Diversification with volatility products

Recent changes to clearing-house regulations have promoted exchange-traded products offering risk premia previously accessible only over-the-counter. Thus, as correlations increase between equity, bonds and commodities, a new strand of research questions the benefits of home-grown diversification using volatility products. First we ask: “What expected returns will induce equity and bond investors to perceive ex-ante diversification benefits from adding volatility?” We call this the optimal diversification threshold. We derive the theoretical thresholds for minimum-variance, mean-variance and Black–Litterman optimization. Empirical analysis of US and European markets shows that volatility diversification is frequently perceived to be optimal, ex-ante, but these apparent benefits are almost never realized, being eroded by high roll and transaction costs. Exchange-traded volatility only proved an effective diversifier during the banking crisis. At other times long equity and bond portfolios diversified with volatility futures have not performed as well as those without diversification, or even those diversified with commodities.     

Active portfolio management with benchmarking: A frontier based on alpha

Active portfolio management often involves the objective of selecting a portfolio with minimum tracking error variance (TEV) for some expected gain in return over a benchmark. However, Roll (1992) shows that such portfolios are generally suboptimal because they do not belong to the mean-variance frontier and are thus overly risky. Our paper proposes an appealing method to lessen this suboptimality that involves the objective of selecting a portfolio from the set of portfolios that have minimum TEV for various levels of ex-ante alpha, which we refer to as the alpha-TEV frontier. Since practitioners commonly use ex-post alpha to assess the performance of managers, the use of this frontier aligns the objectives of managers with how their performance is evaluated. Furthermore, sensible choices of ex-ante alpha lead to the selection of portfolios that are less risky (in variance terms) than the portfolios that active managers would otherwise select.     

Bond portfolio optimization using dynamic factor models

A general class of dynamic factor models is used to obtain optimal bond portfolios, and to develop a duration-constrained mean-variance optimization, which can be used to improve bond indexing. An empirical application involving two large data sets of U.S. Treasuries shows that the proposed portfolio policy outperforms a set of yield curve strategies used in bond desks. Additionally, we propose a dynamic rule to switch among alternative bond investment strategies, and find that the benefits of such dynamic rule are even more pronounced when the set of available policies is augmented with the proposed mean-variance portfolios.     

Market liquidity,closeout procedures and initial margin for CCPs*

ABSTRACT

Closeout procedures enable central counterparties (CCPs) to respond to events that challenge the continuity of their normal operations, most frequently triggered by the default of one or more clearing members. The procedures typically entail three main phases: splitting, hedging, and liquidation. Together, these ensure the regularity of the settlement process through the prudent and orderly liquidation of the defaulters’ portfolios. Traditional approaches to CCPs’ margin requirements typically assume a simple closeout profile, not accounting for the ‘real life’ constraints embedded in the management of a default. The paper proposes an approach to assess how distinct closeout strategies may expose a CCP to different sets of risks and costs taking into account real-life frictions. The proposed approach enables the evaluation of a full spectrum of hedging strategies and the assessment of the trade-offs between the risk-reducing benefits of hedging and the transaction costs associated with it. Using an unexplored set of transactional level data, the proposed framework is evaluated assuming the hypothetical default of a real CCP clearing member. We consider the worst-case loss of a large interest rate swap portfolio observed over the past 10 years (i.e. 2005–2015) and show that an efficient hedging strategy which minimises risk may not be optimal when transaction costs are taken into account. The empirical analysis suggests that transaction costs are a significant factor and should be accounted for when designing a hedging strategy. Specifically, it is shown that the risk-reducing benefits arising from more tailored hedging strategies may introduce higher transaction costs, and therefore may change the effectiveness of the strategies.     

Islamic and conventional portfolios optimization under investor sentiment states: Bayesian vs Markowitz portfolio analysis

This paper investigates the portfolio optimization under investor’s sentiment states of Hidden Markov model and over a different time horizon during the period 2004–2016. To compare the efficient portfolios of the Islamic and the conventional stock indexes, we have employed two approaches: the Bayesian and Markowitz mean-variance. Our findings reveal that the Bayesian efficient frontier of Islamic and conventional stock portfolios is affected by the investor’s sentiment state and the time horizon. Our findings also indicate that the investor’s sentiment regimes change the Islamic and the conventional optimal diversified portfolios.Moreover, the results show that the potential diversification benefits seem to be more important when using the Bayesian approach than when applying the Markowitz approach. This finding is valid for the bearish, depressed, bullish and calm states in Islamic stock markets. However, the diversification of potential portfolios is significant only for the bullish and the bubble states in the conventional financial markets.The findings of the study provided additional evidence for investors to exploit googling investor sentiment states to evaluate the portfolio performance and make an optimal portfolio allocation.     

The Opportunity Cost of a Mean-Variance Efficient Choice

The mean-variance criterion is one of the most frequently used methods for selecting investment portfolios. Yet, because it is an approximation of an investor's maximum expected utility choice, some theoreticians and practitioners have criticized the approach. This paper examines the investment loss that different investors experience by accepting a mean-variance efficient portfolio. Simulated security returns with extreme distributional characteristics are used to determine the extent of an investor's loss. The results indicate that even under very unreasonable investment distributional assumptions, an investor's loss by accepting a mean-variance efficient choice rarely exceeds a small fraction of one percent per invested dollar.     

Stochastic dominance and portfolio analysis

The principle of stochastic dominance is used to characterize the optimal efficient sets when the distributions of the random prospects belong to a family. Most of the well-known distributions are considered. In each case, the optimal efficient sets are characterized by easily verifiable conditions on the parameters of the distributions. These optimal efficient sets are then compared with the corresponding mean-variance (MV) efficient set. It is often found that the optimal efficient sets are proper subsets of the MV efficient set. Thus, the MV criterion is a proper efficiency criterion, but the MV efficient set can be excessively large compared to the optimal efficient set.     

The Economic Value of Volatility Timing

Numerous studies report that standard volatility models have low explanatory power, leading some researchers to question whether these models have economic value. We examine this question by using conditional mean-variance analysis to assess the value of volatility timing to short-horizon investors. We find that the volatility timing strategies outperform the unconditionally efficient static portfolios that have the same target expected return and volatility. This finding is robust to estimation risk and transaction costs.     

International portfolio diversification: Currency,industry and country effects revisited

We examine the relative importance of country, industry, world market and currency risk factors for international stock returns. Our approach focuses on testing the mean-variance efficiency of the various factor portfolios. An unconditional analysis does not show significant differences between country, industry and world portfolios, nor any role for currency risk factors. However, when we allow expected returns, volatilities and correlations to vary over time, we find that equity returns are mainly driven by global industry and currency risk factors. We propose a novel test to evaluate the relative benefits of alternative investment strategies and find that including currencies is critical to take full advantage of the diversification benefits afforded by international markets.     

Multi-asset portfolio optimization and out-of-sample performance: an evaluation of Black–Litterman,mean-variance,and naïve diversification approaches

The Black–Litterman model aims to enhance asset allocation decisions by overcoming the problems of mean-variance portfolio optimization. We propose a sample-based version of the Black–Litterman model and implement it on a multi-asset portfolio consisting of global stocks, bonds, and commodity indices, covering the period from January 1993 to December 2011. We test its out-of-sample performance relative to other asset allocation models and find that Black–Litterman optimized portfolios significantly outperform naïve-diversified portfolios (1/N rule and strategic weights), and consistently perform better than mean-variance, Bayes–Stein, and minimum-variance strategies in terms of out-of-sample Sharpe ratios, even after controlling for different levels of risk aversion, investment constraints, and transaction costs. The BL model generates portfolios with lower risk, less extreme asset allocations, and higher diversification across asset classes. Sensitivity analyses indicate that these advantages are due to more stable mixed return estimates that incorporate the reliability of return predictions, smaller estimation errors, and lower turnover.     

An algebra for evaluating hedge portfolios

This paper introduces a new tool, an ‘algebra’, for analyzing hedge portfolios. A hedge portfolio is defined as comprising PL- (for ‘piecewise linear’) options. The PL-option serves as a unifying concept for describing long and short positions in an unlying security and various options on that security. Additionally, piecewise linear taxes, margin requirements, transactions costs, etc., are all easily incorporated into the PL-option framework. A key result in this integrated treatment of hedge portfolios is the generation of necessary and sufficient rational option pricing theorems. Other applications of the algebra include the topics of option valuation, mean-variance analysis, and options-on-options.     

Improving Skewness of Mean-Variance Portfolios

Abstract

The widely accepted belief that asset returns and insurance product line margins are not normally distributed has motivated the use of skewness (or higher than second-order moments) in the context of optimal risk-reward portfolio allocation. Here we propose an optimization-based methodology to substantially improve the skewness of portfolios in the mean-variance efficient frontier. Unlike other related methods, the proposed methodology is very intuitive, noniterative, and simple to implement, and it can be readily and efficiently carried out using state-of-the-art optimization solvers. These characteristics should be very appealing to risk managers.     

A NOTE ON THE EFFECTS OF EFFICIENCY CRITERIA AND PORTFOLIO SIZE ON CHARACTERISTICS OF EFFICIENT PORTFOLIOS*

Comparisons of the results of using alternative efficiency criteria for portfolio selection, while plentiful overseas, are seemingly scarce in Australia. Here, mean-variance efficient sets are compared with and found to be not too different from sets efficient according to second and third degree stochastic dominance. In examining the effect of increasing the number of securities allowed in each portfolio, it is found that the size of efficient sets of portfolios diminishes, as does the mean return and, most significantly, the variance of return for efficient portfolios.     

Should investors include commodities in their portfolios after all? New evidence

This paper investigates whether an investor is made better off by including commodities in a portfolio that consists of traditional asset classes. First, we revisit the posed question within an in-sample setting by employing mean-variance and non-mean-variance spanning tests. Then, we form optimal portfolios by taking into account the higher order moments of the portfolio returns distribution and evaluate their out-of-sample performance. Under the in-sample setting, we find that commodities are beneficial only to non-mean-variance investors. However, these benefits are not preserved out-of-sample. Our findings challenge the alleged diversification benefits of commodities and are robust across a number of performance evaluation measures, utility functions and datasets. The results hold even when transaction costs are considered and across various sub-periods. Not surprisingly, the only exception appears over the 2005-2008 unprecedented commodity boom period.     

The diversification cost of large,concentrated equity stakes. How big is it? Is it justified?

While the hypothesis that ownership concentration can affect the value of a company has seen a lot of empirical study, little light has been shed on a complementary problem, that these concentrated owners have a cost of their position due to an undiversified portfolio. Using a unique data set of the actual diversification of all Norwegian equity owners, we show that the largest owners of a corporation in fact have very undiversified equity portfolios, and that such owners have significant costs to their concentrated portfolios. At the level of risk of a benchmark portfolio, if they were to move from their present portfolio composition in risky assets to a well diversified portfolio, their returns would have increased by about 13 percentage points in annual terms. We ask whether this cost can be explained by estimated benefits of ownership concentration (private benefits), and show that extant estimates of private benefits are too low to offset our cost estimates.     

Who gains and who loses on stock markets? Risk preferences and timing matter

This paper uses an agent-based multi-asset model to examine the effect of risk preferences and optimal rebalancing frequency on performance measures while tracking profit and risk-adjusted return. We focus on the evolution of portfolios managed by heterogeneous mean-variance optimizers with a quadratic utility function under different market conditions. We show that patient and risk-averse agents are able to outperform aggressive risk-takers in the long-run. Our findings also suggest that the trading frequency determined by the optimal tolerance for the deviation from portfolio targets should be derived from a tradeoff between rebalancing benefits and rebalancing costs. In a relatively calm market, the absolute range of 6% to 8% and the complete-way back rebalancing technique outperforms others. During particular turbulent periods, however, none of the existing rebalancing techniques improves tax-adjusted profits and risk-adjusted returns simultaneously.     

A Shrinkage Approach to Model Uncertainty and Asset Allocation

This article takes a shrinkage approach to examine the empiricalimplications of aversion to model uncertainty. The shrinkageapproach explicitly shows how predictive distributions incorporatedata and prior beliefs. It enables us to solve the optimal portfoliosfor uncertainty-averse investors. Aversion to uncertainty aboutthe capital asset pricing model leads investors to hold a portfoliothat is not mean-variance efficient for any predictive distribution.However, mean-variance efficient portfolios corresponding toextremely strong beliefs in the Fama–French model areapproximately optimal for uncertainty-averse investors. Theempirical Bayes approach does not result in optimal portfoliosfor investors who are averse to model uncertainty.     

Do ETFs provide effective international diversification?

Global investments have been a hot issue for years. Investors can diversify risks and obtain benefits from foreign markets by investing directly in the foreign security market or indirectly in Exchange-Trade Funds (ETFs). Because direct investments are not always feasible, we investigate whether indirect investments can replace direct investments. We create different regional optimal portfolios containing ETFs and ensure optimal asset portfolio allocation. In addition to mean-variance approach, the Sharpe index, we also adopt the Campbell et al. (2001) method to have the efficient frontier under control risks, the Value at Risk. We apply both normal and non-normal distributions for comparisons and find that different assumptions of return distributions affect the results of efficient frontier. The results show that international diversification is a reasonable strategy. In addition, when comparing ETFs and target market index portfolios, ETFs have higher Sharpe measures than target market indices especially in the emerging markets. However, there are no significant performance differences between direct and indirect methods even if we use different performance measures. We also find that the diversification benefits are the same before and after the Subprime crisis. We conclude that it is effective for investors to use indirect methods to create internationally diversified portfolios.     

Portfolio performance gauging in discrete time using a Luenberger productivity indicator

This paper proposes a pragmatic, discrete time indicator to gauge the performance of portfolios over time. Integrating the shortage function (Luenberger, 1995) into a Luenberger portfolio productivity indicator (Chambers, 2002), this study estimates the changes in the relative positions of portfolios with respect to the traditional Markowitz mean-variance efficient frontier, as well as the eventual shifts of this frontier over time. Based on the analysis of local changes relative to these mean-variance and higher moment (in casu, mean-variance-skewness and mean-variance-skewness-kurtosis) frontiers, this methodology allows to neatly separate between on the one hand performance changes due to portfolio strategies and on the other hand performance changes due to the market evolution. This methodology is empirically illustrated using a mimicking portfolio approach (22 and 23) using US monthly data from January 1931 to August 2007.