Continuous Maturity Diversification of Default-Free Bond Portfolios and a Generalization of Efficient Diversification

This paper presents a method for solving the mean-variance portfolio selection problem that is applicable to the case where the number of securities is nondenumerably infinite. Necessary conditions for the existence of an optimal portfolio density are obtained and an expression for the efficient frontier is derived. The conditions for the existence of an optimal portfolio of continuously maturing bonds when their covariance matrix is singular are used to derive an arbitrage-free bond pricing equation. A method for estimating the covariance matrix and the associated efficient frontier is presented.     

Dynamic mean–VaR portfolio selection in continuous time

The value-at-risk (VaR) is one of the most well-known downside risk measures due to its intuitive meaning and wide spectra of applications in practice. In this paper, we investigate the dynamic mean–VaR portfolio selection formulation in continuous time, while the majority of the current literature on mean–VaR portfolio selection mainly focuses on its static versions. Our contributions are twofold, in both building up a tractable formulation and deriving the corresponding optimal portfolio policy. By imposing a limit funding level on the terminal wealth, we conquer the ill-posedness exhibited in the original dynamic mean–VaR portfolio formulation. To overcome the difficulties arising from the VaR constraint and no bankruptcy constraint, we have combined the martingale approach with the quantile optimization technique in our solution framework to derive the optimal portfolio policy. In particular, we have characterized the condition for the existence of the Lagrange multiplier. When the opportunity set of the market setting is deterministic, the portfolio policy becomes analytical. Furthermore, the limit funding level not only enables us to solve the dynamic mean–VaR portfolio selection problem, but also offers a flexibility to tame the aggressiveness of the portfolio policy.     

Recursive risk measures under regime switching applied to portfolio selection

In this paper, we define the conditional risk measure under regime switching and derive a class of time consistent multi-period risk measures. To do so, we describe the information process with regime switching in a product space associated with the product of two filtrations. Moreover, we show how to establish the corresponding multi-stage portfolio selection models using the time consistent multi-period risk measure for medium-term or long-term investments. Take the conditional value-at-risk measure as an example, we demonstrate the resulting multi-stage portfolio selection problem can be transformed into a second-order cone programming problem. Finally, we carry out a series of empirical tests to illustrate the superior performance of the proposed random framework and the corresponding multi-stage portfolio selection model.     

Dynamic portfolio optimization with ambiguity aversion

This paper investigates portfolio selection in the presence of transaction costs and ambiguity about return predictability. By distinguishing between ambiguity aversion to returns and to return predictors, we derive the optimal dynamic trading rule in closed form within the framework of Gârleanu and Pedersen (2013), using the robust optimization method. We characterize its properties and the unique mechanism through which ambiguity aversion impacts the optimal robust strategy. In addition to the two trading principles documented in Gârleanu and Pedersen (2013), our model further implies that the robust strategy aims to reduce the expected loss arising from estimation errors. Ambiguity-averse investors trade toward an aim portfolio that gives less weight to highly volatile return-predicting factors, and loads less on the securities that have large and costly positions in the existing portfolio. Using data on various commodity futures, we show that the robust strategy outperforms the corresponding non-robust strategy in out-of-sample tests.     

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.     

Modelling fundamental analysis in portfolio selection

We derive a closed-form appraisal/information ratio of the investors who are able to observe some information about security fundamentals, by solving a simple instantaneous mean-variance portfolio choice problem in a continuous-time framework. Both analytical and numerical results suggest that investors should choose securities with a more volatile mispricing, a less volatile fundamental, a higher mean-reverting speed and a larger dividend. Our model calibrated with realistic parameters easily outperforms top-percentile portfolio managers in reality, which suggests that the implementation of fundamental analysis may be impeded in practice due to limits of arbitrage. Our paper is a first, necessarily simple, step towards filling the gap of modelling fundamental analysis in portfolio selection.     

Benchmark-based evaluation of portfolio performance: a characterization

Benchmarking is a universal practice in portfolio management and is well-studied in the optimal portfolio selection literature. This paper derives axiomatic foundations of the relative return, which underlies a benchmark-based evaluation of portfolio performance. We show that the existence of a benchmark naturally arises from a few basic axioms and is tightly linked to the economic theory. Our method relies on the use of both axiomatic and economic approaches to index number theory. We also analyze the problem of optimal portfolio selection under complete uncertainty about a future price system, where the objective function is the relative return.     

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.     

Polynomial goal programming and the implicit higher moment preferences of US institutional investors in hedge funds

Polynomial goal programming (PGP) is a flexible method that allows investor preferences for different moments of the return distribution of financial assets to be included in the portfolio optimization. The method is intuitive and particularly suitable for incorporating investor preferences in higher moments of the return distribution. However, until now, PGP has not been able to meet its full potential because it requires quantification of “real” preference parameters towards those moments. To date, the chosen preference parameters have been selected somewhat “arbitrarily”. Our goal is to calculate implied sets of preference parameters using investors’ choices of and the importance they attribute to risk and performance measures. We use three groups of institutional investors—pension funds, insurance companies, and endowments—and derive implied sets of preference parameters in the context of a hedge fund portfolio optimization. To determine “real” preferences for the higher moments of the portfolio return distribution, we first fit implied preference parameters so that the PGP optimal portfolio is identical to the desired hedge fund portfolio. With the obtained economically justified sets of preference parameters, the well-established PGP framework can be employed more efficiently to derive allocations that satisfy institutional investor expectations for hedge fund investments. Furthermore, the implied preference parameters enable fund of hedge fund managers and other investment managers to derive optimal portfolio allocations based on specific investor expectations. Moreover, the importance of individual moments, as well as their marginal rates of substitution, can be assessed.     

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.