment horizon is random and can be correlated with the market. Under this setting, we first provide an analytical approximation to optimal weights, and then identify a class of reference variables associated with the stopping rule that leads to ex-ante improvements in portfolio allocation, vis-a-vis the fixed exit time alternative. The latter conclusion is based on a generalization of the Sharpe ratio, adjusted for horizon uncertainty. The obtained investment suggestion is simple and can be implemented empirically.     

The residual market factor,the APT,and mean-variance efficiency

The rapidly increasing volume of both published and unpublished work on the arbitrage pricing theory (APT) of Ross (1976) has given rise to a number of misunderstandings at the interface of theoretical and econometric work. In this article we extend the theoretical structure of our previous work (McElroy and Burmeister, 1985, 1988; Burmeister and McElroy, 1987, 1988) to provide a broad yet rigorous framework both for econometric estimation and for better economic interpretation of new empirical results. We begin with the case where allK factors are observed, and then present the second case ofK−1≡J observed APT factors and one unobserved factor, theresidual market factor introduced in McElroy and Burmeister (1985). The economic interpretations for equivalent specifications of this model are discussed, and we enumerate several immediate payoffs to these specifications. The main new results are concerned with the sometimes intricate relationships among APT models withK factors and APT models withK factors that are constrained to satisfy mean-variance efficiency restrictions. These results are not only of theoretical interest, but more importantly they provide the basis for econometric estimation and testing of nested hypotheses. These econometric issues are discussed in detail.     

A mean-variance framework for tests of asset pricing models

This article presents a mean-variance framework for likelihood-ratiotests of asset pricing models. A pricing model is tested byexamining the position of one or more reference portfolios insample mean-standard-deviation space. Included are tests ofboth single-beta and multiple-beta relations, with or withouta riskless asset, using either a general or a specific alternativehypothesis. Tests with a factor that is not a portfolio returnare also included. The mean-variance framework is illustratedby testing the zero-beta CAPM, a two-beta pricing model, andthe consumption-beta model.     

Time-consistent mean-variance reinsurance-investment strategy for insurers under CEV model

We consider an optimal time-consistent reinsurance-investment strategy selection problem for an insurer whose surplus is governed by a compound Poisson risk model. In our model, the insurer transfers part of the risk due to insurance claims via a proportional reinsurance and invests the surplus in a simplified financial market consisting of a risk-free asset and a risky stock. The dynamics of the risky stock is governed by a constant elasticity of variance model to incorporate conditional heteroscedasticity as well as the feedback effect of an asset’s price on its volatility. The objective of the insurer is to choose an optimal time-consistent reinsurance-investment strategy so as to maximize the expected terminal surplus while minimizing the variance of the terminal surplus. We investigate the problem using the Hamilton-Jacobi-Bellman dynamic programming approach. Closed-form solutions for the optimal reinsurance-investment strategies and the corresponding value functions are obtained in both the compound Poisson risk model and its diffusion approximation. Numerical examples are also provided to illustrate how the optimal reinsurance-investment strategy changes when some model parameters vary.     

An extension of mean-variance hedging to the discontinuous case

Our goal in this paper is to give a representation of the mean-variance hedging strategy for models whose asset price process is discontinuous as an extension of Gouriéroux, Laurent and Pham (1998) and Rheinländer and Schweizer (1997). However, we have to impose some additional assumptions related to the variance-optimal martingale measure.Received: April 2004, Mathematics Subject Classification (2000): 91B28, 60G48, 60H05JEL Classification: G10I would like to express my gratitude to Martin Schweizer and referees for their much valuable advice. I also would like to express my gratitude to Tsukasa Fujiwara, Hideo Nagai and Jun Sekine for many helpful comments.     

Portfolio selections under mean-variance preference with multiple priors for means and variances

We study portfolio selections under mean-variance preference with multiple priors for means and variances. We introduce two types of multiple priors, the priors for means and the priors for variances of risky asset returns. As our framework, in the absence of a risk-free asset, the global minimum-variance portfolio is optimal when the investor is extremely ambiguity averse with respect to means, and the equally weighted portfolio is optimal when the investor is extremely ambiguity averse with respect to variances.     

Performance evaluation with high moments and disaster risk

Traditional performance evaluation measures do not account for tail events and rare disasters. To address this issue, we reinterpret the riskiness measures of Aumann and Serrano (2008) and Foster and Hart (2009) as performance indices. We derive the moment properties of these indices and their sensitivity to rare disasters and show that they are consistent with the asset pricing literature. As applications, we show that “anomalous” investment strategies such as “momentum” or investment in private equity lose much of their glamour when accounting for high moments and rare events. Furthermore, using the indices to select mutual funds results in desirable high-moment properties out of sample.