Optimal payoffs under state-dependent preferences

Most decision theories, including expected utility theory, rank-dependent utility theory and cumulative prospect theory, assume that investors are only interested in the distribution of returns and not in the states of the economy in which income is received. Optimal payoffs have their lowest outcomes when the economy is in a downturn, and this feature is often at odds with the needs of many investors. We introduce a framework for portfolio selection within which state-dependent preferences can be accommodated. Specifically, we assume that investors care about the distribution of final wealth and its interaction with some benchmark. In this context, we are able to characterize optimal payoffs in explicit form. Furthermore, we extend the classical expected utility optimization problem of Merton to the state-dependent situation. Some applications in security design are discussed in detail and we also solve some stochastic extensions of the target probability optimization problem.     

m-Double Poisson Lévy markets

We develop novel mispricing of markets under asymmetric information and jumps for informed and uninformed investors, called m-Double Poisson markets, driven by independent Double Poisson processes. In the special case m?=?1, called the Double Poisson pure-jump Lévy market, both types of investors hold the same optimal portfolio and expected utility, and hence, the informed investor has no utility advantage over the uninformed. For the general market, instantaneous centralized moments of returns are used to compute optimal portfolios and utilities. The mean, variance, skewness and kurtosis of instantaneous returns are reported using jump amplitudes and frequencies.     

Optimal derivatives: portfolios,payoffs and preferences

This article presents an extension to the growth optimal derivative that can accommodate risk preferences differing from those of logarithmic utility. Analysis of the optimal derivative provides interesting insights into the behaviour of power investors. We show that power investors under the real-world probability can be viewed as logarithmic investors under the myopic probability of Guasoni and Robertson [(2012). “Portfolios and Risk Premia for the Long Run.” Annals of Applied Probability, 22 (1), 239–284]. Furthermore, this intuition provides criteria for establishing whether fractional Kelly betting is optimal for power investors. Finally, the Black–Scholes model is used to demonstrate how the optimal derivative can be implemented and we show that our approach is consistent with classical techniques.     

Asset pricing implications of benchmarking: a two-factor CAPM

The paper considers the equilibrium effects of an institutional investor whose performance is benchmarked to an index. In a partial equilibrium setting, the objective of the institutional investor is modelled as the maximization of expected utility (an increasing and concave function, in order to accommodate risk aversion) of final wealth minus a benchmark. In equilibrium this optimal strategy gives rise to the two-beta CAPM: together with the market beta a new risk-factor (termed active management risk) is brought into the analysis. This new beta is defined as the normalized (to the benchmark's variance) covariance between the asset excess return and the excess return of the market over the benchmark index. The empirical test supports the model's predictions. The cross-section return on the active management risk is positive and significant, especially after 1990, when institutional investors became the representative agent of the market.     

Size and Value Anomalies under Regime Shifts

This paper finds strong evidence of time-variations in the jointdistribution of returns on a stock market portfolio and portfoliostracking size- and value effects. Mean returns, volatilitiesand correlations between these equity portfolios are found tobe driven by underlying regimes that introduce short-run markettiming opportunities for investors. The magnitude of the premiaon the size and value portfolios and their hedging propertiesare found to vary across regimes. Regimes are shown to havea large impact both on the optimal asset allocation—especiallyunder rebalancing—and on investors' utility. Regimes alsohave a considerable impact on hedging demands, which are positivewhen the investor starts from more favorable regimes and negativewhen starting from bad states. Recursive out-of-sample forecastingexperiments show that portfolio strategies based on models thataccount for regimes dominate single-state benchmarks.     

Portfolio concentration and performance of institutional investors worldwide

Using data on security holdings for 10,771 institutional investors from 72 countries, we test whether concentrated investment strategies result in excess risk-adjusted returns. We examine several measures of portfolio concentration with respect to countries and industries and find that portfolio concentration is directly related to risk-adjusted returns for institutional investors worldwide. Results suggest, in contrast to traditional asset pricing theory and in support of information advantage theory, that concentrated investment strategies in international markets can be optimal.     

Variable Selection for Portfolio Choice

We study asset allocation when the conditional moments of returns are partly predictable. Rather than first model the return distribution and subsequently characterize the portfolio choice, we determine directly the dependence of the optimal portfolio weights on the predictive variables. We combine the predictors into a single index that best captures time variations in investment opportunities. This index helps investors determine which economic variables they should track and, more importantly, in what combination. We consider investors with both expected utility (mean variance and CRRA) and nonexpected utility (ambiguity aversion and prospect theory) objectives and characterize their market timing, horizon effects, and hedging demands.     

Risky asset pricing based on safety first fund management

We study a portfolio selection model based on Kataoka's safety-first criterion (KSF model in short). We assume that the market is complete but without risk-free asset, and that the returns are jointly elliptically distributed. With these assumptions, we provide an explicit analytical optimal solution for the KSF model and obtain some geometrical properties of the efficient frontier in the plane of probability risk degree z _α and target return r _α. We further prove a two-fund separation and tangency portfolio theorem in the spirit of the traditional mean-variance analysis. We also establish a risky asset pricing model based on risky funds that is similar to Black's zero-beta capital asset pricing model (CAPM, for short). Moreover, we simplify our risky asset pricing model using a derivative risky fund as a reference for market evaluation.     

Dynamic preferences for popular investment strategies in pension funds

In this paper, we characterize dynamic investment strategies that are consistent with the expected utility setting and more generally with the forward utility setting. Two popular dynamic strategies in the pension funds industry are used to illustrate our results: a constant proportion portfolio insurance (CPPI) strategy and a life-cycle strategy. For the CPPI strategy, we are able to infer preferences of the pension fund’s manager from her investment strategy, and to exhibit the specific expected utility maximization that makes this strategy optimal at any given time horizon. In the Black–Scholes market with deterministic parameters, we are able to show that traditional life-cycle funds are not optimal to any expected utility maximizers. We also prove that a CPPI strategy is optimal for a fund manager with HARA utility function, while an investor with a SAHARA utility function will choose a time-decreasing allocation to risky assets in the same spirit as the life-cycle funds strategy. Finally, we suggest how to modify these strategies if the financial market follows a more general diffusion process than in the Black–Scholes market.     

Optimal investment under multi-factor stochastic volatility

We consider a model for multivariate intertemporal portfolio choice in complete and incomplete markets with a multi-factor stochastic covariance matrix of asset returns. The optimal investment strategies are derived in closed form. We estimate the model parameters and illustrate the optimal investment based on two stock indices: S&P500 and DAX. It is also shown that the model satisfies several stylized facts well known in the literature. We analyse the welfare losses due to suboptimal investment strategies and we find that investors who invest myopically, ignore derivative assets, model volatility by one factor and ignore stochastic covariance between asset returns can incur significant welfare losses.     

In which financial markets do mutual fund theorems hold true?

The mutual fund theorem (MFT) is considered in a general semimartingale financial market S with a finite time horizon T, where agents maximize expected utility of terminal wealth. The main results are:

An Empirical Investigation of Eastern European Bond Markets

We examine the value of Eastern European emerging bond markets to global fixed income managers. In an environment where bonds from traditional developed markets are offering modest yields, emerging market bonds with attractive yields are becoming more popular with institutional managers. Furthermore, the returns on these bonds exhibit low correlations with traditional fixed income investments and thus offer opportunities for portfolio diversification. We develop a multifactor forecasting model and estimate its parameters using a dynamic Kalman filter procedure. The forecasts are then used to construct optimal mean–variance portfolios with and without emerging market bonds. We find that the portfolios that include emerging market bonds have significantly higher Sharpe ratios.     

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.     

The Optimal Log-Utility Asset Management under Incomplete Information

In this paper, we propose a theory for deriving the optimal portfolio that assures the log-utility investors of maximizing their expected utility. Restricting investors' information at defined levels, we propose the sample path-wise optimal portfolio (SPOP), which is consistent with the back-test framework used in actualinvestment. It is proven that, at any finite terminal time, this SPOP is asymptotically optimal among all the portfolios which are predictable under investors' incompleteinformation. The optimality is guaranteed by the continuous Bayesian updating formula. Finally, we discuss an algorithm for searching the SPOP, based on asset prices at discrete time intervals.     

On derivatives with illiquid underlying and market manipulation

In illiquid markets, option traders may have an incentive to increase their portfolio value by using their impact on the dynamics of the underlying. We provide a mathematical framework to construct optimal trading strategies under market impact in a multi-player framework by introducing strategic interactions into the model of Almgren [Appl. Math. Finance, 2003, 10(1), 1–18]. Specifically, we consider a financial market model with several strategically interacting players who hold European contingent claims and whose trading decisions have an impact on the price evolution of the underlying. We establish the existence and uniqueness of equilibrium results for risk-neutral and CARA investors and show that the equilibrium dynamics can be characterized in terms of a coupled system of possibly nonlinear PDEs. For the linear cost function used by Almgren, we obtain a (semi) closed-form solution. Analysing this solution, we show how market manipulation can be reduced.     

Accounting information,disclosure, and expected utility: Do investors really abhor uncertainty?

Investors are said to “abhor uncertainty,” but if there were no uncertainty they could earn only the risk‐free rate. A fundamental result in the analytical accounting literature shows that investors buying into a CARA‐normal CAPM market pay lower asset prices, gain higher ex‐ante expected returns, and obtain higher expected utility, when the market payoff has higher variance. New investors obtain similar “welfare” gains from risk under a log/power utility CAPM. These results do not imply that investors “abhor information.” To realize investors' ex‐ante expectations, the subjective probability distributions representing market expectations must be accurate. Greater payoff risk can add to investors' expected utility, but higher ex‐post(realized) utility comes from better information and more accurate ex‐ante expectations. An important implication for accounting is that greater disclosure can have the simultaneous effects of (i) exposing more fully or perceptibly firms' payoff uncertainty, thereby increasing new investors' expected utility, and (ii) improving market estimates of firms' payoff parameters (means, variances, covariances), thereby giving investors a better chance of realizing their expectations. Paradoxically, better information can be valuable to new investors by exposing more fully and more accurately the risk in firms' business operations and results–new investors maximizing expected utility want both more risk and better information.     

Behavioral currency hedging for international portfolios

The purpose of this paper is to incorporate behavioral issues as it relates to the active currency hedging of international portfolios in the context of traditional expected utility maximization approach. The uniqueness of the approach is that separate risk aversion parameters are introduced for asset and currency markets. The paper is similar in spirit to Black (Black, F. 1989, Universal hedging, Financial Analysts Journal (July-August), 16-22.), who argued that a portion of foreign equity investments should be permanently unhedged, which is basically postulating that one should take a buy-and-hold position in currency with a fraction of the capital. The behavioral twist included in the traditional expected utility maximization approach results in lower hedge ratios, ceteris paribus, partly due to the asymmetric nature of the compensation structure of currency managers.Since the asymmetric nature of incentive schemes of asset and currency managers dictates how one optimizes the investment portfolio of a pension or endowment fund, the unusual behavior of a given institutional fund manager should not be called “irrational,” only because the optimal currency hedging level deviates from the one derived under rational expectations. This only justifies the use of different hedging strategies by various institutional investors. We describe in detail how the level of hedging should be revised downwards because of behavioral factors. Conclusions are in the context of what people would predict to see in the market, if certain investors behave in an “irrational” way.     

Is stochastic volatility relevant for dynamic portfolio choice under ambiguity?

Literature on dynamic portfolio choice has been finding that volatility risk has low impact on portfolio choice. For example, using long-run US data, Chacko and Viceira [2005. “Dynamic Consumption and Portfolio Choice with Stochastic Volatility in Incomplete Markets.” The Review of Financial Studies 18 (4): 1369–1402] found that intertemporal hedging demand (required by investors for protection against adverse changes in volatility) is empirically small even for highly risk-averse investors. We want to assess if this continues to be true in the presence of ambiguity. Adopting robust control and perturbation theory techniques, we study the problem of a long-horizon investor with recursive preferences that faces ambiguity about the stochastic processes that generate the investment opportunity set. We find that ambiguity impacts portfolio choice, with the relevant channel being the return process. Ambiguity about the volatility process is only relevant if, through a specific correlation structure, it also induces ambiguity about the return process. Using the same long-run US data, we find that ambiguity about the return process may be empirically relevant, much more than ambiguity about the volatility process. Anyway, intertemporal hedging demand is still very low: investors are essentially focused on the short-term risk–return characteristics of the risky asset.