NONPECUNIARY BENEFITS AND ASSET MARKET EQUILIBRIUM

Investments that yield nonpecuniary benefits have been studied empirically in previous research; the existence of such benefits has been inferred as the difference between actual returns and returns predicted by the capital asset pricing model. The authors reformulate the security market line to reflect nonpecuniary benefits and examine the equilibrium conditions for a market wherein some assets yield nonpecuniary benefits for some investors. The reformulated security market line is shown to perform better in such a market. The authors also discuss implications for investors.     

Capital market equilibrium with heterogeneous investors

As a two-parameter model that satisfies stochastic dominance, the mean-extended Gini model is used to build efficient portfolios. The model quantifies risk aversion heterogeneity in capital markets. In a simple Edgeworth box framework, we show how capital market equilibrium is achieved for risky assets. This approach provides a richer basis for analysing the pricing of risky assets under heterogeneous preferences. Our main results are: (1) identical investors, who use the same statistic to represent risk, hold identical portfolios of risky assets equal to the market portfolio; and (2) heterogeneous investors as expressed by the variance or the extended Gini hold different risky assets in portfolios, and therefore no one holds the market portfolio.     

Differential Information and Performance Measurement Using a Security Market Line

An uninformed observer using the tools of mean variance and security market line analysis to measure the performance of a portfolio manager who has superior information is unlikely to be able to make any reliable inferences. While some positive results of a very limited nature are possible, e.g., when there is a riskless asset or when information is restricted to be “security specific,” in general anything is possible. In particular, a manager with superior information can appear to the observer to be below or above the security market line and inside or outside of the mean-variance efficient frontier, and any combination of these is possible.     

THE MEAN‐GINI EFFICIENT PORTFOLIO FRONTIER

A main advantage of the mean‐variance (MV) portfolio frontier is its simplicity and ease of derivation. A major shortcoming, however, lies in its familiar restrictions, such as the quadraticity of preferences or the normality of distributions. As a workable alternative to MV, we present the mean‐Gini (MG) efficient portfolio frontier. Using an optimization algorithm, we compute MG and mean‐extended Gini (MEG) efficient frontiers and compare the results with the MV frontier. MEG allows for the explicit introduction of risk aversion in building the efficient frontier. For U.S. classes of assets, MG and MEG efficient portfolios constructed using Ibbotson (2000) monthly returns appear to be more diversified than MV portfolios. When short sales are allowed, distinct investor risk aversions lead to different patterns of portfolio diversification, a result that is less obvious when short sales are foreclosed. Furthermore, we derive analytically the MG efficient portfolio frontier by restricting asset distributions. The MG frontier derivation is identical in structure to that of the MV efficient frontier derivation. The penalty paid for simplifying the search for the MG efficient frontier is the loss of some information about the distribution of assets.     

Sentiment-scaled CAPM and market mispricing

This study explores the conditional version of the capital asset pricing model on sentiment to provide a behavioural intuition behind the value premium and market mispricing. We find betas (β) and the market risk premium to vary over time across different sentiment indices and portfolios. More importantly, the state β derived from this sentiment-scaled model provides a behavioural explanation of the value premium and a set of anomalies driven by mispricing. Different from the static β–return relation that gives a flat security market line, we document upward security market lines when plotting portfolio returns against their state βs and portfolios with higher state βs earn higher returns.     

Value-at-risk capital requirement regulation,risk taking and asset allocation: a mean–variance analysis

In this study, the mean–variance framework is employed to analyze the impact of the Basel value-at-risk (VaR) market risk regulation on the institution's optimal investment policy, the stockholders’ welfare, as well as the tendency of the institution to change the risk profile of the held portfolio. It is shown that with the VaR regulation, the institution faces a new regulated capital market line, which induces resource allocation distortion in the economy. Surprisingly, only when a riskless asset is available does VaR regulation induce the institution to reduce risk. Otherwise, the regulation may induce higher risk, accompanied by asset allocation distortion. On the positive side, the regulation implies an upper bound on the risk the institution takes and it never induces the firm to select an inefficient portfolio. Moreover, when the riskless asset is available, tightening the regulation always increases the amount of maintained eligible capital and decreases risk.     

Conditional risk premia in currency markets and other asset classes

The downside risk capital asset pricing model (DR-CAPM) can price the cross section of currency returns. The market-beta differential between high and low interest rate currencies is higher conditional on bad market returns, when the market price of risk is also high, than it is conditional on good market returns. Correctly accounting for this variation is crucial for the empirical performance of the model. The DR-CAPM can jointly rationalize the cross section of equity, equity index options, commodity, sovereign bond and currency returns, thus offering a unified risk view of these asset classes. In contrast, popular models that have been developed for a specific asset class fail to jointly price other asset classes.     

A Comparative Study of Gini's Mean Difference and Mean Variance in Portfolio Analysis

The methods traditionally used for comparing uncertain prospects are the mean variance and the stochastic dominance approaches. Yitzhaki has recently presented an alternative model based upon Gini's mean difference to compare uncertain prospects. The mean Gini model is similar in nature to the mean variance model in that it uses a two-parameter statistic to describe the probability distribution of risky returns. Theoretically, the mean Gini model is consistent with the behaviour of investors under conditions of uncertainty for a wider class of probability distributions. Thus Gini's mean difference appears to be more adequate than variance as a measure of risk. This study firstly generated the mean Gini efficient frontier and secondly compared the mean variance efficient frontier with it. For the sample data employed, the mean variance model gave a very good approximation to the mean Gini model. Since the computational costs of the mean variance approach were a small fraction of those of the mean Gini approach, the theoretical advantage would not appear in this case to translate into a practical one.     

Changes in Expected Security Returns,Risk, and the Level of Interest Rates

Regressions of security returns on treasury bill rates provide insight about the behavior of risk in rational asset pricing models. The information in one-month bill rates implies time variation in the conditional covariances of portfolios of stocks and fixed-income securities with benchmark pricing variables, over extended samples and within five-year subperiods. There is evidence of changes in conditional “betas” associated with interest rates. Consumption and stock market data are examined as proxies for marginal utility, in a general framework for asset pricing with time-varying conditional covariances.     

A DERIVATION OF THE CAPM FOR PEDAGOGICAL USE

A central paradigm in modern finance theory is the capital asset pricing model (CAPM). While the CAPM is invariably taught in introductory finance courses, a derivation is commonly reserved for postgraduate courses. This is primarily because the available CAPM derivations usually assume an advanced knowledge of pure mathematics. This note provides a simple derivation of the CAPM which requires only an understanding of very basic mathematical concepts. The derivation explicitly highlights the link between the capital market line and the security market line which students often fail to comprehend. Our simple derivation can easily be adopted by instructors at all levels.     

The Role of Learning in Dynamic Portfolio Decisions

This paper analyzes the effect of uncertainty about the mean return on the risky asset on the portfolio decisions of an investor who has a long investment horizon. Building on the earlier work of Detemple (1986), Dothan and Feldman (1986), and Gennotte (1986), it is shown that the possibility of future learning about the mean return on the risky asset induces the investor to take a larger or smaller position in the risky asset than she would if there were no learning, the direction of the effect depending on whether the investor is more or less risk tolerant than the logarithmic investor whose portfolio decisions are unaffected by the possibility of future learning. Numerical calculations show that uncertainty about the mean return on the market portfolio has a significant effect on the portfolio decision of an investor with a 20 year horizon if her assessment of the market risk premium is based solely on the Ibbotson and Sinquefield (1995) data.     

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.     

The Role of Learning in Dynamic Portfolio Decisions

This paper analyzes the effect of uncertainty about the meanreturn on the risky asset on the portfolio decisions of an investorwho has a long investment horizon. Building on the earlier workof Detemple (1986), Dothan and Feldman (1986), and Gennotte(1986), it is shown that the possibility of future learningabout the mean return on the risky asset induces the investorto take a larger or smaller position in the risky asset thanshe would if there were no learning, the direction of the effectdepending on whether the investor is more or less risk tolerantthan the logarithmic investor whose portfolio decisions areunaffected by the possibility of future learning. Numericalcalculations show that uncertainty about the mean return onthe market portfolio has a significant effect on the portfoliodecision of an investor with a 20 year horizon if her assessmentof the market risk premium is based solely on the Ibbotson andSinquefield (1995) data.     

Multi-regime nonlinear capital asset pricing models

A multiple-regime threshold generalized autoregressive conditionally heteroskedastic capital asset pricing model is introduced. The model captures asymmetric risk through allowing market beta to change discretely between regimes that are driven by market information. Asymmetric volatility and mean equation dynamics are also captured. We confirm the time-varying nature of market risk, in response to changes in the market, and that this discrete time variation can differ across assets. These findings could have important implications for optimizing investment decisions: e.g. in risk assessment, portfolio selection and hedging decisions.     

Mean-Gini,Portfolio Theory,and the Pricing of Risky Assets

This paper presents the mean-Gini (MG) approach to analyze risky prospects and construct optimum portfolios. The proposed method has the simplicity of a mean-variance model and the main features of stochastic dominance efficiency. Since mean-Gini is consistent with investor behavior under uncertainty for a wide class of probability distributions, Gini's mean difference is shown to be more adequate than the variance for evaluating the variability of a prospect. The MG approach is then applied to capital markets and the security valuation theorem is derived as a general relationship between average return and risk. This is further extended to include a degree of risk aversion that can be estimated from capital market data. The analysis is concluded with the concentration ratio to allow for the classification of different securities with respect to their relative riskiness.     

The choice of the distribution of asset returns: How extreme value theory can help?

One of the issues of risk management is the choice of the distribution of asset returns. Academics and practitioners have assumed for a long time (for more than three decades) that the distribution of asset returns is a Gaussian distribution. Such an assumption has been used in many fields of finance: building optimal portfolio, pricing and hedging derivatives and managing risks. However, real financial data tend to exhibit extreme price changes such as stock market crashes that seem incompatible with the assumption of normality. This article shows how extreme value theory can be useful to know more precisely the characteristics of the distribution of asset returns and finally help to chose a better model by focusing on the tails of the distribution. An empirical analysis using equity data of the US market is provided to illustrate this point.     

Modelling mean reversion of asset prices towards their fundamental value

In this paper we extend the study of mean reversion behavior by modelling the fundamental value as a stochastic process. The market value of the asset is then modelled as a mean reverting Ornstein Uhlenbeck process towards the fundamental value. Solving backwards, we determine the functional form of the regression equation of changes in asset prices and returns to changes to the fundamental value. Using earnings and dividends as proxies for the fundamental value we test our model empirically. In general, other than the shortest horizon of 1-year, our model shows good explanatory power. Since our model is compatible with Campbell and Shiller (1988) framework in the earnings case and Fama and French (1988) model in the dividend case, the performance of our model has been compared with those two models. In comparison, the performance of our model is comparable to that of Campbell and Shiller and compares favorably with Fama and French.     

Equilibrium relations in a capital asset market: A mean absolute deviation approach

We consider the equilibrium in a capital asset market where the risk is measured by the absolute deviation, instead of the standard deviation of the rate of return of the portfolio. It is shown that the equilibrium relations proved by Mossin for the mean variance (MV) model can also be proved for the mean absolute deviation (MAD) model under similar assumptions on the capital market. In particular, a sufficient condition is derived for the existence of a unique nonnegative equilibrium price vector and derive its explicit formula in terms of exogeneously determined variables. Also, we prove relations between the expected rate of return of individual assets and the market portfolio.     

TRANSITORY MARKET STATES AND THE JOINT OCCURRENCE OF MOMENTUM AND MEAN REVERSION

In this article we derive and investigate the implications of the Fama–French and Poterba–Summers model—in which the market price of equity contains permanent and temporary components—to explain cross‐sectional differences in equity risk premia and returns. Shocks to the transitory component are regarded a Merton risk factor. We obtain estimates from a simple Kalman decomposition of the market price. The transitory component estimate is used in a conditional capital asset pricing model to test implications of the model related to predictability, cross‐sectional performance, and the existence of momentum and mean reversion.