Portfolio selection with qualitative input

We formulate a mean-variance portfolio selection problem that accommodates qualitative input about expected returns and provide an algorithm that solves the problem. This model and algorithm can be used, for example, when a portfolio manager determines that one industry will benefit more from a regulatory change than another but is unable to quantify the degree of difference. Qualitative views are expressed in terms of linear inequalities among expected returns. Our formulation builds on the Black-Litterman model for portfolio selection. The algorithm makes use of an adaptation of the hit-and-run method for Markov chain Monte Carlo simulation. We also present computational results that illustrate advantages of our approach over alternative heuristic methods for incorporating qualitative input.     

Portfolio selection with heavy tails

Consider the portfolio problem of choosing the mix between stocks and bonds under a downside risk constraint. Typically stock returns exhibit fatter tails than bonds corresponding to their greater downside risk. Downside risk criteria like the safety first criterion therefore often select corner solutions in the sense of a bonds only portfolio. This is due to a focus on the asymptotically dominating first order Pareto term of the portfolio return distribution. We show that if second order terms are taken into account, a balanced solution emerges. The theory is applied to empirical examples from the literature.     

Portfolio selection subject to experts' judgments

Since Markowitz [Markowitz, H. M. (1952). Portfolio selection. The Journal of Finance, 7, 77-91.], mean-variance theory has assumed that risky-asset returns to be random variables. The theory deals with this uncertainty by further assuming that investors hold homogeneous beliefs regarding the probability distribution governing return uncertainty. While the theory deals with return uncertainty, it fails to address measurement imprecision. In his original work, Markowitz recognized the need to combine randomness with heterogeneous expert judgment resulting in such imprecision. The main objective contributions of the paper are (i) to explore the implications of fuzzy return indeterminacy on mean-variance optimal portfolio choice, (ii) to use bid-ask spread as a proxy measure of the indeterminacy or “fuzzy” nature of random returns, and (iii) to introduce a brief, self-contained glimpse of empirical representations to practitioners unfamiliar with the fuzzy modeling field. Exposition, such as this one, is expected to open new collaborations between other branches of fuzzy mathematics and asset-pricing theories.     

Portfolio selection with mental accounts and delegation

Das et al. (2010) develop an elegant framework where an investor selects portfolios within mental accounts but ends up holding an aggregate portfolio on the mean-variance frontier. This investor directly allocates the wealth in each account among available assets. In practice, however, investors often delegate the task of allocating wealth among assets to portfolio managers who seek to beat certain benchmarks. Accordingly, we extend their framework to the case where the investor allocates the wealth in each account among portfolio managers. Our contribution is threefold. First, we provide an analytical characterization of the existence and composition of the optimal portfolios within accounts and the aggregate portfolio. Second, we present conditions under which such portfolios are not on the mean-variance frontier, and conditions under which they are. Third, we show that the aforementioned analytical characterization is also applicable within the framework of Das et al. and thus improves upon their numerical approach.     

Portfolio selection with mental accounts and background risk

Das et al. (2010) develop a model where an investor divides his or her wealth among mental accounts with motives such as retirement and bequest. Nevertheless, the investor ends up selecting portfolios within mental accounts and an aggregate portfolio that lie on the mean–variance frontier. Importantly, they assume that the investor only faces portfolio risk. In practice, however, many individuals also face background risk. Accordingly, our paper expands upon theirs by considering the case where the investor faces background risk. Our contribution is threefold. First, we provide an analytical characterization of the existence and composition of the optimal portfolios within accounts and the aggregate portfolio. Second, we show that these portfolios lie away from the mean–variance frontier under fairly general conditions. Third, we find that the composition and location of such portfolios can differ notably from those of portfolios on the mean–variance frontier.     

Portfolio selection with skewness: A multiple-objective approach

In the presence of skewness, the portfolio selection entails considering competing and conflicting objectives, such as maximizing both its expected returns and skewness, and minimizing its risk for decreasing absolute risk-aversion investors. Since it is unlikely that a portfolio can solve the multiple-objectives problem simultaneously, a portfolio selection must depend on the investor's preference among objectives. This article shows that investor preference can be incorporated into a polynomial goal programming problem from which a portfolio selection with skewness is determined. An inefficient mean-variance portfolio may be optimal in the mean-variance-skewness content. The features of applying polynomial goal programming in portfolio selection are 1) the existence of an optimal solution, 2) the flexibility of the incorporation of investor preference, and 3) the relative simplicity of computational requirements.     

Portfolio allocation using multivariate variance gamma models

In this paper, we investigate empirically the effect of using higher moments in portfolio allocation when parametric and nonparametric models are used. The nonparametric model considered in this paper is the sample approach; the parametric model is constructed assuming multivariate variance gamma (MVG) joint distribution for asset returns.We consider the MVG models proposed by Madan and Seneta (1990), Semeraro (2008) and Wang (2009). We perform an out-of-sample analysis comparing the optimal portfolios obtained using the MVG models and the sample approach. Our portfolio is composed of 18 assets selected from the S&P500 Index and the dataset consists of daily returns observed from 01/04/2000 to 01/09/2011.     

Portfolio selection, diversification and fund-of-funds: a note

The present paper examines the performance and diversification properties of active Australian equity fund‐of‐funds (FoF). Simulation analysis is employed to examine portfolio performance as a function of the number of funds in the portfolio. The present paper finds that as the number of funds in an FoF portfolio increases, performance improves in a mean–variance setting; however, measures of skewness and kurtosis behave less favourably given an investor's preferences for the higher moments of the return distribution. The majority of diversification benefits are realized when a portfolio of approximately 6 active equity funds are included in the FoF portfolio.     

Portfolio performance of linear SDF models: an out-of-sample assessment

We evaluate linear stochastic discount factor models using an ex-post portfolio metric: the realized out-of-sample Sharpe ratio of mean–variance portfolios backed by alternative linear factor models. Using a sample of monthly US portfolio returns spanning the period 1968–2016, we find evidence that multifactor linear models have better empirical properties than the CAPM, not only when the cross-section of expected returns is evaluated in-sample, but also when they are used to inform one-month ahead portfolio selection. When we compare portfolios associated to multifactor models with mean–variance decisions implied by the single-factor CAPM, we document statistically significant differences in Sharpe ratios of up to 10 percent. Linear multifactor models that provide the best in-sample fit also yield the highest realized Sharpe ratios.     

Portfolio optimization algorithms,simplified criteria,and security selection: A contrast and evaluation

The Markowitz full covariance model provides a general framework for analysis of the porfolio selection problem. Three alternative solution methodologies have been developed to facilitate normative applications, but this article shows that they lead to markedly different stock selection and portfolio weighting decisions. In sample-based applications, incompatibilities arise due to model misspecifications and different distributional assumptions, and from the interactive effects of estimation error, optimization model selection bias, and conflicting distributional assumptions.     

Portfolio Selection in Stochastic Environments

In this article, I explicitly solve dynamic portfolio choiceproblems, up to the solution of an ordinary differential equation(ODE), when the asset returns are quadratic and the agent hasa constant relative risk aversion (CRRA) coefficient. My solutionincludes as special cases many existing explicit solutions ofdynamic portfolio choice problems. I also present three applicationsthat are not in the literature. Application 1 is the bond portfolioselection problem when bond returns are described by "quadraticterm structure models." Application 2 is the stock portfolioselection problem when stock return volatility is stochasticas in Heston model. Application 3 is a bond and stock portfolioselection problem when the interest rate is stochastic and stockreturns display stochastic volatility. (JEL G11)     

Portfolio returns and manager activity: How to decompose tracking error into security selection and market timing

We develop a new method for detecting portfolio manager activity. Our method relies exclusively on portfolio returns and, consequently, avoids the pitfalls associated with disclosed portfolio holdings. We investigate the link between activity and performance of actively managed U.S. equity funds from 2000 to 2007 and document robust evidence that future performance is positively related to past stock picking and negatively associated with past market timing. Finally, we find that portfolio manager activity is highly persistent over time, which supports the conclusion that stock picking increases performance while market timing decreases performance.     

Portfolio credit-risk optimization

This paper evaluates several alternative formulations for minimizing the credit risk of a portfolio of financial contracts with different counterparties. Credit risk optimization is challenging because the portfolio loss distribution is typically unavailable in closed form. This makes it difficult to accurately compute Value-at-Risk (VaR) and expected shortfall (ES) at the extreme quantiles that are of practical interest to financial institutions. Our formulations all exploit the conditional independence of counterparties under a structural credit risk model. We consider various approximations to the conditional portfolio loss distribution and formulate VaR and ES minimization problems for each case. We use two realistic credit portfolios to assess the in- and out-of-sample performance for the resulting VaR- and ES-optimized portfolios, as well as for those which we obtain by minimizing the variance or the second moment of the portfolio losses. We find that a Normal approximation to the conditional loss distribution performs best from a practical standpoint.     

Graphical Portfolio Analysis

This paper presents a new methodology for portfolio analysis based on the correspondence between the expression for the standard deviation of a two-asset portfolio and the magnitude of the sum of two complex numbers. This approach offers a geometric alternative to traditional portfolio analysis. The pedagogical advantages of the new framework are illustrated by rederiving many efficient set mathematics results. A previously unrecognized fact is uncovered using the graphical technique that the sum of the maximum and minimum betas for efficient portfolios is 1, so knowledge of one extreme beta implies knowledge of the other.     

Asset pricing models: implications for expected returns and portfolio selection

When a risk factor is missing from an asset pricing model, theresulting mispricing is embedded within the residual covariancematrix. Exploiting this phenomenon leads to expected returnestimates that are more stable and precise than estimates deliveredby standard methods. Portfolio selection can also be improved.At an extreme, optimal portfolio weights are proportional toexpected returns when no factors are observable. We find thatsuch portfolios perform well in simulations and in out-of-samplecomparisons.     

“KLICing” there and back again: Portfolio selection using the empirical likelihood divergence and Hellinger distance

Stutzer (2000, 2003) proposes the decay-rate maximizing portfolio selection rule wherein the investor selects the asset mix that maximizes the rate at which the probability of shortfall decays to zero. A close examination of this rule reveals that it ranks portfolios by computing the divergence, in the Kullback-Leibler sense, between the unweighted portfolio return distribution and a tilted distribution meaned at the predetermined target or benchmark rate of return selected by or imposed upon the investor. This result implies, in the IID case, that Stutzer's rules can be written as a benchmark constrained Kullback-Leibler-based optimization problem with an endogenous utility interpretation. Here we expand on this idea by introducing two closely related portfolio selection rules based on the empirical likelihood divergence and the Hellinger-Matusita distance. The first of these is the reversed Kullback-Leibler divergence and the second is proportional to the average of the two divergences. The theoretical and in-sample properties of the new criteria suggest them to be competitive with and in some cases better than existing methods, especially in terms of skewness preference.     

Time-Invariant Portfolio Insurance Strategies

This paper characterizes the complete class of time-invariant portfolio insurance strategies and derives the corresponding value functions that relate the wealth accumulated under the strategy to the value of the underlying insured portfolio. Time-invariant strategies are shown to correspond to the long-run policies for a broad class of portfolio insurance payoff functions.     

Corporate Portfolio Management Roundtable

The dean of a top ten business school, the chair of a large investment management firm, two corporate M&A leaders, a CFO, a leading M&A investment banker, and a corporate finance advisor discuss the following questions:

• ? What are today's best practices in corporate portfolio management? What roles should be played by boards, senior managers, and business unit leaders?
• ? What are the typical barriers to successful implementation and how can they be overcome?
• ? Should portfolio management be linked to financial policies such as decisions on capital structure, dividends, and share repurchase?
• ? How should all of the above be disclosed to the investor community?

After acknowledging the considerable challenges to optimal portfolio management in public companies, the panelists offer suggestions that include:

• ? Companies should establish an independent group that functions like a “SWAT team” to support portfolio management. Such groups would be given access to (or produce themselves) business‐unit level data on economic returns and capital employed, and develop an “outside‐in” view of each business's standalone valuation.
• ? Boards should consider using their annual strategy “off‐sites” to explore all possible alternatives for driving share‐holder value, including organic growth, divestitures and acquisitions, as well as changes in dividends, share repurchases, and capital structure.
• ? Performance measurement and compensation frameworks need to be revamped to encourage line managers to think more like investors, not only seeking value‐creating growth but also making divestitures at the right time. CEOs and CFOs should take the lead in developing a shared value creation model that clearly articulates how capital will be allocated.