Bonds versus stocks: Investors’ age and risk taking

It has become increasingly popular to advise investors to relocate their funds from a primarily stock portfolio to a primarily bond portfolio as they get older. However, the well-known decision rules such as mean–variance or stochastic dominance rules are unable to explain this common practice. Almost stochastic dominance (ASD) and almost mean–variance (AMV) approaches are used to examine the dominance of stock and bond portfolios. ASD and AMV rules unambiguously support the popular practice of advising higher stock to bond ratio for long investment horizons. Hence, we provide an explanation to the practitioners’ recommendation within the expected utility paradigm.     

Utility and the Skewness of Return in Gambling

This paper demonstrates that the intuitively appealing argument based on the postulated trade-off between expected return, variance and skewness of return of a risk-averse gambler does not provide an explanation of observed betting behaviour. It is shown how the expected utility of a representative gambler faced with a single-prized outcome event can be expressed in terms of the mean and variance of return, the mean and skewness of return or, generally, of the mean and any other single moment of return: and the standard practice of taking a Taylor series expansion/approximation of the expected utility involving moments of return is usually incorrect. Previous analyses have suggested that a punter will accept a lower mean return for higher skewness and this work seems to have involved invalid expansions of the utility function. The upshot is that with certain utility functions which have been used in a number of studies, any analysis based on expansion and estimation of the derivatives of the utility function may be valid only for data based on odds-on favourites and not for longshots.     

Reward–risk portfolio selection and stochastic dominance

The portfolio selection problem is traditionally modelled by two different approaches. The first one is based on an axiomatic model of risk-averse preferences, where decision makers are assumed to possess a utility function and the portfolio choice consists in maximizing the expected utility over the set of feasible portfolios. The second approach, first proposed by Markowitz is very intuitive and reduces the portfolio choice to a set of two criteria, reward and risk, with possible tradeoff analysis. Usually the reward–risk model is not consistent with the first approach, even when the decision is independent from the specific form of the risk-averse expected utility function, i.e. when one investment dominates another one by second-order stochastic dominance. In this paper we generalize the reward–risk model for portfolio selection. We define reward measures and risk measures by giving a set of properties these measures should satisfy. One of these properties will be the consistency with second-order stochastic dominance, to obtain a link with the expected utility portfolio selection. We characterize reward and risk measures and we discuss the implication for portfolio selection.     

How does beta explain stochastic dominance efficiency?

Stochastic dominance rules provide necessary and sufficient conditions for characterizing efficient portfolios that suit all expected utility maximizers. For the finance practitioner, though, these conditions are not easy to apply or interpret. Portfolio selection models like the mean–variance model offer intuitive investment rules that are easy to understand, as they are based on parameters of risk and return. We present stochastic dominance rules for portfolio choices that can be interpreted in terms of simple financial concepts of systematic risk and mean return. Stochastic dominance is expressed in terms of Lorenz curves, and systematic risk is expressed in terms of Gini. To accommodate for risk aversion differentials across investors, we expand the conditions using the extended Gini.     

Volatility‐Managed Portfolios

Managed portfolios that take less risk when volatility is high produce large alphas, increase Sharpe ratios, and produce large utility gains for mean‐variance investors. We document this for the market, value, momentum, profitability, return on equity, investment, and betting‐against‐beta factors, as well as the currency carry trade. Volatility timing increases Sharpe ratios because changes in volatility are not offset by proportional changes in expected returns. Our strategy is contrary to conventional wisdom because it takes relatively less risk in recessions. This rules out typical risk‐based explanations and is a challenge to structural models of time‐varying expected returns.     

Multivariate utility maximization with proportional transaction costs

We present an optimal investment theorem for a currency exchange model with random and possibly discontinuous proportional transaction costs. The investor’s preferences are represented by a multivariate utility function, allowing for simultaneous consumption of any prescribed selection of the currencies at a given terminal date. We prove the existence of an optimal portfolio process under the assumption of asymptotic satiability of the value function. Sufficient conditions for this include reasonable asymptotic elasticity of the utility function, or a growth condition on its dual function. We show that the portfolio optimization problem can be reformulated in terms of maximization of a terminal liquidation utility function, and that both problems have a common optimizer.     

International exchange risk and asset substitutability

This paper estimates subsitutability/complementarity relations among financial assets denominated in foreign currencies. Utilizing a representative investor and a flexible functional form methodology, a mean-variance utility function was estimated and used to determine expected return and variance elasticities between assets in the world portfolio. The hypothesis that international assets are perfect substitutes was rejected. It was also found that relative changes in variance tended to have a bigger impact on asset demand than did relative changes in expected returns. Substituability/complementarity relationships were not strong except in specific cases where strong relationships were expected a priori.     

The Impact of Investment Constraints on Portfolio Performance Measurement: The Power Utility Function Case

This paper examines the effect of investment constraints on performance measurement of institutionally managed funds. Assuming that these funds have a power utility function and using an optimal portfolio choice model, one can show that the Security Market Line remains a valid benchmark for these constrained funds under the perfect market assumption. Relaxing the perfect market assumption, one can prove that a non-stationary constrained investment policy will bias traditional measures of timing ability differently across managers types. Finally, the magnitude of this bias is illustrated with a numerical example.     

Optimal investment strategies for general utilities under dynamic elasticity of variance models

This paper studies the optimal investment strategies under the dynamic elasticity of variance (DEV) model which maximize the expected utility of terminal wealth. The DEV model is an extension of the constant elasticity of variance model, in which the volatility term is a power function of stock prices with the power being a nonparametric time function. It is not possible to find the explicit solution to the utility maximization problem under the DEV model. In this paper, a dual-control Monte-Carlo method is developed to compute the optimal investment strategies for a variety of utility functions, including power, non-hyperbolic absolute risk aversion and symmetric asymptotic hyperbolic absolute risk aversion utilities. Numerical examples show that this dual-control Monte-Carlo method is quite efficient.     

Wealth-driven competition in a speculative financial market: examples with maximizing agents

This paper demonstrates how both the quantitative and qualitative results of a general, analytically tractable asset-pricing model in which heterogeneous agents behave consistently with a constant relative risk-aversion assumption can be applied to the special case of optimizing behaviour. The analysis of the asymptotic properties of the market is performed using a geometric approach that allows the visualization of all possible equilibria by means of a simple one-dimensional Equilibrium Market Curve. The case of linear (particularly, mean–variance) investment functions is thoroughly analysed. This analysis highlights the features that are specific to linear investment functions. As a consequence, some previous contributions of the agent-based literature are generalized.     

A Generalisation of the Mean-Variance Analysis

In this paper we consider a decision maker whose utility function has a kink at the reference point with different functions below and above this reference point. We also suppose that the decision maker generally distorts the objective probabilities. First we show that the expected utility function of this decision maker can be approximated by a function of mean and partial moments of distribution. This 'mean-partial moments' utility generalises not only mean-variance utility of Tobin and Markowitz, but also mean-semivariance utility of Markowitz. Then, in the spirit of Arrow and Pratt, we derive an expression for a risk premium when risk is small. Our analysis shows that a decision maker in this framework exhibits three types of aversions: aversion to loss, aversion to uncertainty in gains, and aversion to uncertainty in losses. Finally we present a solution to the optimal capital allocation problem and derive an expression for a portfolio performance measure which generalises the Sharpe and Sortino ratios. We demonstrate that in this framework the decision maker's skewness preferences have first-order impact on risk measurement even when the risk is small.     

RESIDUAL INCOME,REVERSIBILITY AND THE VALUATION OF EQUITY

Using a continuous time reformulation of the Garman & Ohlson (1980) equity valuation model, we show that the linear pricing technologies, which characterize this area of accounting research, are special cases of a more general non-linear pricing relationship. These non-linearities arise from the fact that firms have the option of terminating their production and investment plans, especially if they turn out to be ‘significant’ loss-making ventures. We demonstrate the potential significance of these non-linearities for a parsimonious interpretation of the Ohlson (1995) model based on the assumption that the firm’s residual income stream is generated by the Student distributions of Praetz (1972) and Blattberg & Gonedes (1974). These processes are based on the assumption that the residual income variable is generated by an elastic (or mean reverting) random walk whose increments have a variance that depends on its current instantaneous value. Since several other well-known processes are nested within the Student distributions (e.g. random walk, Ornstein–Uhlenbeck process), they are a very useful set of distributions through which to demonstrate the potential impact of non-linearities on the pricing relationships of this area.     

The Impact of Sampling Errors on the Choice of Portfolio Efficiency Analysis Rules with Borrowing and Lending of a Riskless Asset

This paper evaluates the impact of sampling errors on portfolio decisions using mean-variance and stochastic dominance rules where riskless borrowing and lending opportunities exist. The paper establishes criteria for comparing the alternative decision rules (for example, mean variance versus stochastic dominance) according to their effectiveness and the cost (in sampling error terms). Normal distributions are simulated using various assumed means, standard deviations, correlations, and sample sizes. These simulations enable one to evaluate the impact of sampling errors on the potential effectiveness of the empirical stochastic dominance and mean variance rules that include borrowing and lending of a riskless asset.     

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.     

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.     

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.     

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.     

CVP under uncertainty and the manager's utility function

Cost-volume-profit analysis has focused on the firm's short-run output decision assuming that the manager maximizes the firm's objective function rather than his or her own. This study argues that the decision problem facing the manager is to determine not only the level of output, but also the level of investment in risky assets in such a way that the expected utility of the manager's own end-of-period wealth can be maximized when the manager's wealth function is dependent on vested interests both within and outside of the firm, possibly in competition with the firm. Through analytical work, it is demonstrated that a change in fixed costs of the firm affects not only the production decision of a manager, but also his orher decision to invest in risky assets. The direction of this fixed cost effect depends on the particular type of risk aversion displayed by the manager. From the analytical work, five propositions are developed for empirical investigation in the future.The most helpful comments of Professor Cheng-few Lee are greatly acknowledged. We wish to thank anonymous referees who's comments have improved the paper. Furthermore, participants at the seminar at the University of Massachusetts Lowell also provided helpful comments.