Optimal hedge fund portfolios under liquidation risk

We use an expected utility framework to integrate the liquidation risk of hedge funds into portfolio allocation problems. The introduction of realistic investment constraints complicates the determination of the optimal solution, which is solved using a genetic algorithm that mimics the mechanism of natural evolution. We analyse the impact of the liquidation risk, of the investment constraints and of the agent's degree of risk aversion on the optimal allocation and on the optimal certainty equivalent of hedge fund portfolios. We observe, in particular, that the portfolio weights and their performance are significantly affected by liquidation risk. Finally, tight portfolio constraints can only provide limited protection against liquidation risk. This approach is of special interest to fund of hedge fund managers who wish to include the hedge fund liquidation risk in their portfolio optimization scheme.     

Performance analysis of a collateralized fund obligation (CFO) equity tranche

This article examines the performance of the junior tranche of a collateralized fund obligation (CFO), i.e. the residual claim (equity) on a securitized portfolio of hedge funds. We use a polynomial goal programming model to create optimal portfolios of hedge funds, conditional to investor preferences and diversification constraints (maximum allocation per strategy). For each portfolio, we build CFO structures that have different levels of leverage, and analyze both the stand-alone performance as well as potential diversification benefits (low systematic risk exposures) of investing in the equity tranche of these structures. We find that the unconstrained mean-variance portfolio yields a high performance, but greater exposure to systematic risk. We observe the exact opposite picture in the case of unconstrained optimization, where a skewness bias is added, thus proving the existence of a trade-off between stand-alone performance and low exposure to systematic risk factors. We provide evidence that leveraged exposure to these hedge fund portfolios through the structuring of CFOs creates value for the equity tranche investor, even during the recent financial crisis.     

Nonlinearly weighted convex risk measure and its application

We propose a new class of risk measures which satisfy convexity and monotonicity, two well-accepted axioms a reasonable and realistic risk measure should satisfy. Through a nonlinear weight function, the new measure can flexibly reflect the investor’s degree of risk aversion, and can control the fat-tail phenomenon of the loss distribution. A realistic portfolio selection model with typical market frictions taken into account is established based on the new measure. Real data from the Chinese stock markets and American stock markets are used for empirical comparison of the new risk measure with the expected shortfall risk measure. The in-sample and out-of-sample empirical results show that the new risk measure and the corresponding portfolio selection model can not only reflect the investor’s risk-averse attitude and the impact of different trading constraints, but can find robust optimal portfolios, which are superior to the corresponding optimal portfolios obtained under the expected shortfall risk measure.     

The Effect of Shortfall as a Risk Measure for Portfolios with Hedge Funds

Abstract:  Current research suggests that the large downside risk in hedge fund returns disqualifies the variance as an appropriate risk measure. For example, one can easily construct portfolios with nonlinear pay-offs that have both a high Sharpe ratio and a high downside risk. This paper examines the consequences of shortfall-based risk measures in the context of portfolio optimization. In contrast to popular belief, we show that negative skewness for optimal mean-shortfall portfolios can be much greater than for mean-variance portfolios. Using empirical hedge fund return data we show that the optimal mean-shortfall portfolio substantially reduces the probability of small shortfalls at the expense of an increased extreme crash probability. We explain this by proving analytically under what conditions short-put payoffs are optimal for a mean-shortfall investor. Finally, we show that quadratic shortfall or semivariance is less prone to these problems. This suggests that the precise choice of the downside risk measure is highly relevant for optimal portfolio construction under loss averse preferences.     

Household portfolio optimization with XTFs? An empirical study using the SHS-base

XTFs are plain-vanilla Exchange Traded Funds (ETFs) which replicate a broad, internationally diversified market index. We question, if XTFs can optimize the performance of households’ portfolios when taking multiple relevant asset classes into account, not only stocks. As opposed to most existing studies, we apply representative household portfolio data to estimate households’ portfolios. Households’ portfolios in our sample show similar compositions and can be grouped into one of three stylized portfolio compositions which exhibit asset class concentrations on cash/savings, mutual funds and individual stocks. For each stylized portfolio, we first investigate if an easily investable 60/40 stock/bond XTF portfolio which is risk-adjusted (including (de-)leverage costs) to the risk of the stylized portfolios, achieves higher returns than the stylized portfolios. This is the case for all stylized portfolios, even those with concentrations on cash/savings or mutual funds. Second, we examine risk/return-changes when replacing the entire risky assets of the stylized portfolios with the 60/40 stock/bond XTF portfolio including transaction costs. This leads to return enhancements in all stylized portfolios and particularly in the portfolio with high stock concentrations to risk reductions. Overall, we find that XTFs are generally suitable to optimize the performance of households’ portfolios under consideration of multiple relevant asset classes.     

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.     

Optimal commodity asset allocation with a coherent market risk modeling

This paper fills a fundamental gap in commodity price risk management and optimal portfolio selection literatures by contributing a thorough reflection on trading risk modeling with a dynamic asset allocation process and under the supposition of illiquid and adverse market settings. This paper analyzes, from a portfolio managers' perspective, the performance of liquidity adjusted risk modeling in obtaining efficient and coherent investable commodity portfolios under normal and adverse market conditions. As such, the author argues that liquidity risk associated with the uncertainty of liquidating multiple commodity assets over given holding periods is a key factor in formalizing and measuring overall trading risk and is thus an important component to model, particularly in the wake of the repercussions of the recent 2008 financial crisis. To this end, this article proposes a practical technique for the quantification of liquidity trading risk for large portfolios that consist of multiple commodity assets and whereby the holding periods are adjusted according to the specific needs of each trading portfolio. Specifically, the paper proposes a robust technique to commodity optimal portfolio selection, in a liquidity-adjusted value-at-risk (L-VaR) framework, and particularly from the perspective of large portfolios that have both long and short positions or portfolios that consist of merely pure long trading positions. Moreover, in this paper, the author develops a portfolio selection model and an optimization-algorithm which allocates commodity assets by minimizing the L-VaR subject to applying credible operational and financial constraints based on fundamental asset management considerations. The empirical optimization results indicate that this alternate L-VaR technique can be regarded as a robust portfolio management tool and can have many uses and applications in real-world asset management practices and predominantly for fund managers with large commodity portfolios.     

Leverage constraints and asset prices: Insights from mutual fund risk taking

Prior theory suggests that time variation in the degree to which leverage constraints bind affects the pricing kernel. We propose a measure for this leverage constraint tightness by inverting the argument that constrained investors tilt their portfolios to riskier assets. We show that the average market beta of actively managed mutual funds—intermediaries facing leverage restrictions—captures their desire for leverage and thus the tightness of constraints. Consistent with theory, it strongly predicts returns of the betting-against-beta portfolio, and is a priced risk factor in the cross-section of mutual funds and stocks. Funds with low exposure to the factor outperform high-exposure funds by 5% annually, and for stocks this difference reaches 7%. Our results show that the tightness of leverage constraints has important implications for asset prices.     

Asymptotic behaviour of mean-quantile efficient portfolios

In this paper we investigate portfolio optimization in the Black–Scholes continuous-time setting under quantile based risk measures: value at risk, capital at risk and relative value at risk. We show that the optimization results are consistent with Merton’s two-fund separation theorem, i.e., that every optimal strategy is a weighted average of the bond and Merton’s portfolio. We present optimization results for constrained portfolios with respect to these risk measures, showing for instance that under value at risk, in better markets and during longer time horizons, it is optimal to invest less into the risky assets.This research was partially supported by the National Science and Engineering Research Council of Canada, and the Mathematics of Information Technology and Complex Systems (MITACS) Network of Centres of Excellence.     

Measuring Mutual Fund Performance with Characteristic-Based Benchmarks

This article develops and applies new measures of portfolio performance which use benchmarks based on the characteristics of stocks held by the portfolios that are evaluated. Specifically, the benchmarks are constructed from the returns of 125 passive portfolios that are matched with stocks held in the evaluated portfolio on the basis of the market capitalization, book-to-market, and prior-year return characteristics of those stocks. Based on these benchmarks, “Characteristic Timing” and “Characteristic Selectivity” measures are developed that detect, respectively, whether portfolio managers successfully time their portfolio weightings on these characteristics and whether managers can select stocks that outperform the average stock having the same characteristics. We apply these measures to a new database of mutual fund holdings covering over 2500 equity funds from 1975 to 1994. Our results show that mutual funds, particularly aggressive-growth funds, exhibit some selectivity ability, but that funds exhibit no characteristic timing ability.     

Fund portfolio networks: A climate risk perspective

Within Europe, investment funds are more exposed to climate-sensitive economic sectors than banks, insurers, and pension funds. However, few climate-related financial risk assessments of the fund sector have been conducted. We use 8 trillion EUR of fund portfolio holdings to help fill this gap, using the network of portfolio overlaps. Funds with more polluting portfolios (brown funds) invest across more firms than funds with cleaner portfolios (green funds). This apparent diversification hides a concentration risk: brown funds are more closely connected with each other (have more similar portfolios) than green funds, which tend to herd less (have less similar portfolios with each other). This suggests that, in the event of a widespread climate-related financial shock, brown funds will face greater stress levels than green funds. A climate risk scenario exercise confirms this: among total system losses of 443 billion EUR, brown funds' losses are typically between two and three times higher than green funds' losses. Brown funds also have more systemic impact: because they play a more central role in the investment fund network, brown funds contribute twice as much towards system-wide losses as green funds. These findings suggest that, despite the growing attention paid to sustainable investing, systemic vulnerabilities remain and many funds' portfolio diversification approaches do not yet adequately incorporate climate risk.     

Learning risk preferences from investment portfolios using inverse optimization

The level of risk an investor can endure, known as risk-preference, is a subjective choice that is tightly related to psychology and behavioral science in decision making. This paper presents a novel approach of measuring risk preference from existing portfolios using inverse optimization on mean–variance portfolio allocation framework. Our approach allows the learner to continuously estimate real-time risk preferences using concurrent observed portfolios and market price data. We demonstrate our methods on robotic investment portfolios and real market data that consists of 20 years of asset pricing and 10 years of mutual fund portfolio holdings. Moreover, the quantified risk preference parameters are validated with two well-known risk measurements currently applied in the field. The proposed methods could lead to practical and fruitful innovations in automated/personalized portfolio management, such as Robo-advising, to augment financial advisors’ decision intelligence in a long-term investment horizon.     

Econometrics of efficient fitted portfolios

In this paper we propose a mean variance analysis of the portfolio choice under constraints. An efficient portfolio under constraint is called fitted. We show that the fitted portfolios can consistently be estimated and used to assess the performances of the portfolio management. The explicit formula of the individual demand function for assets is also derived, and generalizes the demand function of the standard portfolio choice theory. The performance measures and associated statistics can be used to test the hypothesis of the portfolio efficiency under constraint. Moreover, we explain how to estimate subsets of constraints faced by an individual. Finally, we show that our framework is also adequate for the analysis of incomplete information.     

On measuring nonlinear risk with scarce observations

We propose a methodology for estimating the risk of portfolios that exhibit nonlinear dependence on the risk driving factors and have scarce observations, which is typical for portfolios of investments in hedge funds. The methodology consists of two steps: first, regressing the portfolio return on nonlinear functions of each single risk driving factor and second, merging together the obtained estimates taking into account the dependence between different factors. Performing the second step leads us to a certain probabilistic problem, for which we propose an analytic and computationally feasible solution for the case where the joint law of the factors is a Gaussian copula. A typical practical application can be to estimate the risk of a hedge fund or a portfolio of hedge funds. As a theoretical consequence of our results, we propose a new definition of the factor risk, i.e., the risk of a portfolio brought by a given factor.     

Conditional Value-at-Risk,spectral risk measures and (non-)diversification in portfolio selection problems – A comparison with mean–variance analysis

We study portfolio selection under Conditional Value-at-Risk and, as its natural extension, spectral risk measures, and compare it with traditional mean–variance analysis. Unlike the previous literature that considers an investor’s mean-spectral risk preferences for the choice of optimal portfolios only implicitly, we explicitly model these preferences in the form of a so-called spectral utility function. Within this more general framework, spectral risk measures tend towards corner solutions. If a risk free asset exists, diversification is never optimal. Similarly, without a risk free asset, only limited diversification is obtained. The reason is that spectral risk measures are based on a regulatory concept of diversification that differs fundamentally from the reward-risk tradeoff underlying the mean–variance framework.     

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.     

Socially responsible investment portfolios: Does the optimization process matter?

This study investigates the impact of the choice of optimization technique when constructing Socially Responsible Investment (SRI) portfolios. Corporate Social Performance (CSP) scores are price sensitive information that is subject to considerable estimation risk. Therefore, uncertainty in the input parameters is greater for SRI portfolios than conventional portfolios, and this affects the selection of the appropriate optimization method. We form SRI portfolios based on six different approaches and compare their performance along the dimensions of risk, risk-return trade-off, diversification and stability. Our results for SRI portfolios contradict those of the conventional portfolio optimization literature. We find that the more “formal” optimization approaches (Black-Litterman, Markowitz and robust estimation) lead to SRI portfolios that are both less risky and have superior risk-return trade-offs than do more simplistic approaches; although they also have more unstable asset allocations and lower diversification. Our conclusions are robust to a series of tests, including the use of different estimation windows and stricter screening criteria.     

A model for tax advantages of portfolios with many assets

Taxable portfolios present challenges for optimization models with even a limited number of assets. Holding many assets, however, has a distinct tax advantage over holding few assets. In this paper, we develop a model that takes an extreme view of a portfolio as a continuum of assets to gain the broadest possible advantage from holding many assets. We find the optimal strategy for trading in this portfolio in the absence of transaction costs and develop bounding approximations on the optimal value. We compare the results in a simulation study to a portfolio consisting only of a market index and show that the multi-asset portfolio’s tax advantage can lead either to significant consumption or bequest increases.     

The Diversification Effects of Initial Public Offerings

Abstract:  A firm's stock becomes publicly tradable through an initial public offering (IPO). This study suggests a portfolio diversification perspective to explore IPOs. We examine whether investors can gain diversification benefits by adding an IPO portfolio to a set of benchmark portfolios sorted by firm size and book-to-market ratio. Using US IPOs from 1980-2002, we find that adding a value-weighted IPO portfolio does lead to a statistically and economically significant enlargement of the investment opportunity set for investors relative to investing solely in a set of benchmark portfolios. Specifically, the Sharpe ratio of the tangency portfolio increases by 5.50% on average after including IPO stocks. Furthermore, IPOs associated with prestigious lead underwriters are the main source of this augmentation of the mean-variance investment opportunity set. Finally, our study implies that issuing IPO exchange traded funds or similar products can provide diversification gains to investors.     

Two-sided coherent risk measures and their application in realistic portfolio optimization

By using a different derivation scheme, a new class of two-sided coherent risk measures is constructed in this paper. Different from existing coherent risk measures, both positive and negative deviations from the expected return are considered in the new measure simultaneously but differently. This innovation makes it easy to reasonably describe and control the asymmetry and fat-tail characteristics of the loss distribution and to properly reflect the investor’s risk attitude. With its easy computation of the new risk measure, a realistic portfolio selection model is established by taking into account typical market frictions such as taxes, transaction costs, and value constraints. Empirical results demonstrate that our new portfolio selection model can not only suitably reflect the impact of different trading constraints, but find more robust optimal portfolios, which are better than the optimal portfolio obtained under the conditional value-at-risk measure in terms of diversification and typical performance ratios.