RISK HORIZON AND REBALANCING HORIZON IN PORTFOLIO RISK MEASUREMENT

This paper analyzes portfolio risk and volatility in the presence of constraints on portfolio rebalancing frequency. This investigation is motivated by the incremental risk charge (IRC) introduced by the Basel Committee on Banking Supervision. In contrast to the standard market risk measure based on a 10‐day value‐at‐risk calculated at 99% confidence, the IRC considers more extreme losses and is measured over a 1‐year horizon. More importantly, whereas 10‐day VaR is ordinarily calculated with a portfolio’s holdings held fixed, the IRC assumes a portfolio is managed dynamically to a target level of risk, with constraints on rebalancing frequency. The IRC uses discrete rebalancing intervals (e.g., monthly or quarterly) as a rough measure of potential illiquidity in underlying assets. We analyze the effect of these rebalancing intervals on the portfolio’s profit and loss distribution over a risk‐measurement horizon. We derive limiting results, as the rebalancing frequency increases, for the difference between discretely and continuously rebalanced portfolios; we use these to approximate the loss distribution for the discretely rebalanced portfolio relative to the continuously rebalanced portfolio. Our analysis leads to explicit measures of the impact of discrete rebalancing under a simple model of asset dynamics.     

Who should sell stocks?

Never selling stocks is optimal for investors with a long horizon and a realistic range of preference and market parameters, if relative risk aversion, investment opportunities, proportional transaction costs, and dividend yields are constant. Such investors should buy stocks when their portfolio weight is too low and otherwise hold them, letting dividends rebalance to cash over time rather than selling. With capital gains taxes, this policy outperforms both static buy‐and‐hold and dynamic rebalancing strategies that account for transaction costs. Selling stocks becomes optimal if either their target weight is low or intermediate consumption is substantial.     

Choosing an optimal investment strategy: The role of robust pair-copulas based portfolios

This paper is concerned with the efficient allocation of a set of financial assets and its successful management. Efficient diversification of investments is achieved by inputing robust pair-copulas based estimates of the expected return and covariances in the mean-variance analysis of Markowitz. Although the whole point of diversifying a portfolio is to avoid rebalancing, very often one needs to rebalance to restore the portfolio to its original balance or target. But when and why to rebalance is a critical issue, and this paper investigates several managers' strategies to keep the allocations optimal. Findings for an emerging market target return and minimum risk investments are highly significant and convincing. Although the best strategy depends on the investor risk profile, it is empirically shown that the proposed robust portfolios always outperform the classical versions based on the sample estimates, yielding higher gains in the long run and requiring a smaller number of updates. We found that the pair-copulas based robust minimum risk portfolio monitored by a manager which checks its composition twice a year provides the best long run investment.     

Does it Really Hurt to be Responsible?

Prior literature on socially responsible investment has contended that excluding “sin stocks” from a portfolio (negative screening) will reduce performance and increase risk. Further, incorporating stocks of firms with positive social responsibility scores (positive screening) will improve performance and reduce risk. We simulate portfolios designed to mimic typical equity mutual funds’ holdings and investigate these propositions. We remove the potentially confounding influences of differences in manager skill, transaction costs and fees, and conduct a clean experiment on the effect of positive and negative portfolio screening. We find no difference in the return or risk of screened and unscreened portfolios. We conclude that a typical socially responsible fund will neither gain nor lose from screening its portfolio.     

Equally Weighted Portfolios of Randomly Selected Stocks and the Individual Investor

The article contrasts 500 randomly formed equally weighted portfolios (1/N) to 221 actively managed stock funds, individual stocks, and the IBrX-50 index, representing indexed stock funds, considering transaction costs. The sample are the 50 stocks in IBrX-50 index in January 2007 throughout 60 months. Investors are likely to achieve greater returns and return-to-risk ratios with a randomly formed 1/N portfolio than with a stock fund, particularly those targeting retail investors, or one of the 50 stocks also randomly drawn. These portfolios would also outperform the IBrX-50. Robustness tests with variations in size and frequency of rebalancing do not change conclusions.     

A Combination Rule for Portfolio Selection with Transaction Costs

We propose a new portfolio rule for portfolio selection problems in the presence of transaction costs. The new portfolio rule is formed by combining an extant portfolio rule with the no‐rebalancing portfolio rule, which specifies the current portfolio weights before rebalancing as the desired portfolio weights. The new portfolio rule can be applied into most extant portfolio rules. Simulation and out‐of‐sample evidence show that the new portfolio rule can greatly improve portfolio performance, in comparison with the extant portfolio rules to be combined.     

ASYMPTOTICALLY OPTIMAL PORTFOLIOS

This paper extends to continuous time the concept of universal portfolio introduced by Cover (1991). Being a performance weighted average of constant rebalanced portfolios, the universal portfolio outperforms constant rebalanced and buy-and-hold portfolios exponentially over the long run. an asymptotic formula summarizing its long-term performance is reported that supplements the one given by Cover. A criterion in terms of long-term averages of instantaneous stock drifts and covariances is found which determines the particular form of the asymptotic growth. A formula for the expected universal wealth is given.     

Discrete-time risk sensitive portfolio optimization with proportional transaction costs

In this paper we consider a discrete-time risk sensitive portfolio optimization over a long time horizon with proportional transaction costs. We show that within the log-return i.i.d. framework the solution to a suitable Bellman equation exists under minimal assumptions and can be used to characterize the optimal strategies for both risk-averse and risk-seeking cases. Moreover, using numerical examples, we show how a Bellman equation analysis can be used to construct or refine optimal trading strategies in the presence of transaction costs.     

Price and Earnings Momentum,Transaction Costs,and an Innovative Practitioner Technique

We use an innovative practitioner technique to investigate the interplay between the ex post performance of momentum strategies and transaction costs, rebalancing frequency, turnover constraints, and fund size. We have three interrelated main results: first, the level of and correlation between active returns to price momentum and earnings momentum strategies vary dramatically with these factors; second, strategies that are fearful of ex ante transaction costs generate returns net of transaction costs that are far superior to the net returns of naive strategies; and third, obtaining better traction with the unique elements of each strategy yields a more profitable combined strategy.     

Equally Weighted Strategic Allocation and Balanced Funds in Brazil

This article analyzes equally weighted strategic asset allocation portfolios in Brazil between 2004 and 2016 and shows that their average returns are not always statistically greater than those of balanced funds, with significance changing in sub-periods. Fixed-income portfolios frequently outperform balanced funds, whose active management underperforms their declared benchmark portfolios. Balanced funds underperformed probably because they deviated from their investment policy. Transaction costs and other rebalancing frequencies do not change the conclusions. Robustness tests indicate that this evidence is valid out-of-the-sample. Investors can mimic balanced-fund policy and possibly do better by means of indexing according to this policy.     

DISCRETE TIME HEDGING OF THE AMERICAN OPTION

In a complete financial market we consider the discrete time hedging of the American option with a convex payoff. It is well known that for the perfect hedging the writer of the option must trade continuously in time, which is impossible in practice. In reality, the writer hedges only at some discrete time instants. The perfect hedging requires the knowledge of the partial derivative of the value function of the American option in the underlying asset, the explicit form of which is unknown in most cases of practical importance. Several approximation methods have been developed for the calculation of the value function of the American option. We claim in this paper that having at hand any uniform approximation of the American option value function at equidistant discrete rebalancing times it is possible to construct a discrete time hedging portfolio, the value process of which uniformly approximates the value process of the continuous time perfect delta‐hedging portfolio. We are able to estimate the corresponding discrete time hedging error that leads to a complete justification of our hedging method for nonincreasing convex payoff functions including the important case of the American put. This method is essentially based on a new type square integral estimate for the derivative of an arbitrary convex function recently found by Shashiashvili.     

Including emerging markets in international momentum investment strategies

Momentum return investment strategies that diversify across countries provide lower portfolio standard deviations and/or increased expected returns. These diversification benefits are larger when adding emerging markets than when adding developed markets, and they are larger than would be suggested by diversifying with long-only portfolios. Using data on almost 16,000 firms from 22 developed and 18 emerging markets over the 1990–2004 period, we confirm the profitability of momentum trading strategies in both developed and emerging markets and document the diversification benefits of including emerging markets in an international momentum portfolio investment strategy.     

Selection of Socially Responsible Portfolios Using Hedonic Prices

This paper presents a novel framework for selecting socially responsible investment (SRI) portfolios. The Hedonic Price Method (HPM) is applied to obtain an evaluation of SRI criteria that is integrated into a multi-objective mathematical programming model. The HPM breaks away from the traditional view that goods are the direct object of utility; on the contrary, it assumes that utility is derived from the properties or characteristics of the goods themselves. As far as the investment decision is concerned, we assume that socially responsible investmentmutual funds (SRI funds) constitute heterogeneous goods. Our approach allows us to obtain a portfolio, the financial performance of which is similar to that which the investor would have reached if he or she had not taken into account social, ethical, and environmental considerations when making his or her investment decisions. This is achieved by designing a two-stage multi-objective mathematical programming procedure. In the first stage, we achieve the maximum level of financial satisfaction that the investor can receive. In the second stage, the portfolio with the best financial–social behavior is built. For the purpose of this second stage, the first stage portfolio is used as a benchmark for the financial performance of a socially responsible portfolio. To apply this methodology, we use portfolios composed of socially responsible and conventional mutual funds domiciled in Spain.     

PORTFOLIO MANAGEMENT WITH TRANSACTION COSTS: AN ASYMPTOTIC ANALYSIS OF THE MORTON AND PLISKA MODEL

We examine the Morton and Pliska (1993) model for the optimal management of a portfolio when there are transaction costs proportional to a fixed fraction of the portfolio value. We analyze this model in the realistic case of small transaction costs by conducting a perturbation analysis about the no-transaction-cost solution. Although the full problem is a free-boundary diffusion problem in as many dimensions as there are assets in the portfolio, we find explicit solutions for the optimal trading policy in this limit. This makes the solution for a realistically large number of assets a practical possibility.     

Optimal consumption and investment with liquid and illiquid assets

I consider an optimal consumption/investment problem to maximize expected utility from consumption. In this market model, the investor is allowed to choose a portfolio that consists of one bond, one liquid risky asset (no transaction costs), and one illiquid risky asset (proportional transaction costs). I fully characterize the optimal consumption and trading strategies in terms of the solution of the free boundary ordinary differential equation (ODE) with an integral constraint. I find an explicit characterization of model parameters for the well‐posedness of the problem, and show that the problem is well posed if and only if there exists a shadow price process. Finally, I describe how the investor's optimal strategy is affected by the additional opportunity of trading the liquid risky asset, compared to the simpler model with one bond and one illiquid risky asset.     

Randomized Stopping Times and American Option Pricing with Transaction Costs

In a general discrete-time market model with proportional transaction costs, we derive new expectation representations of the range of arbitrage-free prices of an arbitrary American option. The upper bound of this range is called the upper hedging price, and is the smallest initial wealth needed to construct a self-financing portfolio whose value dominates the option payoff at all times. A surprising feature of our upper hedging price representation is that it requires the use of randomized stopping times (Baxter and Chacon 1977), just as ordinary stopping times are needed in the absence of transaction costs. We also represent the upper hedging price as the optimum value of a variety of optimization problems. Additionally, we show a two-player game where at Nash equilibrium the value to both players is the upper hedging price, and one of the players must in general choose a mixture of stopping times. We derive similar representations for the lower hedging price as well. Our results make use of strong duality in linear programming.     

MULTIVARIATE RISK MEASURES: A CONSTRUCTIVE APPROACH BASED ON SELECTIONS

Since risky positions in multivariate portfolios can be offset by various choices of capital requirements that depend on the exchange rules and related transaction costs, it is natural to assume that the risk measures of random vectors are set‐valued. Furthermore, it is reasonable to include the exchange rules in the argument of the risk measure and so consider risk measures of set‐valued portfolios. This situation includes the classical Kabanov's transaction costs model, where the set‐valued portfolio is given by the sum of a random vector and an exchange cone, but also a number of further cases of additional liquidity constraints. We suggest a definition of the risk measure based on calling a set‐valued portfolio acceptable if it possesses a selection with all individually acceptable marginals. The obtained selection risk measure is coherent (or convex), law invariant, and has values being upper convex closed sets. We describe the dual representation of the selection risk measure and suggest efficient ways of approximating it from below and from above. In the case of Kabanov's exchange cone model, it is shown how the selection risk measure relates to the set‐valued risk measures considered by Kulikov (2008, Theory Probab. Appl. 52, 614–635), Hamel and Heyde (2010, SIAM J. Financ. Math. 1, 66–95), and Hamel, Heyde, and Rudloff (2013, Math. Financ. Econ. 5, 1–28).     

The limits of leverage

When trading incurs proportional costs, leverage can scale an asset's return only up to a maximum multiple, which is sensitive to its volatility and liquidity. In a model with one safe and one risky asset, with constant investment opportunities and proportional costs, we find strategies that maximize long‐term returns given average volatility. As leverage increases, rising rebalancing costs imply declining Sharpe ratios. Beyond a critical level, even returns decline. Holding the Sharpe ratio constant, higher asset volatility leads to superior returns through lower costs.     

Cover's universal portfolio,stochastic portfolio theory,and the numéraire portfolio

Cover's celebrated theorem states that the long‐run yield of a properly chosen “universal” portfolio is almost as good as that of the best retrospectively chosen constant rebalanced portfolio. The “universality” refers to the fact that this result is model‐free, that is, not dependent on an underlying stochastic process. We extend Cover's theorem to the setting of stochastic portfolio theory: the market portfolio is taken as the numéraire, and the rebalancing rule need not be constant anymore but may depend on the current state of the stock market. By fixing a stochastic model of the stock market this model‐free result is complemented by a comparison with the numéraire portfolio. Roughly speaking, under appropriate assumptions the asymptotic growth rate coincides for the three approaches mentioned in the title of this paper. We present results in both discrete and continuous time.     

The Profitability of Option‐Based Contrarian Strategies: An Empirical Analysis

Short‐selling restrictions limit investors' opportunities to profit from contrarian strategies in equity markets. We examine the proposition that incorporating options into contrarian strategies constitute a viable alternative to investors when short‐selling restrictions are in place. In particular, we combine equities with the call and put options traded on the Australian Stock Exchange to investigate the profitability of contrarian strategies in the hybrid market and options market alone. We assess the practical issues in the execution of these approaches, including testing for the effects of limited liquidity and transaction costs. We also investigate how fundamental factors (such as dividend yield, firm size, book‐to‐market ratio, earnings per share, price‐earnings ratio, value stocks, and market conditions) affect contrarian portfolios. The results show that employing options can enhance the profitability of contrarian strategies under certain market conditions.