Multi-scale variation,path risk and long-term portfolio management

Mean–variance analysis is constrained to weight the frequency bands in a return time series equally. A more flexible approach allows the user to assign preference weightings to short or longer run frequencies. Wavelet analysis provides further flexibility, removing the need to assume asset returns are stationary and encompassing alternative return concepts. The resulting portfolio choice methodology establishes a reward–energy efficient frontier that allows the user to trade off expected reward against path risk, reflecting preferences as between long or short run variation. The approach leads to dynamic analogues of mean–variance such as band pass portfolios that are more sensitive to variability at designated scales.     

Skewness Preference,Risk Taking and Expected Utility Maximisation

Available empirical evidence suggests that skewness preference plays an important role in understanding asset pricing and gambling. This paper establishes a skewness-comparability condition on probability distributions that is necessary and sufficient for any decision-maker's preferences over the distributions to depend on their means, variances, and third moments only. Under the condition, an Expected Utility maximizer's preferences for a larger mean, a smaller variance, and a larger third moment are shown to parallel, respectively, his preferences for a first-degree stochastic dominant improvement, a mean-preserving contraction, and a downside risk decrease and are characterized in terms of the von Neumann-Morgenstern utility function in exactly the same way. By showing that all Bernoulli distributions are mutually skewness comparable, we further show that in the wide range of economic models where these distributions are used individuals’ decisions under risk can be understood as trade-offs between mean, variance, and skewness. Our results on skewness-inducing transformations of random variables can also be applied to analyze the effects of progressive tax reforms on the incentive to make risky investments.     

Are Smart Beta strategies suitable for hedge fund portfolios?

In the equity context different Smart Beta strategies (such as the equally weighted, global minimum variance, equal risk contribution and maximum diversified ratio) have been proposed as alternatives to the cap-weighted index. These new approaches have attracted the attention of equity managers as different empirical analyses demonstrate the superiority of these strategies with respect to cap-weighted and to strategies that consider only mean and variance. In this paper we focus our attention to hedge fund index portfolios and analyze if the results reported in the equity framework are still valid. We consider hedge fund index and equity portfolios, the approaches used for portfolio selection are the four ‘Smart Beta’ strategies, mean–variance and mean–variance–skewness. In the two latter approaches the Taylor approximation of a CARA expected utility function and the Polynomial Goal Programing (PGP) have been used. The obtained portfolios are analyzed in the in-sample as well as in the out-of-sample perspectives.     

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.     

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.     

The price of variance risk

Between 1996 and 2014, it was costless on average to hedge news about future variance at horizons ranging from 1 quarter to 14 years. Only unexpected, transitory realized variance was significantly priced. These results present a challenge to many structural models of the variance risk premium, such as the intertemporal CAPM and recent models with Epstein–Zin preferences and long-run risks. The results are also difficult to reconcile with macro models in which volatility affects investment decisions. At the same time, the data allows us to distinguish between different disaster models; a model in which the stock market has a time-varying exposure to disasters and investors have power utility fits the major features of the variance term structure.     

How does the underlying affect the risk-return profiles of structured products?

Regulators of some of the major markets have adopted value at risk (VaR) as the risk measure for structured products. Under the mean-VaR framework, this paper discusses the impact of the underlying’s distribution on structured products. We expand the expected return and the VaR of a structured product with its underlying’s moments (mean, variance, skewness, and kurtosis), so that the impact of the moments can be investigated simultaneously. Results are tested by Monte Carlo and historical simulations. The findings show that for the majority of structured products, underlyings with large positive skewness are preferred. The preferences for the variance and the kurtosis of the underlying are both ambiguous.     

Risk,return and mean‐variance efficiency of Islamic and non‐Islamic stocks: evidence from a unique Malaysian data set

We find that Islamic stocks are more mean–variance efficient than non‐Islamic stocks and the market because they reduce risk of the same level of returns. We combine a unique Malaysian data set of individual Islamic stocks (as opposed to aggregate stock indices) since 1997 with a new method where we apply Islamic business activity and financial ratio screens to the universe of Malaysian stocks. Both data sets show that Islamic stocks have an annualised standard deviation that is on average 3.43–3.78 percent points lower compared to non‐Islamic stocks. This lower variance of Islamic stocks is exclusively driven by financial ratio screens.     

Composition of robust equity portfolios

Robust portfolios resolve the sensitivity issue identified as a concern in implementing mean–variance analysis. Because robust approaches are not widely used in practice due to a limited understanding regarding the portfolios constructed from these methods, we present an analysis of the composition of robust equity portfolios. We find that compared to the Markowitz mean–variance formulation, robust optimization formulations form portfolios that contain a fewer number of stocks, avoid large exposure to individual stocks, have higher portfolio beta, and show low correlation between weight and beta of the stocks composing the portfolio. These properties are also found for global minimum-variance portfolios.     

Dynamic portfolio choice without cash

We consider the dynamic mean–variance portfolio choice without cash under a game theoretic framework. The mean–variance criterion is investigated in the situation where an investor allocates the wealth among risky assets while keeping no cash in a bank account. The problem is solved explicitly up to solutions of ordinary differential equations by applying the extended Hamilton–Jacobi–Bellman equation system. Given a constant risk aversion coefficient, the optimal allocation without a risk-free asset depends linearly on the current wealth, while that with a risk-free asset turns out to be independent of the current wealth. We also study the minimum-variance criterion, which can be viewed as an extension of the mean–variance model when the risk aversion coefficient tends to infinity. Calibration exercises demonstrate that for large investments, the mean–variance model without cash yields the highest certainty equivalent return for both short-term and long-term investments. Furthermore, the mean–variance portfolio choices with and without cash yield almost the same Sharpe ratio for an investment with large initial wealth.     

On the Distributional Conditions for a Consumption-oriented Three Moment CAPM

In this paper, we develop sufficient conditions on probability distributions for a three moment (mean, variance, and skewness) consumption-oriented capital asset pricing model (CAPM) to price correctly a subset of assets. The assumptions that individuals in an allocationally efficient capital market have identical probability beliefs and monotone increasing strictly concave utility functions displaying nonincreasing absolute risk aversion imply an aggregate preference function that exhibits preference for expected return, aversion to variance of return, and preference for positive skewness. For otherwise arbitrary preferences, we show that quadratic characteristic lines are sufficient for a subset of assets to be priced according to a three moment consumption-oriented CAPM.     

Portfolio selection based on the mean–VaR efficient frontier

Value-at-Risk (VaR) has become one of the standard measures for assessing risk not only in the financial industry but also for asset allocations of individual investors. The traditional mean–variance framework for portfolio selection should, however, be revised when the investor's concern is the VaR instead of the standard deviation. This is especially true when asset returns are not normal. In this paper, we incorporate VaR in portfolio selection, and we propose a mean–VaR efficient frontier. Due to the two-objective optimization problem that is associated with the mean–VaR framework, an evolutionary multi-objective approach is required to construct the mean–VaR efficient frontier. Specifically, we consider the elitist non-dominated sorting Genetic Algorithm (NSGA-II). From our empirical analysis, we conclude that the risk-averse investor might inefficiently allocate his/her wealth if his/her decision is based on the mean–variance framework.     

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.     

On the performance of the minimum VaR portfolio

Alexander and Baptista [2002. Economic implications of using a mean-value-at-risk (VaR) model for portfolio selection: A comparison with mean–variance analysis. Journal of Economic Dynamics and Control 26: 1159–93] develop the concept of mean-VaR efficiency for portfolios and demonstrate its very close connection with mean–variance efficiency. In particular, they identify the minimum VaR portfolio as a special type of mean–variance efficient portfolio. Our empirical analysis finds that, for commonly used VaR breach probabilities, minimum VaR portfolios yield ex post returns that conform well with the specified VaR breach probabilities and with return/risk expectations. These results provide a considerable extension of evidence supporting the empirical validity and tractability of the mean-VaR efficiency concept.     

Risk optimizations on basis portfolios: The role of sorting

This paper investigates the mean–variance and diversification properties of risk-based strategies executed on style or basis portfolios. We show that the performance of these risk strategies is highly sensitive to the sorting procedure used to form the basis assets. Whereas the extant literature provides mixed support for the outperformance of smart beta strategies based on scientific diversification, our designed strategies outperform both the market model and multifactor model. Our testing framework is based on bootstrapped mean–variance spanning tests and shows valid conclusions when controlling for multiple testing, transaction costs, and luck from random basis portfolio construction rules. Economically, our results are supported by diversification-based properties.     

Searching for a listed infrastructure asset class using mean–variance spanning

This study examines the portfolio-diversification benefits of listed infrastructure stocks. We employ three different definitions of listed infrastructure and tests of mean–variance spanning. The evidence shows that viewing infrastructure as an asset class is misguided. We employ different schemes of infrastructure asset selection (both traditional asset classes and factor exposures) and discover that they do not provide portfolio-diversification benefits to existing asset allocation choices. We also find that defining and selecting infrastructure investments by business model as opposed to industrial sectors can reveal a very different investment profile, albeit one that improves the mean–variance efficient frontier since the global financial crisis. This study provides new insights into defining and benchmarking infrastructure equity investments in general, as well as into the extent to which public markets can be used to proxy the risk-adjusted performance of privately held infrastructure investments.     

Optimal asset allocation using a combination of implied and historical information

This paper investigates the contribution of option-implied information for strategic asset allocation for individuals with minimum-variance preferences and portfolios with a variety of assets. We propose a covariance matrix that exploits a mixture of historical and option-implied information. Implied variance measures are proposed for those assets for which option-implied information is available. Historical variance and correlation measures are applied to the remaining assets. The performance of this novel approach for constructing optimal investment portfolios is assessed out-of-sample using statistical and economic measures. An empirical application to a sophisticated portfolio comprised by a combination of equities, fixed income, alternative securities and cash deposits shows that implied variance measures with risk premium correction outperform variance measures constructed from historical data and implied variance without correction. This result is robust across investment portfolios, volatility and portfolio performance metrics, and rebalancing schemes.     

Are TIPS the “real” deal?: A conditional assessment of their role in a nominal portfolio

This paper documents predictable time-variation in the real return beta of US Treasury Inflation Protected Securities (TIPS) and in the Sharpe ratios of both indexed and conventional bonds. The conditional mean and volatility of both bonds and their conditional correlation first are estimated from predetermined variables. These estimates then are used to compute conditional real return betas and Sharpe ratios. The time-variation in real return betas and the correlation between TIPS and nominal bonds coincides with major developments in the fixed-income market. One implication of this predictability is that portfolio managers can assess more efficiently the risk of investing in TIPS versus conventional bonds. Conditional Sharpe ratios indicate that over the sample period, TIPS had superior volatility-adjusted returns relative to nominal bonds. This finding is striking in view of the absence of a major inflation scare during the sample period from February 1997 through August 2001, but is loosely consistent with the possibility that TIPS elevated rather than reduced Treasury borrowing costs. On the other hand, mean–variance spanning tests indicate that TIPS did not enhance the mean–variance efficiency of diversified portfolios.     

Bond Pricing with a Time‐Varying Price of Risk in an Estimated Medium‐Scale Bayesian DSGE Model

New Keynesian model in which households have Epstein–Zin preferences with time‐varying risk aversion and the central bank has a time‐varying inflation target can match the dynamics of nominal bond prices in the U.S. economy well. The model generates a large steady‐state term spread and its fitting errors for bond yields are comparable to those obtained from a nonstructural three‐factor model, and one‐third smaller than in models with a constant inflation target or risk aversion. Including data on interest rates has large effects on variance decompositions, making investment technology shocks much less important than found in other recent papers.     

Portfolio selection with a drawdown constraint

When identifying optimal portfolios, practitioners often impose a drawdown constraint. This constraint is even explicit in some money management contracts such as the one recently involving Merrill Lynch’ management of Unilever’s pension fund. In this setting, we provide a characterization of optimal portfolios using mean–variance analysis. In the absence of a benchmark, we find that while the constraint typically decreases the optimal portfolio’s standard deviation, the constrained optimal portfolio can be notably mean–variance inefficient. In the presence of a benchmark such as in the Merrill Lynch–Unilever contract, we find that the constraint increases the optimal portfolio’s standard deviation and tracking error volatility. Thus, the constraint negatively affects a portfolio manager’s ability to track a benchmark.