TESTING THE PREDICTIVE POWER OF EX-POST EFFICIENT PORTFOLIOS

Tested here is the hypothesis that portfolios selected from among ex-post efficient assets will attain better results ex-ante than by following the naive strategy of holding an equally weighted portfolio of all the assets. The tests are conducted using the returns of the one hundred mutual funds that were continuously in operation from 1959 to 1980. Ex-post efficient funds are identified using nine investment decision rules (Stochastic Dominance and Mean-Variance rules with and without riskless asset and the Geometric Mean rule). Ex-ante performance is assessed in terms of terminal wealth and expected utility. Results indicate that over the twenty-two years tested, significantly better performance could be attained ex-ante by investing in mutual funds selected by ex-post efficiency analysis using the distribution-free Second- and Third-Degree Stochastic Dominance tests with Riskless Asset as well as by the more traditional Mean-Variance test with Riskless Asset. Excess returns from using ex-post information exceed the substantial transaction costs incorporated in the analysis.     

On the Exclusion of Assets from Tests of the Mean Variance Efficiency of the Market Portfolio

This paper presents an analysis of the testability of the mean variance efficiency of a market index when the returns on some components of the index itself are not perfectly observable. The results are basically not supportive of the notion that mean variance efficiency is testable on a subset of the assets. Bounding the market share of the missing asset and its expected return is not sufficient to produce a valid test. When the variance of the missing asset is bounded, and the amount of wealth that might be missing is small, it is possible, in principle, to reject correctly the mean variance efficiency of a market index.     

Empirical Tests for Stochastic Dominance Efficiency

We derive empirical tests for the stochastic dominance efficiency of a given portfolio with respect to all possible portfolios constructed from a set of assets. The tests can be computed using straightforward linear programming. Bootstrapping techniques and asymptotic distribution theory can approximate the sampling properties of the test results and allow for statistical inference. Our results could provide a stimulus to the further proliferation of stochastic dominance for the problem of portfolio selection and evaluation. Using our tests, the Fama and French market portfolio is significantly inefficient relative to benchmark portfolios formed on market capitalization and book‐to‐market equity ratio.     

Multivariate proxies and asset pricing relations: Living with the Roll critique

A framework is developed in which inferences can be made about the validity of an equilibrium asset pricing relation, even though the central aggregate in this relation is unobservable. A multivariate proxy for the true market portfolio, consisting of an equal-weighted stock index and a long-term government bond index, is employed in an investigation of the Sharpe-Lintner CAPM. The empirical evidence suggests that we can reject the joint hypothesis that (a) CAPM is valid, and (b) multiple correlation between the true market portfolio and proxy assets exceeds 0.7. Connections to the equilibrium factor pricing literature are also explored.     

Markowitz投资组合模型的最小二乘算法

本文从一个新的视角来研究Markowitz均值—方差模型。通过将Markowitz均值—方差模型表述为约束最小二乘问题,继而使用约束最小二乘问题的算法研究了协方差矩阵正定和半正定时模型的求解问题,我们给出了计算投资组合有效前沿及最小方差组合的新算法。实证分析表明：最小二乘算法在计算稳定和计算速度方面优于传统算法。     

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.     

International Portfolio Investment Flows

This article develops a model of international equity portfolio investment flows based on differences in informational endowments between foreign and domestic investors. It is shown that when domestic investors possess a cumulative information advantage over foreign investors about their domestic market, investors tend to purchase foreign assets in periods when the return on foreign assets is high and to sell when the return is low. The implications of the model are tested using data on United States (U.S.) equity portfolio flows.     

Asset-pricing anomalies and spanning: Multivariate and multifactor tests with heavy-tailed distributions

In this paper we propose a multivariate regression based assessment of the multifactor model first developed by Fama and French (1993). We study mean-variance efficiency and spanning, as well as factor relevance. In particular, we assess the relative contribution of the factors in accounting for asset pricing anomalies. Our tests are motivated by a finite-sample distributional theory, invariant to portfolio repackaging, and achieve size control exactly conditioning on observed factors, in normal and non-normal contexts. We focus on the multivariate normal and Student-t distributions, in which case we rely on the simulation procedure proposed and applied in Beaulieu et al. (2007). We also assess, from a finite-sample and multivariate test perspective, the specification and fit of the model and error distributions considered. In its most general form, the model considered includes six factors: the market portfolio, size, the ratio of book equity to market equity as well as term structure variables (a term premium and a default premium) and momentum. Portfolio returns (coming from assets traded at NYSE, AMEX and NASDAQ) from Fama and French's data base are analyzed on monthly frequencies from 1961–2000.Our results show the following. (1) Normality in model residuals becomes more dependable as a working hypothesis, over short time spans, when the book to market equity and size factors or when the momentum factor are accounted for. (2) Allowing for heavy tailed distributions empirically accommodates some stylized asset pricing anomalies. (3) Loadings on the term structure variables and the momentum factor seem (jointly, across portfolios) statistically insignificant at usual levels in many sub-periods. (4) Mean-variance efficiency is rejected in fewer subperiods allowing for non-normal errors in multi-factor settings; the book to market equity and size factors contribute importantly in reinforcing efficiency. (5) Enlarging the set of assets [from a one factor to a six factor model] does not reinforce the mean-variance spanning hypothesis, which is globally rejected at usual levels.     

International portfolio selection with exchange rate risk: A behavioural portfolio theory perspective

This paper analyzes international portfolio selection with exchange rate risk based on behavioural portfolio theory (BPT). We characterize the conditions under which the BPT problem with a single foreign market has an optimal solution, and show that the optimal portfolio contains the traditional mean–variance efficient portfolio without consideration of exchange rate risk, and an uncorrelated component constructed to hedge against exchange rate risk. We illustrate that the optimal portfolio must be mean–variance efficient with exchange rate risk, while the same is not true from the perspective of local investors unless certain conditions are satisfied. We further establish that international portfolio selection in the BPT with multiple foreign markets consists of two sequential decisions. Investors first select the optimal BPT portfolio in each market, overlooking covariances among markets, and then allocate funds across markets according to a specific rule to achieve mean–variance efficiency or to minimize the loss in efficiency.     

The term structure of euromarket interest rates: An empirical investigation

This paper is an empirical investigation of the predictability and co-movement of risk premia in the term structure of Euromarket interest rates. We present regression results which suggest that risk premia in three Euromarket term structures and on uncovered foreign asset positions move together. We test formally the hypothesis that these risk premia move in proportion to a single latent variable. We are unable to reject this hypothesis. The single latent variable model can be interpreted as in Hansen and Hodrick (1983) and Hodrick and Srivastava (1984) as a specialization of the ICAPM in which assets have constant betas on a single, unobservable benchmark portfolio.     

Portfolio Selection and Optimization with Higher Moments: Evidence from the Indian Stock Market

The Markowitz portfolio optimization model, popularly known as the Mean-Variance model, assumes that stockreturns follow normal distribution. But when stock returns do not follow normal distribution, this model wouldbe inadequate as it would prescribe sub-optimal portfolios. Stock market literature often deliberates that stock returns are non-normal. In such context the Markowitz model would not be sufficient to estimate the portfolio risks. The purpose of this paper is to expand the original Markowitz portfolio theory (mean-variance) via adding the higher order moments like skewness (third moment about the mean) and kurtosis (fourth moment about the mean) in the return characteristics. The research paper investigates the impact of including higher moments using multi-objective programming model for portfolio stock selection and optimization. The empirical results indicate that the inclusion of higher moments had a considerable impact in estimating the returns behavior of portfolios. The portfolios optimized using all the four moments, generated higher returns for the given level of risk in comparison to the returns of the Markowitz model during the study period 2000–2011. The results of this study would be immensely useful to fund managers, portfolio managers and investors as it would help them in understanding the Indian stock market behavior better and also in selecting alternative portfolio selection models.     

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.     

Sources of risk and expected returns in global equity markets

This paper empirically examines multifactor asset pricing models for the returns and expected returns on eighteen national equity markets. The factors are chosen to measure global economic risks. Although previous studies do not reject the unconditional mean variance efficiency of a world market portfolio, our evidence indicates that the tests are low in power, and the world market betas do not provide a good explanation of cross-sectional differences in average returns. Multiple beta models provide an improved explanation of the equity returns.     

International capital market equilibrium with investment barriers

This paper outlines models of capital market equilibrium when there are explicit barriers to international investment in the form of a tax on holdings of assets in one country by residents of another country. There is a corresponding subsidy on short positions in foreign assets. Asset prices deviate from the predictions of the world capital asset pricing model. Investors do not hold a mixture of national market portfolios, but the mix of risky assets is the same for every investor in a country. Optimal portfolios tend to be heavy in domestic assets, and light in foreign assets. Tax free investors, however, tend to hold assets anywhere in the world that are taxed heavily. Estimates of the magnitude of the average tax (or the magnitude of effective barriers to international investment) can be made by comparing the average return on the minimum variance zero β portfolio, z, with the average across countries and time of the short-term interest rate. When barriers are ineffective, the expected return on portfolio z will be the average short-term interest rate, and the world capital asset pricing model will hold.     

Portfolio choice and equilibrium in capital markets with safety-first investors

This paper develops optimal portfolio choice and market equilibrium when investors behave according to a generalized lexicographic safety-first rule. We show that the mutual fund separation property holds for the optimal portfolio choice of a risk-averse safety-first investor. We also derive an explicit valuation formula for the equilibrium value of assets. The valuation formula reduces to the well-known two-parameter capital asset pricing model (CAPM) when investors approximate the tail of the portfolio distribution using Tchebychev's inequality or when the assets have normal or stable Paretian distributions. This shows the robustness of the CAPM to safety-first investors under traditional distributional assumptions. In addition, we indicate how additional information about the portfolio distribution can be incorporated to the safety-first valuation formula to obtain alternative empirically testable models.     

Testing the CAPM with broader market indexes: A problem of mean-deficiency

This study addresses a problem that can arise when a broader market index is used to test the CAPM: a return series used in the index can exclude part of an asset's return. If the excluded return is constant, then a test of mean-variance efficiency can be constructed, but an additional parameter must be estimated. This point is illustrated in tests with both broader market indexes and stocks-only indexes. The broader indexes exclude the rental return on real estate and durables. The excluded rental return is estimated under the assumption that the index portfolio is mean-variance efficient.     

PORTFOLIO CHOICES,CONSUMPTION, AND PRICES IN A MARKET WITH DURABLE ASSETS

Recent research in investments has focused almost exclusively on financial assets such as corporate stocks. Although durable assets constitute an important part of investors' holdings, little effort has been made to explore their role in individuals' investments decisions and on assets pricing. This paper establishes results concerning the role of durable assets in the determination of optimum portfolio choices. The paper explores the effect of consumption considerations related to the service flows generated by durable assets on optimum portfolio considerations and asset prices. The main result is tied to the existence, or lack thereof, of efficient rental markets. In the absence of rental markets (or with restrictions on renting), investors' portfolio choices are not independent of consumption considerations as they are assumed to be in the standard CAPM. Individuals may thus hold different portfolios, and prices reflect the owner's inability to trade consumption flows. Under perfect market assumptions with unrestricted rental markets, optimum portfolio choices are undistinguishable from those implied by the standard CAPM in the sense that they are mean-variance efficient and identical for all individuals. Consumption is adjusted by trading service flows in the rental market. Prices, and the price of risk, however, reflect the existence of durable assets service flows as well as the risks involved in trading these flows in the rental market. In the model, risky rental income is introduced by uncertain rental costs. Equilibrium rental rates, an important part of the return expected from holding durable assets, are determined in the context of the mean-variance framework as a function of return and undiversifiable risk.     

A Note on the Analytics and Geometry of Limiting Mean—Variance Investment Opportunity Sets

This paper extends the mathematics developed by Merton (1972) to the limiting investment opportunity set as smaller risk assets are added. Investment opportunity sets of risky assets are well-known to be described by hyperbolae in mean-standard deviation space. In practice, the asset classes in portfolios may vary from high risk common stocks to near cash assets. Low variability assets change the appearance of the investment opportunity set to the extent that a unique optimum risky asset portfolio disappears. The limiting result is similar to the investment opportunity set that arises when two assets are perfectly correlated. The location of the IOS is shown to mathematically depend upon the level of the riskless interest rate and one slope parameter. The slope parameter is estimable, using a finite number of assets, and represents a bound on market Sharpe ratios.     

互联网金融资产的多目标投资组合研究

互联网金融的快速发展和不断创新,正在悄然改变着公众的投资理财行为。本文在分析互联网金融创新下公众流动性偏好、投资行为变化与资产选择的基础上,构建基于CRRA(常数相对风险厌恶)期末财富期望效用最大化和VaR最小化的多目标投资组合模型。同时引入多目标优化的NSGA-Ⅱ遗传算法,并选择实际数据对模型进行求解,得出最优的互联网金融资产组合。研究表明:(1)互联网金融给传统金融业带来冲击的同时,也改变了人们的流动性偏好、投资行为和资产组合选择。(2)互联网金融在一定程度上调和了金融资产“流动性、收益性和安全性”之间的矛盾,并兼顾了“三性”的相对统一。(3)模型求解结果显示,投资者对互联网金融资产的投资组合为低风险类资产60%左右、高风险类资产40%左右。     

A Bayesian approach to testing portfolio efficiency

This paper develops a Bayesian test of portfolio efficiency and derives a computationally convenient posterior-odds ratio. The analysis indicates that significance levels higher than the traditional 0.05 level are recommended for many test situations. In an example from the literature, the classical test fails to reject with p-value 0.082, yet the odds are nearly two to one against efficiency under apparently reasonable assumptions. Procedures for testing approximate efficiency and for aggregating subperiod results are also considered.