Covariance Of Returns Research Articles

Nonsynchronous Data and the Covariance‐Factor Structure of Returns

ABSTRACTEvidence is presented that indicates that the standard estimator of the covariance matrix of daily returns provides a distorted view of the true covariance‐factor structure. An alternative estimator, based on a model of the price‐adjustment delay process, reveals roughly twice as much covariation in individual security returns. The number of factors identified also appears to increase when this estimator is employed. Since the linear space spanned by the estimated factor‐loading vectors is quite sensitive to the estimator used, it is important that the consistent estimator be considered in the usual two‐stage empirical investigations of the APT.

Intra-industry information releases: A recursive systems approach

This paper investigates the extent of intra-industry information transfers associated with the half-yearly earnings announcements of a sample of Australian firms. The ‘omitted factor’ interpretation of Foster's (1981) results is examined using a recursive systems specification of the return generating process to model extra-market return covariation in cross-section. Although some aspects of the results do appear sensitive to the alternative methodologies, the overall conclusion is consistent with Foster (1981) and supports the existence of intra-industry information transfers associated with firms' earnings releases.

Minimizing the geographical risk of foreign direct investment

Increasingly, it has been recognized that the location decision of multinational firms (MNFs) is the direct result of investment decisions. While MNFs can geographically distribute their products through export diversification and productlicensing agreements, evidence indicates that foreign direct investment (FDI) insures greater profit stability. Although a number of theories have been advanced to explain the global pattern of FDI by a MNF, none have considered the interdependence of production environments in the MNF's investment decision. This paper presents a mean-variance portfolio model as a method of risk aversion that an MNF can use when planning a locational strategy. In this approach, risk is measured by the covariance of production return over a given time. It is hypothesized here that production correlation and hence risk is a distance-decay function. Thus, a covariance risk aversion strategy would result in a global distribution of investment for a given commodity rather than being concentrated in a single country. An empirical example of automobile production supports this risk-distance hypothesis and demonstrates that international cross-investment is a logically consistent mode of firm behavior.

Risk and Return: Consumption Beta Versus Market Beta

Much recent work emphasizes the joint nature of the consumption decision and the portfolio allocation decision. In this paper, we compare two formulations of the Capital Asset Pricing Model. The traditional CAPM suggests that the appropriate measure of an asset's risk is the covariance of the asset's return with the market return. The consumption CAPM, on the other hand, implies that a better measure of risk is the covariance with aggregate consumption growth. We examine a cross-section of 464 stocks and find that the beta measured with respect to a stock market index outperforms the beta measured with respect to consumption growth.

A Simple Exposition of The Arbitrage Pricing Theory Approximation

This paper presents the Arbitrage Pricing Theory (APT) in a finite economy for the familiar case of quadratic utility functions. The standard APT result of a linear relationship between expected returns and the covariances of returns is shown to be approximately true, and an expression for the error of the approximation is given. Some suggestive calculations indicate that the error in the approximation is likely to be small.

Agroforestry and portfolio theory

Portfolio theory is used to analyse the risk of hypothetical agroforestry systems. It is shown that the relationship of the returns of the components of an agroforestry system, expressed in terms of the covariance or correlation of returns, is of vital importance in correctly defining risk. Agroforestry systems can be classified as efficient or inefficient. Inefficient systems are such that an alternative system exists which has a greater return for the same level of risk. Thus, inefficient systems do not represent rational choices for agroforestry systems. Finally, the conclusion is reached that it is impossible to design a ‘best’ system, but rather a set of efficient systems of differing risk and return can be defined. This set of efficient systems is referred to as the efficient frontier.

The Arbitrage Pricing Model and Returns on Assets Under Uncertain Inflation*

THE IMPACT OF INFLATION on equilibrium returns in capital markets has been the subject of several articles in recent years. Chen and Boness [1], Friend, Landskroner and Losq [4], Long [7] and Roll [13] have all constructed general equilibrium models which incorporate the impact of uncertain inflation on returns.' All of these authors have derived models in a mean-variance world utilizing methodologies similar to that first utilized by Mossin [9] or Merton [8]. The basic underlying tenet of mean-variance analysis is that for any given level of expected return investors wish to minimize the variance of return. In mean-variance equilibrium models the only risk that cannot be diversified away is the covariance of an asset's return with the market return. Assets which have the same covariance with the market have the same equilibrium required return. Thus in a mean-variance world if each member of the following pairs of assets had the same covariance with the market each member would have the same expected return: (a) a stock which was a perfect hedge against inflation versus one which was not, (b) a stock which was a perfect hedge against oil price changes versus one which was not, (c) a security that hedged against interest rate changes versus one which did not. In this article we break out of the limitations of the mean variance assumptions by utilizing the Arbitrage Pricing Theory (APT) of Ross [15], [16], [17]. This

Asset prices, asset stocks and rational expectations

This paper explores the relationship between asset return covariances and the impact of asset stock changes on asset prices. In the process the paper reconciles recent contradictory results on the effect of changes in the stock of government debt on equity prices. A solution for asset prices in a rational expectations equilibrium is also derived. This solution has the property that at the prices implied by the solution the demand for each asset equals its supply and the distribution of future asset prices implied by the solution is identical to the distribution upon which asset holders base their demands.

THE CAPITAL MARKET VALUE OF A MULTIPERIOD INVESTMENT WITH THE OPTION OF PREMATURE ABANDONMENT

Conventional approaches to determining optimal abandonment of a project under uncertainty either assume risk‐neutrality or impose a mean‐variance criterion. Risk‐neutrality is unrealistic while the mean‐variance criterion precludes determination of the optimal strategy without consideration of covariances of returns among projects. Further, the use of variance of present value as a risk measure may result in the “optimality” of a time 0 strategy that involves maintaining a position at time t that will be “suboptimal” and would not be maintained. The use of the multiperiod capital asset pricing model (CAPM) as a decision criterion is consistent with contemporary theory of market behavior and remedies the deficiencies of the mean‐variance approach noted above. Computationally, the optimal strategy for abandonment, when the commitment must be made at time 0 (a lease, say), can be determined with little difficulty beyond that of mean‐variance models. When time of abandonment can remain unspecified, the value of the prospect that abandonment will occur at the optimal time can be determined, though the technique necessary is considerably more complicated. In both cases, the marginal costs of commitments that limit discretion over abandonment can be determined and attributed to those commitments.

Risk and capital asset prices

This paper is an empirical examination of the statistical significance of the residual variance of individual assets as compared with the covariance of returns with various market portfolio proxies in predicting expected return. The data and analysis we present suggest that measures of covariance are no more significant than residual variance in predicting expected return. In this sense our paper is not supportive of the Sharpe-Lintner or Black versions of the capital asset pricing model.

Common Stocks as Hedges Against Shifts in the Consumption or Investment Opportunity Set

The purpose of this paper is to explore the potential of using common stocks as hedges against unanticipated shifts over time in investors' consumption or investment opportunity sets. The generalized or multiperiod capital asset pricing model (CAPM) developed in different forms by Merton (1973), Long (1974), Richard (1977), and Breeden (1979) forms the basis for this exploration. In this model, shifts in investors' consumption or investment opportunity sets are caused by changes in the stochastic elements of the state of the world that affect investor taste for wealth. The state of the world is defined in terms of the level of state variables so that unanticipated changes in the levels of the state variables imply or are associated with changes in the state of the world. The analysis of this paper does not constitute a test of the generalized CAPM, because hedging potential is a necessary but not sufficient condition for the generalized CAPM to improve upon the traditional two-factor model. The existence of hedging potential is of interest in itself, howThis paper contains an investigation of the potential for using NYSE stocks as hedges against changes in the consumptioninvestment opportunity set. We perform this investigation under two characterizations of a multiperiod or generalized capital asset pricing model. We find sufficient crosssectional dispersion in common stock return covariances with unanticipated changes in real GNP, the price level, and aggregate consumption that hedge portfolios offer meaningful hedging potential in the portfolioformation period. The positive hedging potential persists out of the portfolio-formation period, but is strongly significant only for consumption.

A Semi‐Strong Form Evaluation of the Efficiency of the Hog Futures Market: Comment

greater forecasting merit than did the respective futures prices, the authors concluded that the hog futures market is semi-strong inefficient. As LH observe, an efficient market has been defined by Fama as one in which prices fully reflect all available information. For any test of the efficient markets hypothesis (EMH) to be operational, one must identify relevant explanatory variables and the specific nature of the linking relation. Thus, any test of the EMH is, at the same time, a test of the postulated model. LH model has little, if any, basis in theory; therefore, the model itself would be a prime suspect in any test of market efficiency. LH state, The hog futures prices cannot consistently be relied upon to reflect accurately subsequent spot prices, and thereby the market is not considered efficient. LH have destroyed a straw man; the EMH does not say, imply, or hint that futures prices in an efficient market can be relied upon to reflect subsequent cash prices accurately. Instead, the EMH does state that known information is impounded in current price, so that all desirable characteristics of the investment (usually expected return) are in equilibrium with all undesirable characteristics of the investment (usually covariance of return with that of the market portfolio). Unless returns resulting from the use of a pricing model like that of LH are found to be in excess of returns justified by risk, the EMH cannot reasonably be rejected. Thus, for an appropriate test of market efficiency, it would be necessary to determine whether returns received from trading based on the econometric model exceed normal returns adjusted for risk. As Rendleman and Carabini (p. 913) state, To determine the extent of the (Treasury Bill Futures) market, it is necessary to assess the significance of the quasi-arbitrage returns that could have been earned. If risk cannot be

Gains from Portfolio Diversification into Less Developed Countries' Securities: A Comment

The thesis that there are gains from international diversification has been made several times in the professional literature as a reading of several of Errunza's citations clearly illustrates. The diversification argument that is presented consists essentially of indicating that (1) both the derived efficient frontier and optimal portfolio depend upon, among other things, the covariances of returns between securities and (2) intracountry covariances are indeed higher than intercountry convariances.1 Ergo, the presumption that international diversification results in a more desirable mean-variance efficiency locus-optimal portfolio. This argument has considerable intuitive appeal. However, a more general as well as more rigorous delineation would have been to structure the argument in terms of optimal portfolio choice in a two-parameter equilibrium capital market with homogenous expectations. This in turn would imply that (1) the mean-variance portfolio decision rule would exhibit the separation property-i.e., the decision with regard to the composition of the risky assets in the portfolio would be independent of the decision with regard to the proportion of the risky assets in the portfolio; (2) the investment opportunity set consists of two assets-i.e., the market portfolio consisting of all risky assets and the riskless asset; and (3) any portfolio which includes only a subset of the market portfolio would be characterized by having some diversifiable or residual risk, and hence, by definition, would be inefficient. If the argument for international diversification were presented in this manner, an important limitation of Errunza's empirical procedure would have been transparent. The procedure employed by Errunza to generate the efficiency locus was via a quadratic programming algorithm of Boles, et al. The utilized data inputs were historical (19571971; 1959-1972) means, variances, and co-variances of quarterly and annual returns of various countries' national stock price indices adjusted for U.S. exchange rate fluctuations.2'3 This procedure incorporates a crucial assumption about the set of investor expectations which concommittantly may lead to implications that conflict with our prior portfolio choice discussion. Specifically, as indicated, the set of investor beliefs about a country's returns, variances, and covariances is identical to the historical magnitudes of these variables.4 Thus, the estimated gains from portfolio diversification A la Errunza's procedure hold precisely only for individuals having this specific expectations generator. Hence, depending upon the particular sequence of history, there may be little, if any, correspondence between the risky Errunza portfolio and the portfolio of all risky marketable assets, or for that matter, with the risky portfolio generated by a different expectations generator under ceteris paribus Errunza conditions.5 Indeed, Tables 1 and 2 of Errunza aptly illustrate the first point above. Further, there is no presumption, particularly given capital market equilibrium, of any correspondence between historical mean-variance portfolio dominance of period 1 and ex ante mean-variance portfolio efficiency of period 2.6,7 Accordingly, two useful and interesting exercises would have been to assess the stationarity of the intercountry pairwise covariances and the serial correspondence la portfolio composition between

A Portfolio Approach to Capital Budgeting: An Application to the Expansion to Additional Product Lines

The importance of the covariance of returns between capital assets is one of the basic principles of modern portfolio theory. An investor should seek capital assets which have negative covariance of returns, or if such capital assets are not available, capital assets with low covariance should be sought for a portfolio. From the variance-covariance structure of returns of the capital assets and the expected returns for each capital asset, a risk-reward trade-off or efficient frontier can be generated. The trade-off represents the minimum risk, as measured by portfolio variance, that could be incurred to realize a desired rate of return for the portfolio. This concept applies to a portfolio of capital budgeting projects as well as to a portfolio of securities. This paper demonstrates how this concept of portfolio diversification can be applied to a capital budgeting problem. The problem involves an actual problem faced by a U.S. distributor who must decide whether to expand sales into one of two industries. Quadratic programming is used to generate the risk-reward relationships and it is shown that the entry into one industry clearly provides a superior risk-reward relationship than entry into the other industry and compared to the company's present sales policy.

Interest Rate Sensitivity and Portfolio Risk

Since its inception the single-index market model has been the subject of a large body of theoretical and empirical research. This study deals with the very difficult issue surrounding the practical implementation of the model in portfolio analysis where significant, nonmarket sources of covariation in security returns are believed to be present.

E-V and E-S Capital Asset Pricing Models: Some Empirical Tests

The purpose of this study was to test empirically the risk and return relationships for a mean-variance (E-V) and a mean-semivariance (E-S) capital asset pricing model (CAPM). To date, virtually all empirical work has focused on the Sharpe-Lintner [28,17] E-V model. In the E-V model, the risk of an efficient portfolio is measured by the standard deviation of return, σp. For individual securities, the appropriate measure of risk is the covariance of return on the security and the market portfolio. The E-V model states that the expected return of any security or portfolio equals the risk-free rate of return plus a risk premium that is η times the difference between the expected return on the market portfolio and the risk-free rate of return, i.e.,where the tildes denote random variables, and = expected rate of return on security i,Rf = risk-free rate of return, = expected rate of return on the market portfolio, and.

The Effect of Homogeneous Stock Groupings on Portfolio Risk

Recent evidence concerning the presence of significant sources of covariation in common-stock returns has raised serious questions as to the usefulness of the single-index market model.' These sources of covariation have been variously described as effects2 or, in more general terms, as simply group effects.3 Regardless of their origin, the presence of important systematic nonmarket sources of covariation in common-stock returns seriously impairs the usefulness of the single-index market model as a tool for constructing efficient portfolios. In an attempt to isolate the industry factor as an extramarket source of covariation in common-stock returns, King4 studied the returns of a sample of 63 firms chosen from six industry groups where industries were defined in terms of the SEC two-digit industry code. Using both cluster and factor analysis, he found that the factor loadings of the individual securities conformed very closely to their a priori industry classes. Campanella' also found evidence to support the existence of industry effects by observing the significant covariances among the residual returns of the market model for 100 common stocks covering a 246-month period. The evidence regarding the importance of industry effects has not gone unchallenged. Based on what he believed to be serious limitations in

The Association Between Market-Determined and Accounting-Determined Measures of Systematic Risk: Some Further Evidence

The measurement and determination of risk have received considerable attention in recent years. One measure of risk is systematic risk, defined in terms of the covariance of a security's return with the return from the market portfolio. The relationship is often standardized by dividing the covariance by the variance of return from the market portfolio. Hereafter, this measure of standardized systematic risk shall be referred to as beta.

AN ANALYSIS OF ALTERNATIVE MEASURES OF INVESTMENT RISK

DESPITE THE THEORETICAL and empirical difficulties in defining and measuring risk, the community is concerned with the investment of alternative securities and firms. This study restricts itself to an analysis of the similarity between two widely employed measures of risk: common stock systematic risk and corporate bond ratings.' The capital asset pricing model [11, 14, 21] specifies that in a properly diversified portfolio, the relevant measure of risk is the covariance of the asset return with the market return divided by the variance of the market return-known as systematic risk or beta. In an efficient market an investor is rewarded only for bearing systematic (i.e., market-wide or non-diversifiable) risk. Systematic risk information is now routinely provided investors by many advisory agencies on a large number of common stocks. A number of recent studies [2, 4, 7] have indicated varying relationships between systematic risk and financialor firm-related estimates of risk. Corporate bond ratings provide a simple indication of the relative risk associated with the fixed income offerings of a large number of publicly owned firms. These ratings, which attempt to look at 'worst' potentialities in the 'visible' future. . [13, p.v.], appear to be based on a combination of objective and subjective factors [16]. Earlier studies have indicated a consistent relationship between bond ratings and actual rates of default [1, 9]. In recent years a number of models for predicting ratings, incorporating a combination of bondrelated and financialor firm-related variables, have been developed [10, 15, 17, 22]. While bond rating agencies do not claim complete precision, the ratings seek to provide the American investor with a simple system of gradation by which relative qualities of bonds may be noted [13, p.v.]. The purpose of this study is to examine the relationship between these two different measures of risk that are readily available to virtually all investors. Given the high level of efficiency in our capital markets [5], and the fact that previous studies of both common stock systematic risk and bond ratings have indicated definite relationships with certain financial variables, we hypothesize that common stock sys-

Portfolio Selection: The Effects of Uncertain Means, Variances, and Covariances

Present models for selecting portfolios according to the mean-variance criteria do not account for the simultaneous effect of error in estimating means, variances, and covariances of security returns. This paper describes an experiment in which the impact of estimation error is so strong that the usefulness of present mean-variance approaches to portfolio selection is brought into question.