Computing optimal rebalance frequency for log-optimal portfolios in linear time

The pure form of log-optimal investment strategies are often considered to be impractical due to the inherent need for continuous rebalancing. It is however possible to improve investor log utility by adopting a discrete-time periodic rebalancing strategy. Under the assumptions of geometric Brownian motion for assets and approximate log-normality for a sum of log-normal random variables, we find that the optimum rebalance frequency is a piecewise continuous function of investment horizon. One can construct this rebalance strategy function, called the optimal rebalance frequency function, up to a specified investment horizon given a limited trajectory of the expected log of portfolio growth when the initial portfolio is never rebalanced. We develop the analytical framework to compute the optimal rebalance strategy in linear time, a significant improvement from the previously proposed search-based quadratic time algorithm.     

Maximizing an equity portfolio excess growth rate: a new form of smart beta strategy?

It has been claimed that, for dynamic investment strategies, the simple act of rebalancing a portfolio can be a source of additional performance, sometimes referred to as the volatility pumping effect or the diversification bonus because volatility and diversification turn out to be key drivers of the portfolio performance. Stochastic portfolio theory suggests that the portfolio excess growth rate, defined as the difference between the portfolio expected growth rate and the weighted-average expected growth rate of the assets in the portfolio, is an important component of this additional performance (see Fernholz [Stochastic Portfolio Theory, 2002 (Springer)]). In this context, one might wonder whether maximizing a portfolio excess growth rate would lead to an improvement in the portfolio performance or risk-adjusted performance. This paper provides a thorough empirical analysis of the maximization of an equity portfolio excess growth rate in a portfolio construction context for individual stocks. In out-of-sample empirical tests conducted on individual stocks from 4 different regions (US, UK, Eurozone and Japan), we find that portfolios that maximize the excess growth rate are characterized by a strong negative exposure to the low volatility factor and a higher than 1 exposure to the market factor, implying that such portfolios are attractive alternatives to competing smart portfolios in markets where the low volatility anomaly does not hold (e.g. in the UK, or in rising interest rate scenarios) or in bull market environments.     

Portfolio optimization under a generalized hyperbolic skewed t distribution and exponential utility

In this paper, we show that if asset returns follow a generalized hyperbolic skewed t distribution, the investor has an exponential utility function and a riskless asset is available, the optimal portfolio weights can be found either in closed form or using a successive approximation scheme. We also derive lower bounds for the certainty equivalent return generated by the optimal portfolios. Finally, we present a study of the performance of mean–variance analysis and Taylor’s series expected utility expansion (up to the fourth moment) to compute optimal portfolios in this framework.     

Continuous-time delegated portfolio management with homogeneous expectations: can an agency conflict be avoided?

In a continuous-time framework, the issue of how to delegate an investor’s portfolio decision to a portfolio manager is studied. First, we solve the first-best problem. For the second-best case, a specific quadratic contract is introduced resolving the agency conflict completely in the sense that the solutions to the first-best and second-best problems coincide. This contract can be implemented if the investor is able to observe the value of the growth optimal portfolio at her investment horizon. If the investment opportunity set is assumed to be constant, in equilibrium the value of the market portfolio is a sufficient statistic for the value of the growth optimal portfolio. Throughout the paper, we assume that the investor and the manager have homogeneous expectations about the investment opportunity set. This, however, does not necessarily mean that investor and manager are symmetrically informed about all prices.

Welfare effects of information and rationality in portfolio decisions under parameter uncertainty

We analyse and quantify, in a financial market with parameter uncertainty and for a Constant Relative Risk Aversion investor, the utility effects of two different boundedly rational (i.e. sub-optimal) investment strategies (namely, myopic and unconditional strategies) and compare them with each other and with the utility effect of full information. We show that effects are mainly caused by full information and predictability, being the effect of learning marginal. We also investigate the saver's decision regarding whether to manage her/his portfolio personally (DIY investor) or hire, against the payment of a management fee, a professional investor and find that delegation is mainly motivated by the belief that professional advisors are, depending on investment horizon and risk aversion, either better informed (‘insiders’) or more capable of gathering and processing information, rather than possessing the ability to learn from financial data. In particular, for very short investment horizons, delegation is primarily, if not exclusively, motivated by the beliefs that professional investors are better informed.     

Multivariate Shrinkage for Optimal Portfolio Weights

Abstract

This paper proposes a multivariate shrinkage estimator for the optimal portfolio weights. The estimated classical Markowitz weights are shrunk to the deterministic target portfolio weights. Assuming log asset returns to be i.i.d. Gaussian, explicit solutions are derived for the optimal shrinkage factors. The properties of the estimated shrinkage weights are investigated both analytically and using Monte Carlo simulations. The empirical study compares the competing portfolio selection approaches. Both simulation and empirical studies show that the proposed shrinkage estimator is robust and provides significant gains to the investor compared to benchmark procedures.     

Performance Evaluation,Portfolio Selection,and HARA Utility

Absract

The main goal of this work is the generalization of the approach of Jobson and Korkie for funds performance evaluation. Therefore, the paper considers the portfolio selection problem of an investor who faces short sales restrictions when choosing among F different investment funds and assumes the investor’s utility function to be of the HARA type. A performance measure is developed and its relationship to previously proposed measures is discussed. Particular attention is given to the special case of cubic utility implying skewness preferences. Findings are illustrated by an empirical example.     

A Benchmark Approach to Portfolio Optimization under Partial Information

This paper proposes a filtering methodology for portfolio optimization when some factors of the underlying model are only partially observed. The level of information is given by the observed quantities that are here supposed to be the primary securities and empirical log-price covariations. For a given level of information we determine the growth optimal portfolio, identify locally optimal portfolios that are located on a corresponding Markowitz efficient frontier and present an approach for expected utility maximization. We also present an expected utility indifference pricing approach under partial information for the pricing of nonreplicable contracts. This results in a real world pricing formula under partial information that turns out to be independent of the subjective utility of the investor and for which an equivalent risk neutral probability measure need not exist.      

Analytical solutions of optimal portfolio rebalancing

We study optimal portfolio rebalancing in a mean-variance type framework and present new analytical results for the general case of multiple risky assets. We first derive the equation of the no-trade region, and then provide analytical solutions and conditions for the optimal portfolio under several simplifying yet important models of asset covariance matrix: uncorrelated returns, same non-zero pairwise correlation, and a one-factor model. In some cases, the analytical conditions involve one or two parameters whose values are determined by combinatorial, rather than numerical, algorithms. Our results provide useful and interesting insights on portfolio rebalancing, and sharpen our understanding of the optimal portfolio.     

Asset Allocation and the Liquidity Premium for Illiquid Annuities

Academics and practitioners alike have developed numerous techniques for benchmarking investment returns to properly adjust seemingly high numbers for excessive levels of risk. The same, however, cannot be said for liquidity, or the lack thereof. This article develops a model for analyzing the ex ante liquidity premium demanded by the holder of an illiquid annuity. The annuity is an insurance product that is akin to a pension savings account with both an accumulation and decumulation phase. We compute the yield (spread) needed to compensate for the utility welfare loss, which is induced by the inability to rebalance and maintain an optimal portfolio when holding an annuity. Our analysis goes beyond the current literature, by focusing on the interaction between time horizon (both deterministic and stochastic), risk aversion, and preexisting portfolio holdings. More specifically, we derive a negative relationship between a greater level of individual risk aversion and the demanded liquidity premium. We also confirm that, ceteris paribus, the required liquidity premium is an increasing function of the holding period restriction, the subjective return from the market, and is quite sensitive to the individual's endowed (preexisting) portfolio.     

A note on portfolio choice for sovereign wealth funds

The current vast account surpluses of commodity-rich nations, combined with record account deficits in developed markets (the United States, Britain) have created a new type of investor. Sovereign wealth funds (SWF) are instrumental in deciding how these surpluses will be invested. We need to better understand the investment problem for an SWF in order to project future investment flows. Extending Gintschel and Scherer (J. Asset Manag. 9(3):215–238, 2008), we apply the portfolio choice problem for a sovereign wealth fund in a Campbell and Viceira (Strategic Asset Allocation, 2002) strategic asset allocation framework. Changing the analysis from a one to a multi-period framework allows us to establish a three-fund separation. We split the optimal portfolio for an SWF into speculative demand as well as hedge demand against oil price shocks and shocks to the short-term risk-free rate. In addition, all terms now depend on the investor’s time horizon. We show that oil-rich countries should hold bonds and that the optimal investment policy for an SWF as a long-term investor is determined by long-run covariance matrices that differ from the correlation inputs that one-period (myopic) investors use.

What determines mutual fund trading in foreign stocks?

We examine the portfolio rebalancing, measured by the equity churn rate, of mutual funds from 29 countries based on annual stockholdings over the 1999–2006 period. We find that funds more often trade the stocks of companies located in countries with higher degree of information asymmetry and are less familiar to fund managers, after we control for the effects of stock market development and investor protection. Consistent with the behavioral bias, fund managers more often rebalance stocks in foreign markets that perform well. This bias is exacerbated when fund managers are less familiar with and less informed about those markets.     

Equilibrium Block Trading and Asymmetric Information

This paper investigates the existence of equilibria with information-based block trading in a multiperiod market when no investor is constrained to block trade. Attention is restricted to equilibria in which a strategic uninformed institution (i.e., one which is forced to rebalance its portfolio but is free to choose an optimal rebalancing strategy) is willing to trade a block rather than “break up” the block into a series of smaller trades. Examples of such equilibria are found and analyzed.     

Investor induced contagion during the banking and European sovereign debt crisis of 2007–2012: Wealth effect or portfolio rebalancing?

This study investigates the way a crisis spreads within a country and across borders by testing the investor induced contagion hypothesis through the liquidity channel on stock-bond relationships of the US and five European countries before and during the global banking and European sovereign debt crisis of 2007–2012. We provide evidence consistent with the wealth effect as a source of contagion for the majority of countries. Nevertheless, we uncover evidence of investor induced contagion sourced by the portfolio rebalancing effect for correlations involving Spanish and Italian bonds during the debt crisis. Further, we find that tight (narrow) credit spreads reduce (magnify) the wealth and portfolio rebalancing effects, which are offset by the opposite effects of risk aversion amongst investors, a dynamic that is not restricted to crisis periods.     

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.     

Decomposing the persistence of international equity flows

The portfolio flows of institutional investors are widely known to be persistent. What is less well-known, however, is the source of this persistence. One possibility is the ‘informed trading hypothesis:’ that persistence arises from autocorrelated trades of individual investors who believe they have information about value and who face an imperfectly liquid market. Another possibility is that there are asynchroneities with respect to investment decisions across funds, across investments, or both. These asynchroneities could be due to wealth effects (across investments for a single fund), investor herding (across funds for a single investment), or generalized contagion (across funds and across investments). We use daily data on institutional flows into 21 developed countries by 471 funds to measure and decompose aggregate flow persistence. We find that the informed trading hypothesis explains about 75% of total persistence, and that the remaining amount is attributable entirely to cross-fund own-country persistence. While asynchroneities across funds investing in the same country are important, asynchroneities across countries, either within a given fund, or across funds, are not important. The cross-fund flow lags we identify might result from different fund investment processes, or from some funds mimicking others' decisions. We reject the hypothesis that wealth effects explain persistence.     

Optimal Time to Sell in Real Estate Portfolio Management

This paper examines the properties of optimal times to sell a diversified real estate portfolio. The portfolio value is supposed to be the sum of the discounted free cash flows and the discounted terminal value (the discounted selling price). According to Baroni et al. (Journal of Property Investment and Finance 25(6):603–625, 2007b), we assume that the terminal value corresponds to the real estate index. The optimization problem corresponds to the maximization of a quasi-linear utility function. We consider three cases. The first one assumes that the investor knows the probability distribution of the real estate index. However, at the initial time, he has to choose one deterministic optimal time to sell. The second one considers an investor who is perfectly informed about the market dynamics. Whatever the random event that generates the path, he knows the entire path from the beginning. Then, given the realization of the random variable, the path is deterministic for this investor. Therefore, at the initial time, he can determine the optimal time to sell for each path of the index. Finally, the last case is devoted to the analysis of the intertemporal optimization, based on the American option approach. We compute the optimal solution for each of these three cases and compare their properties. The comparison is also made with the buy-and-hold strategy.

Predictability and Transaction Costs: The Impact on Rebalancing Rules and Behavior

Recent papers show that predictability calibrated to U.S. data has a large effect on the rebalancing behavior of a multiperiod investor. We find that this continues to be true in the presence of realistic transaction costs. In particular, predictability causes the no-trade region for the risky-asset holding to become state dependent and, on average, wider and higher. Predictability also motivates the investor to spend considerably more on rebalancing and to rebalance more often. In other results, we find that introducing costly liquidation of the risky asset for consumption lowers the average allocation to the risky asset, though only marginally early in life. Our experiments also vary the nature of the return predictability and introduce return heteroskedasticity.     

Optimal Hedging and Valuation of Nontraded Assets

This paper examines a number of valuation problems faced by an expected-utility-maximizing investor who, over a given time horizon, is constrained to hold an asset which cannot be replicated by dynamic trading and which therefore does not have a unique no-arbitrage price. We first derive the private valuation which the investor assigns to the nontradedasset in order to determine his optimal investment in the traded assets. We thereby show that, as part of this portfolio, the investor hedges the private valuation process of the nontraded asset, rather than its market price process. We also study the price at which the investor would be willing to sell the nontraded asset if he were subsequently prohibited from trading in it, as well as the amount the investor would be willing to pay to removethe trading restriction. All three values are shown to depend in an intuitive manner on the investor's risk aversion, the residual risk of the nontraded asset unhedged by the traded assets, the difference between the constrained holding and optimal unconstrained holding of the asset and the length of the time horizon over which the asset cannot be traded.