Can long-run dynamic optimal strategies outperform fixed-mix portfolios? Evidence from multiple data sets

Using five alternative data sets and a range of specifications concerning the underlying linear predictability models, we study whether long-run dynamic optimizing portfolio strategies may actually outperform simpler benchmarks in out-of-sample tests. The dynamic portfolio problems are solved using a combination of dynamic programming and Monte Carlo methods. The benchmarks are represented by two typical fixed mix strategies: the celebrated equally-weighted portfolio and a myopic, Markowitz-style strategy that fails to account for any predictability in asset returns. Within a framework in which the investor maximizes expected HARA (constant relative risk aversion) utility in a frictionless market, our key finding is that there are enormous difference in optimal long-horizon (in-sample) weights between the mean–variance benchmark and the optimal dynamic weights. In out-of-sample comparisons, there is however no clear-cut, systematic, evidence that long-horizon dynamic strategies outperform naively diversified portfolios.     

Mean–variance approximations to expected utility

It is often asserted that the application of mean–variance analysis assumes normal (Gaussian) return distributions or quadratic utility functions. This common mistake confuses sufficient versus necessary conditions for the applicability of modern portfolio theory. If one believes (as does the author) that choice should be guided by the expected utility maxim, then the necessary and sufficient condition for the practical use of mean–variance analysis is that a careful choice from a mean–variance efficient frontier will approximately maximize expected utility for a wide variety of concave (risk-averse) utility functions. This paper reviews a half-century of research on mean–variance approximations to expected utility. The many studies in this field have been generally supportive of mean–variance analysis, subject to certain (initially unanticipated) caveats.     

Integrated portfolio management with options

In this paper we examine the problem of managing portfolios consisting of both, stocks and options. For the simultaneous optimization of stock and option positions we base our analysis on the generally accepted mean–variance framework. First, we analyze the effects of options on the mean–variance efficient frontier if they are considered as separate investment alternatives. Due to the resulting asymmetric portfolio return distribution mean–variance analysis will be not sufficient to identify optimal optioned portfolios. Additional investor preferences which are expressed in terms of shortfall constraints allow a more detailed portfolio specification. Under a mean–variance and shortfall preference structure we then derive optioned portfolios with a maximum expected return. To circumvent the technical optimization problems arising from stochastic constraints we use an approximation of the return distribution and develop economically meaningful conditions under which the complex optimization problem can be transformed into a linear problem being comparably easy to solve. Empirical results based on both, empirical market data and Monte Carlo simulations, illustrate the portfolio optimization procedure with options.     

On the equivalence of quadratic optimization problems commonly used in portfolio theory

In the paper, we consider three quadratic optimization problems which are frequently applied in portfolio theory, i.e., the Markowitz mean–variance problem as well as the problems based on the mean–variance utility function and the quadratic utility. Conditions are derived under which the solutions of these three optimization procedures coincide and are lying on the efficient frontier, the set of mean–variance optimal portfolios. It is shown that the solutions of the Markowitz optimization problem and the quadratic utility problem are not always mean–variance efficient.     

Robust portfolios that do not tilt factor exposure

Robust portfolios reduce the uncertainty in portfolio performance. In particular, the worst-case optimization approach is based on the Markowitz model and form portfolios that are more robust compared to mean–variance portfolios. However, since the robust formulation finds a different portfolio from the optimal mean–variance portfolio, the two portfolios may have dissimilar levels of factor exposure. In most cases, investors need a portfolio that is not only robust but also has a desired level of dependency on factor movement for managing the total portfolio risk. Therefore, we introduce new robust formulations that allow investors to control the factor exposure of portfolios. Empirical analysis shows that the robust portfolios from the proposed formulations are more robust than the classical mean–variance approach with comparable levels of exposure on fundamental factors.     

Subjective mean–variance preferences without expected utility

Classical derivations of mean–variance preferences have all relied on the expected utility hypothesis. Numerous experimental studies have revealed that the expected utility model is systematically violated in practice. Such findings and the simplicity of the mean–variance framework have led researchers and practitioners to employ the mean–variance model without expected utility. However, the theoretical foundations of these models are scant.I provide behavioral foundations for a class of mean–variance preferences. My set of axioms characterizes an individual who assigns subjective probability to events and judges each portfolio solely on the basis of the mean and variance of its implied distribution over returns but does not necessarily rank the portfolios according to expected utility. I clarify the differences across specifications of my model. In addition, this model is robust to the consideration of a wide body of observed behaviors under uncertainty, which are inconsistent with the classical mean–variance model.     

Geometric representation of the mean–variance–skewness portfolio frontier based upon the shortage function

The literature suggests that investors prefer portfolios based on mean, variance and skewness rather than portfolios based on mean–variance (MV) criteria solely. Furthermore, a small variety of methods have been proposed to determine mean–variance–skewness (MVS) optimal portfolios. Recently, the shortage function has been introduced as a measure of efficiency, allowing to characterize MVS optimal portfolios using non-parametric mathematical programming tools. While tracing the MV portfolio frontier has become trivial, the geometric representation of the MVS frontier is an open challenge. A hitherto unnoticed advantage of the shortage function is that it allows to geometrically represent the MVS portfolio frontier. The purpose of this contribution is to systematically develop geometric representations of the MVS portfolio frontier using the shortage function and related approaches.     

A conditional-SGT-VaR approach with alternative GARCH models

This paper proposes a conditional technique for the estimation of VaR and expected shortfall measures based on the skewed generalized t (SGT) distribution. The estimation of the conditional mean and conditional variance of returns is based on ten popular variations of the GARCH model. The results indicate that the TS-GARCH and EGARCH models have the best overall performance. The remaining GARCH specifications, except in a few cases, produce acceptable results. An unconditional SGT-VaR performs well on an in-sample evaluation and fails the tests on an out-of-sample evaluation. The latter indicates the need to incorporate time-varying mean and volatility estimates in the computation of VaR and expected shortfall measures.     

Robust portfolio optimization with a hybrid heuristic algorithm

Estimation errors in both the expected returns and the covariance matrix hamper the construction of reliable portfolios within the Markowitz framework. Robust techniques that incorporate the uncertainty about the unknown parameters are suggested in the literature. We propose a modification as well as an extension of such a technique and compare both with another robust approach. In order to eliminate oversimplifications of Markowitz’ portfolio theory, we generalize the optimization framework to better emulate a more realistic investment environment. Because the adjusted optimization problem is no longer solvable with standard algorithms, we employ a hybrid heuristic to tackle this problem. Our empirical analysis is conducted with a moving time window for returns of the German stock index DAX100. The results of all three robust approaches yield more stable portfolio compositions than those of the original Markowitz framework. Moreover, the out-of-sample risk of the robust approaches is lower and less volatile while their returns are not necessarily smaller.     

Mean–variance optimal portfolios in the presence of a benchmark with applications to fraud detection

We first study mean–variance efficient portfolios when there are no trading constraints and show that optimal strategies perform poorly in bear markets. We then assume that investors use a stochastic benchmark (linked to the market) as a reference portfolio. We derive mean–variance efficient portfolios when investors aim to achieve a given correlation (or a given dependence structure) with this benchmark. We also provide upper bounds on Sharpe ratios and show how these bounds can be useful for fraud detection. For example, it is shown that under some conditions it is not possible for investment funds to display a negative correlation with the financial market and to have a positive Sharpe ratio. All the results are illustrated in a Black–Scholes market.