[Numerous studies have examined the mean/variance efficiency of various market proxies by employing sample parameters and have concluded that these proxies are inefficient. These findings cast doubt about the capital asset pricing model (CAPM), one of the cornerstones of modern finance. This study adopts a reverse-engineering approach: given a particular market proxy, we find the minimal variations in sample parameters required to ensure that the proxy is mean/variance efficient. Surprisingly, slight variations in parameters, well within estimation error bounds, suffice to make the proxy efficient. Thus, many conventional market proxies could be perfectly consistent with the CAPM and useful for estimating expected returns.]

The experimental results of prospect theory (PT) reveal suggest that investors make decisions based on change of wealth rather than total wealth, that preferences are S-shaped with a risk-seeking segment, and that probabilities are subjectively distorted. This article shows that while PT's findings are in sharp contradiction to the foundations of mean-variance (MV) analysis, counterintuitively, when diversification between assets is allowed, the MV and PT-efficient sets almost coincide. Thus one can employ the MV optimization algorithm to construct PT-efficient portfolios.

Jan Eeckhout (2004) reports that the empirical city size distribution is lognormal, consistent with Gibrat's Law. We show that for the top 0.6 percent of the largest cities, the empirical distribution is dramatically different from the lognormal, and follows a power law. This top part is extremely important as it accounts for more than 23 percent of the population. The empirical hybrid lognormal-power-law distribution revealed may be characteristic of other key distributions, such as the wealth distribution and the income distribution. This distribution is not consistent with a simple Gibrat proportionate effect process, and its origin presents a puzzle yet to be answered. (JEL R11, R12, R23)

Numerous studies have examined the mean/variance efficiency of various market proxies by employing sample parameters and have concluded that these proxies are inefficient. These findings cast doubt about the capital asset pricing model (CAPM), one of the cornerstones of modern finance. This study adopts a reverse-engineering approach: given a particular market proxy, we find the minimal variations in sample parameters required to ensure that the proxy is mean/variance efficient. Surprisingly, slight variations in parameters, well within estimation error bounds, suffice to make the proxy efficient. Thus, many conventional market proxies could be perfectly consistent with the CAPM and useful for estimating expected returns.

Abstract Disagreement, a key factor inducing trading, has been receiving ever increasing attention in recent years. Most research has focused on disagreement about the expected returns. Several authors have shown that if the average belief coincides with the true expected return, in the portfolio context prices are unaffected by disagreement. In this paper we study the pricing effects of disagreement about return variances. We show that i) disagreement about variances has systematic and significant pricing effects—more disagreement leads to higher prices, and ii) prices are very sensitive to the degree of disagreement: Even if the average belief about the variance is constant, tiny fluctuations in the disagreement about the variance lead to substantial price fluctuations. This second result may offer an explanation for the excess volatility puzzle: When small changes in the degree of disagreement occur, they induce relatively large price changes. Yet, the changes in disagreement may be hard to directly detect empirically, leading to apparent “excess volatility.”

The experimental results of prospect theory (PT) reveal suggest that investors make decisions based on change of wealth rather than total wealth, that preferences are S-shaped with a risk-seeking segment, and that probabilities are subjectively distorted. This article shows that while PT's findings are in sharp contradiction to the foundations of mean-variance (MV) analysis, counterintuitively, when diversification between assets is allowed, the MV and PT-efficient sets almost coincide. Thus one can employ the MV optimization algorithm to construct PT-efficient portfolios.

Diversification across time means changing the asset allocation over time. We show that under mild conditions diversification across time is inferior for all risk-averters and for all investment horizons, relative to a portfolio with the same average asset allocation, held constant over time. Target-date funds help reduce the variation in the asset allocation throughout the lifecycle, by implicitly considering the reduction in human capital with age. However, their structure implies two systematic deviations from constant asset allocation. We suggest a simple correction leading to a typical increase of 5%-22% in welfare.

Does the famous idiom “stocks for the long run” have an empirical or a theoretical foundation? Bali et al. (2009) show that the cumulative return distributions of stocks and bonds intersect for all investment horizons, implying that stocks do not dominate bonds, regardless of the horizon. This paper shows that adding the riskless asset to the analysis yields a clear-cut dominance of stocks over bonds: for any combination of bonds with the riskless asset, one can find a combination of stocks with the riskless asset that dominates it. This dominance holds for all non-decreasing preferences as long as the investment horizon is 3 years or longer. However, this strong result does not imply that arbitrage opportunities exist.

Peer-effects have been shown to affect behavior, and can generally lead to investments choices that are mean–variance inefficient. This paper analyzes optimal diversification with peer-effects. We show that if individuals have keeping-up with the Joneses preferences and they take their peer-group reference as the market portfolio, Markowitz’s mean–variance efficiency analysis and the CAPM equilibrium are intact. This holds for any keeping-up preferences, as well as heterogeneous combinations of such preferences. These results also extend to the Merton–Levy segmented-market model.

Over the last 15years, dramatically decreasing foreign investment costs have not reduced the home bias. We show that the home bias induced by a given cost is proportional to the factor ρ/(1−ρ), where ρ is the average correlation between markets. This factor is very sensitive to the correlation, especially when the correlation is high. Empirically, correlations have been steadily increasing from 0.4 in the 90’s to about 0.9 today. Thus, the decreasing extra costs are increasingly magnified, explaining the persistence of the home bias, and predicting its continuation.