Estimating the Correlation Structure of International Share Prices

Recently, the case for international portfolio diversification has been convincingly argued in the framework of mean-variance portfolio analysis by a number of researchers. However, virtually no empirical documentation exists concerning the best method for estimating the correlation structure of international share prices. In this paper, 12 models for estimating the international correlation matrix are presented and empirically tested relative to full historical extrapolation. The major evaluation criteria are the mean squared error and stochastic dominance based on the frequency distribution of the squared forecast errors. The results indicate that the National Mean Model strictly dominates all the others in terms of forecasting accuracy.     

International portfolio selection and efficiency analysis

In the risk-return tradeoff, the traditional mean-variance analysis has been widely used for studies of international portfolio efficiency and diversification. Without prior knowledge about either the parametric structure of assets' return distributions or the form of investors' preference functions, the variance may no longer serve as a suitable risk proxy. This article examines international portfolio efficiency and diversification effects through mean-variance and various distribution-free (or less restrictive) risk-return measures. We show empirically that the mean-variance model is appropriate for large or well-diversified portfolios, but may provide biased results for single assets and less diversified portfolios. While stochastic dominance stands as theoretically the most appropriate method of international portfolio selection and efficiency analysis, the lack of optimal search algorithms reduces its practical usefulness. Very little gain is obtained by using the Gini-mean-difference risk measure as compared to the semivariance measure. The semivariance measure is a powerful and convenient discriminator of risky prospects, while stochastic dominance can serve as a benchmark to justify portfolio efficiency.     

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.     

Ordering Uncertain Options under Inflation: A Note

Stochastic dominance rules (SD) have been extended to the case where investors are allowed to borrow and lend at the riskless interest rate. Stochastic dominance rules with a riskless asset (SDR) are much more effective than SD rules. However, it seems that this benefit is eliminated by an uncertain inflation, since riskless assets become risky once uncertain inflation is considered. We prove in this paper that SDR criteria are valid also in the face of uncertain (and independent) inflation. Moreover, while the mean-variance (MV) efficient set increases with uncertain inflation, the stochastic dominance efficient sets decrease.     

The British investor's gains from international portfolio investment

This paper analyses the effects of exchange controls on the ranking of British and overseas investments. A method is developed by which the costs of such controls can be incorporated into return calculations. It is shown that the adjustment of returns for exchange controls significantly alters the rankings of investments. An additional aspect of the paper is to rank domestic and foreign investments by stochastic dominance and compare the derived rankings with mean-variance. Again a significant differences in rankings is identifiable. It is concluded that the exchange rate regime, institutional exchange controls and the entire distribution of returns should be considered in ranking domestic and foreign investments.     

SINGLE-PERIOD MEAN-VARIANCE IN A MULTIPERIOD CONTEXT

It is not readily apparent that the single-period mean and variance are sufficient to specify the investor choice problem when the investor horizon is greater than one period. It is pointed out that the standard justifications for use of single-period mean-variance analysis are inconsistent with the assumptions usually made in the multiperiod problem. It is argued, however, that if the investor horizon is long enough, the single-period mean and variance will be approximately sufficient. The argument is much less restrictive than the standard justifications for the use of single-period mean-variance analysis. The predictions of this alternative justification are empirically tested and found to be quite accurate for the time frames found in the literature.     

Stochastic dominance analysis of Asian hedge funds

We employ the stochastic dominance approach that utilizes the entire return distribution to rank the performance of Asian hedge funds as traditional mean-variance and CAPM approaches could be inappropriate given the nature of non-normal returns. We find both first-order and higher-order stochastic dominance relationships amongst the funds and conclude that investors would be better off by investing in the first-order dominant funds to maximize their expected wealth. By investing in higher-order dominant funds, risk-averse investors can maximize their expected utilities but not their wealth. In addition, we find the common characteristic for most pairs of funds is that one fund is preferred to another in the negative domain whereas the preference reverses in the positive domain. We conclude that the stochastic dominance approach is more appropriate compared with traditional approaches as a filter in hedge fund selection. Compared with traditional approaches, the SD approach, not only is assumption free, but also provides greater insights to the performance and risk inherent in a hedge fund's track record.     

Time diversification and security preferences: A stochastic dominance analysis

We use stochastic dominance to test whether investor should prefer riskier securities as the investment horizon lengthens. Return distributions for stocks, bonds, and U.S. Treasury bills are generated for holding periods of one to 25 years by simulation. For each holding period, stochastic dominance tests are run to establish preferences between the alternative security classes. Contrary to previous mean-variance based studies, we find no evidence that high-risk securities (stocks) dominate low-risk securities (bonds, Treasury bills) as the investment horizon lengthens. However, we do find that corporate bonds systematically dominate government bonds.     

Mean-variance vs. stochastic dominance some empirical findings on efficient sets

The study attempts to shed additional light on the issue of the costs and benefits of using the mean-variance criterion as opposed to stochastic dominance criteria for investment decisions. Relevant probabilities which facilitate measurement of these costs and benefits are identified. The mean-variance criterion is shown to be useful to some extent in identifying potentially optimal portfolios. However, it is shown that the informationally less demanding mean-variance criterion admits two types of errors: (i) including portfolios that no expected utility maximizing risk averters would choose, and (ii) excluding portfolios which some risk averters would find optimal. The empirical investigation also indicates that although the composition of the efficient sets appears to be unstable over time, the relationships between the efficient sets are persistent over time.     

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.     

Stochastic dominance and portfolio analysis

The principle of stochastic dominance is used to characterize the optimal efficient sets when the distributions of the random prospects belong to a family. Most of the well-known distributions are considered. In each case, the optimal efficient sets are characterized by easily verifiable conditions on the parameters of the distributions. These optimal efficient sets are then compared with the corresponding mean-variance (MV) efficient set. It is often found that the optimal efficient sets are proper subsets of the MV efficient set. Thus, the MV criterion is a proper efficiency criterion, but the MV efficient set can be excessively large compared to the optimal efficient set.     

A NOTE ON THE EFFECTS OF EFFICIENCY CRITERIA AND PORTFOLIO SIZE ON CHARACTERISTICS OF EFFICIENT PORTFOLIOS*

Comparisons of the results of using alternative efficiency criteria for portfolio selection, while plentiful overseas, are seemingly scarce in Australia. Here, mean-variance efficient sets are compared with and found to be not too different from sets efficient according to second and third degree stochastic dominance. In examining the effect of increasing the number of securities allowed in each portfolio, it is found that the size of efficient sets of portfolios diminishes, as does the mean return and, most significantly, the variance of return for efficient portfolios.     

Revisiting calendar anomalies in Asian stock markets using a stochastic dominance approach

Extensive evidence on the prevalence of calendar effects suggests that there exist abnormal returns. Some recent studies, however, have concluded that calendar effects have largely disappeared. In spite of the non-normal nature of stock returns, most previous studies have employed the mean-variance criterion or CAPM statistics. These methods rely on the normality assumption and depend only on the first two moments to test for calendar effects. A limitation of these approaches is that they miss important information contained in the data such as higher moments. In this paper we use a stochastic dominance (SD) test to test for the existence of day-of-the-week and January effects. We use daily data for 1988–2002 for several Asian markets. Our empirical results support the existence of weekday and monthly seasonality effects in some Asian markets, but suggest that first-order SD for the January effect has largely disappeared.     

Bootstrapping a distance test for stochastic dominance analysis

A major impediment to measuring portfolio performance under stochastic dominance has been the lack of test statistics for orders of stochastic dominance above first degree. In this article, the Bootstrap method, introduced by Efron (1979), is used to estimate critical values for distance statistics in order to test the null hypothesis of no dominance, under second- and third-degree stochastic dominance, for several samples of stock returns. These test statistics, suggested by Whitmore (1978), are analogous to the Kolmogorov-Smirnov distance statistics that can be used to test for first-degree stochastic dominance. Stochastic dominance is shown to accurately assess portfolio performance of sample distributions when the population distributions are controlled and Bootstrap statistics are employed in the analysis. In addition, second- and third-degree stochastic dominance analysis of the smallfirm January anomaly indicates that, over the 23-year time period 1964 to 1986, small firms statistically dominate a diversified market index in only one calendar year.     

CAPITAL BUDGETING DECISIONS WHEN CASH FLOWS AND PROJECT LIVES ARE STOCHASTIC AND DEPENDENT

The purpose of this study is twofold: (1) to develop an operational economic state and simulation capital budgeting procedure for allowing cash flows and project lives to be dependent and (2) to provide empirical evidence of the impact of stochastic project lives on mean-variance and mean-semivariance capital budgeting decisions. The required number of input estimates for the proposed model is small. For individual projects, incorrectly assuming deterministic project lives when project lives are stochastic often results in large overestimates of expected net present values and large underestimates of the variance of the net present value. Similar results occur for the mean-variance and mean-semivariance portfolio models. The primary managerial implication of this study is that the inclusion of stochastic project lives in capital budgeting decisions is critical to obtain appropriate risk-return estimates.     

Dominance of a Class of Stein type Estimators for Optimal Portfolio Weights When the Covariance Matrix is Unknown

For the estimation problem of mean-variance optimal portfolio weights, several previous studies have proposed applying Stein type estimators. However, few studies have addressed this problem analytically. Since the form of the loss function used in this problem is not of the quadratic type commonly used in statistical studies, there have been some difficulties in showing analytically the general dominance results. However, dominance results are given here of a class of Stein type estimators for the mean-variance optimal portfolio weights when the covariance matrix is unknown and is estimated. The class of estimators is broader than the one given in a previous study. The results we have obtained enable us to clarify conditions for some previously proposed estimators in finance to have smaller risks than the estimator which we obtain by plugging in the sample estimates.     

Robust optimal strategies for an insurer with reinsurance and investment under benchmark and mean-variance criteria

In this paper, an ambiguity-averse insurer (AAI) whose surplus process is approximated by a Brownian motion with drift, hopes to manage risk by both investing in a Black–Scholes financial market and transferring some risk to a reinsurer, but worries about uncertainty in model parameters. She chooses to find investment and reinsurance strategies that are robust with respect to this uncertainty, and to optimize her decisions in a mean-variance framework. By the stochastic dynamic programming approach, we derive closed-form expressions for a robust optimal benchmark strategy and its corresponding value function, in the sense of viscosity solutions, which allows us to find a mean-variance efficient strategy and the efficient frontier. Furthermore, economic implications are analyzed via numerical examples. In particular, our conclusion in the mean-variance framework differs qualitatively, for certain parameter ranges, with model-uncertainty robustness conclusions in the framework of utility functions: model uncertainty does not always result in an agent deciding to reduce risk exposure under mean-variance criteria, opposite to the conclusions for utility functions in Maenhout and Liu. Our conclusion can be interpreted as saying that the mean-variance problem for the AAI explains certain counter-intuitive investor behaviors, by which the attitude to risk exposure, for an AAI facing model uncertainty, depends on positive past experience.     

An empirical analysis of marginal conditional stochastic dominance

Stochastic dominance is a more general approach to expected utility maximization than the widely accepted mean–variance analysis. However, when applied to portfolios of assets, stochastic dominance rules become too complicated for meaningful empirical analysis, and, thus, its practical relevance has been difficult to establish. This paper develops a framework based on the concept of Marginal Conditional Stochastic Dominance (MCSD), introduced by Shalit and Yitzhaki (1994), to test for the first time the relationship between second order stochastic dominance (SSD) and stock returns. We find evidence that MCSD is a significant determinant of stock returns. Our results are robust with respect to the most popular pricing models.     

Orthogonal Frontiers and Alternative Mean-Variance Efficiency Tests

This paper catalogues properties of minimum norm orthogonal portfolios: portfolios which minimize a quadratic objective function and have returns uncorrelated with those of a candidate portfolio that is not mean-variance efficient. The analysis shows that the dollar versions of these portfolios correspond to estimators of zero beta rates based on alternative statistical criteria and grouping procedures while costless orthogonal portfolios represent candidate mean-variance efficiency tests. It also develops inference procedures for zero and unit net investment portfolios of individual securities (instead of grouped portfolios) that have zero expected betas. The resulting mean-variance efficiency tests are reasonably insensitive to the underlying statistical assumptions.