OPTIMAL PORTFOLIOS: MARKOWITZ FULL COVARIANCE VERSUS SIMPLE SELECTION RULES

Two major problems faced by portfolio managers are estimating the risk and return characteristics of individual securities and combining individual security risk and return estimates into optimal portfolios. The second problem is investigated in this paper by using the simple ranking criteria suggested by Elton, Gruber, and Padberg (EGP). The empirical results indicate that the EGP procedure is effective in estimating Markowitz efficient portfolios and can be an effective screening procedure for large numbers of securities.     

Risk measurement when shares are subject to infrequent trading: Comment

When securities are thinly traded OLS techniques yield biased beta estimates. Procedures for calculating consistent estimates are proposed by Scholes and Williams (1977) and by Dimson (1979). This comment examines both procedures and concludes that the Dimson procedure is incorrect and cannot generally be expected to yield consistent beta estimates. However, a variant of this procedure can yield results which are identical to Scholes and Williams' and is, therefore, correct.     

GROUP EFFECTS AND BETA NONSTATIONARITY

Recent evidence indicates that while random diversification can lead to the elimination of the majority of systematic risk, the systematic selection of securities can result in significant group effects blocking this dissipation of unsystematic risk. The group effects associated with investment in growth, cyclical, stable and oil stocks found by Farrell and Martin and Klemkosky were reexamined while allowing for beta nonstationarity. It was found that the beta nonstationarity effect, while quite large for individual stocks and small portfolios tended diversify away quite quickly. It was further found that much of what has in the past been termed a group effect is actually the result of beta nonstationarity.     

SELECTIVITY,MARKET TIMING,AND RANDOM BETA BEHAVIOR OF MUTUAL FUNDS: A GENERALIZED MODEL

This paper presents a generalized varying parameter model to investigate the performance of mutual funds. The model allows beta nonstationarity to include both market timing and random beta behavior; therefore, it can be regarded as a general case of previous research. Forty-three funds with a wide range of objectives are examined. The generalized varying parameter results indicate that about 30 percent of the funds show selectivity, 19 percent have random betas, and 14 percent indicate significant, yet negative, market timing performance. Therefore, mutual funds, as a group, show no market timing ability. The apparent ability to select undervalued securities, however, seems to conflict with the efficient markets hypothesis.     

Friction in the trading process and the estimation of systematic risk

This paper considers how estimates of the market model beta parameter can be biased by friction in the trading process (information, decision, and transaction costs) that (a) leads to a distinction between observed and ‘true’ returns; (b) causes observed returns to be generated asynchronously for a set of interdependent securities; and (c) thereby introduces serial cross-correlation into security returns. Several propositions are derived from which consistent estimators of beta are obtained, and the effect of differencing interval length on beta estimates is specified. The formulation is contrasted with the related analyses of Scholes-Williams (1977) and Dimson (1979).     

On the process of risk reduction through diversification

This paper examines the celebrated empirical study of J.L. Evans and S.H. Archer on the relationship between risk reduction and the size of a portfolio. By specifying a suitable return generation model, this widely supported empirical result is shown to be a statistical consequence of their methodology. The mathematical structure of their methodology is presented together with some fresh empirical results on this relationship. Finally the question as to whether a larger number of assets are required in order to achieve the same level of diversification for high beta securities is examined based on a sample of U.K. securities. The results of the tests would not appear to be in support of such a proposition.     

The E-V stationarity of secure returns: Some empirical evidence

The joint hypothesis that the expected return vector and the variance-covariance matrix of returns are intertemporally stationary is rejected for the monthly return data for securities included on the CRSP file. This finding is robust in that it is invariant to the type of sampling procedure used and to whether nominal or real security returns are used. In contrast, the hypothesis that the correlation matrix of returns is intertemporally stationary could not be rejected for the same samples of securities.     

Constructing Asset Pricing Models With Specific Factor Loadings

We demonstrate how one can build pricing formulae in which factors other than beta may be viewed as determinants of asset returns. This is important conceptually as it demonstrates how the additional factors can compensate for a market portfolio proxy that is mis‐specified, and also shows how such a pricing model can be specified ex ante. The procedure is implemented by first selecting an ‘orthogonal’ portfolio which falls on the mean‐variance efficient frontier computed from the empirical average returns, variances and covariances on the equity securities of a large sample of firms. One then determines the inefficient index portfolio which leads to a vector of betas that when multiplied by the average return on the orthogonal portfolio, and which when subtracted from the vector of average returns for the firms comprising the sample, yields an error vector that is equal to the vector of numerical values for the variables that are to form the basis of the asset pricing formula. There will then be a perfect linear relationship between the vector of average returns for the firms comprising the sample, the vector of betas based on the inefficient index portfolio and such other factors that are deemed to be important in the asset pricing process. We illustrate computational procedures using a numerical example based on the quality of information contained in published corporate financial statements.     

The Time-Series Behavior of IPO Betas

We examine individual IPO betas and provide further evidence that the documented decline in IPO betas results primarily from a seasoning or information effect and not from the delisting of high beta securities. We employ stochastic coefficient regression analysis which permits the estimation of individual IPO betas at all points in time, and therefore avoids disadvantages associated with grouped cross-sectional beta estimates and average individual time-series beta estimates. We find that IPO firms with the lowest betas are more likely to delist, and that individual IPO betas, on average, decline over time which provides support for the information hypothesis.     

THIN TRADING AND THE ESTIMATION OF BETAS: THE EFFICACY OF ALTERNATIVE TECHNIQUES

Infrequent trading induces biased estimates of the beta risk coefficient. This paper reports on the efficacy of approaches that seek to correct for this bias and documents the extent of thin trading among New Zealand securities. Parameter estimates free of the thin-trading bias are obtained. These are compared with estimates obtained using ordinary least squares (OLS) applied in the conventional manner to nonsynchronous data, with and without bias-correcting procedures. OLS beta estimates are found to be less biased, more efficient, and as consistent when compared with Dimson or Scholes-Williams estimators. Lower beta estimates are associated with lower trading frequencies.     

The extent of nonstationarity of beta

This paper investigates the extent of nonstationarity of beta across the firm size and the beta magnitude by suggesting the sequential parameter stationarity model and estimating change-points of betas. The high-beta firm has shorter stationary interval, which means that its beta changes more frequently than do the low-beta firm's. The firm size, however, does not have a monotonic relation with the length of stationary interval. The small and large firms have relatively shorter stationary interval than do the mid-sized firms. The average length of stationary interval is estimated about five years (exactly 54.19 months). This fact could support the currently widely-used arbitrary 5-year assumption of beta stationarity. The fluctuation of the large firm's beta is more severe than the small firm's, and the high- and low-beta firms have the relatively greater fluctuating betas than do the mid-beta firms. The frequency of detected change-points is found to be positively related to market returns. When the market return is high, the systematic risk changes more frequently, and vice versa.     

SYSTEMATIC RISK IN A PURELY RANDOM MARKET MODEL: SOME EMPIRICAL EVIDENCE FOR INDIVIDUAL PUBLIC UTILITIES

A minimum norm quadratic (MINQU-) type of OLS estimator is derived. The estimator is used to test if the betas of the single factor market (SFM) model are random for a sample of utilities for two contiguous periods. The estimated betas for individual utilities vary considerably over time. The statistical significance of such nonstationarity depends on both the utilities and period studied. The relative reduction in the mean square error (MSE) from using a GLS (and not OLS) estimator of beta, when beta is purely random, can be substantial for some utilities but is modest on average.     

Wavelet timescales and conditional relationship between higher-order systematic co-moments and portfolio returns

This paper investigates the association between portfolio returns and higher-order systematic co-moments at different timescales obtained through wavelet multi-scaling, a technique that decomposes a given return series into timescales enabling investigation at different return intervals. In Australian industry portfolios, the relative risk positions indicated by systematic co-moments at some timescales are different from those revealed in daily returns. A strong positive (negative) linear association between beta and portfolio return and co-kurtosis and portfolio return in the up (down) market is observed in daily returns and at different timescales. The beta risk is priced in the up and down markets. Co-kurtosis is not priced when the beta is in the pricing model. Co-skewness appears to be priced at a relatively high timescale and this is observed only after the up and down separation of market returns.     

Conditional beta pricing models: A nonparametric approach

We propose a two-stage procedure to estimate conditional beta pricing models that allows for flexibility in the dynamics of asset betas and market prices of risk (MPR). First, conditional betas are estimated nonparametrically for each asset and period using the time-series of previous data. Then, time-varying MPR are estimated from the cross-section of returns and betas. We prove the consistency and asymptotic normality of the estimators. We also perform Monte Carlo simulations for the conditional version of the three-factor model of Fama and French (1993) and show that nonparametrically estimated betas outperform rolling betas under different specifications of beta dynamics. Using return data on the 25 size and book-to-market sorted portfolios, we find that the nonparametric procedure produces a better fit of the three-factor model to the data, less biased estimates of MPR and lower pricing errors than the Fama–MacBeth procedure with betas estimated under several alternative parametric specifications.     

A censored stochastic volatility approach to the estimation of price limit moves

A censored stochastic volatility model is developed to reconstruct a return series censored by price limits, one popular form of market stabilization mechanisms. When price limits are reached, the observed prices are truncated and the equilibrium prices are unobservable, which makes further financial analyses difficult. The model offers theoretically sound estimates of censored returns and is demonstrated via simulations to outperform existing approaches with respect to the estimates of model parameters, unconditional means, and standard deviations. The algorithm is applied to model stock and futures returns and results are consistent with the simulation outcomes.     

Differences in Perstistence in Aggregated and Disaggregated UK Stock Returns: A Reconciliation

Studies of the persistence in the returns series of UK stocks, using inter alia variance ratios, have documented clear differences between the relatively low levels of persistence in individual security returns and the relatively high levels of persistence in the returns of portfolios composed of these same securities. In this paper, I reconcile this contrast by showing that portfolio return variance ratios should not be expected to reflect (own) persistence levels in the component security returns, but instead should reflect a 'cross-persistence' between the securities. I calculate synthetic portfolio variance ratios from measures of security return 'cross-persistence' and find that they replicate closely the observed portfolio return variance ratios, which provides empirical support for the theoretical results.     

THE EFFECT OF TRADING IN EIGHTHS ON SECURITY RETURN BEHAVIOR

Currently the equity securities of most British, Canadian and US firms trade in eighths. However, this pricing system may soon be abandoned in the US. Specifically, the US Securities and Exchange Commission (SEC) is currently studying the feasibility of changing the pricing of US securities to dollars and cents from dollars and eighths. 'SEC officials contend that moving to a system that quotes stock prices in dollars and cents would create efficiency in the stock market that eighths and sometimes sixteenths can't permit' (Torres and Salwen, 1991). This paper demonstrates the inefficiencies that result from constraining stocks to trade in eighths of a dollar. It describes the effects on returns and betas; then, it presents empirical evidence consistent with the effects. Systematic differences in the distributions of returns of low and high-priced stocks are documented. The covariance of returns with a market index is shown to vary systematically across stocks of different prices and to depend on the return interval used to estimate market model parameters. The variations are explainable by an observed lag between the returns of low-priced stocks relative to those of high-priced stocks. The lag is partially attributable to trading in eighths. A systematic relationship that varies with share price is observed between market model residual returns and unadjusted returns. This relationship is not eliminated by using longer return intervals alone. The extent of the relationship is reduced when longer return intervals are combined with the use of a market index composed of stocks that are priced similarly to those of the securities being tested. The implications of these results for capital market studies are discussed.     

Reversal of 3‐day losers and continuation of 3‐day winners on the NASDAQ

Using only the 200 large-cap securities that make up the NYSE 100 and NASDAQ 100, this study investigates 130 randomly selected formation periods from January 2000 through December 2012. During these formation periods, the three worst and three best performing stocks (based on excess return) are flagged. Once flagged, the subsequent 10-day holding period excess returns are calculated. Results indicate that NYSE securities demonstrate significant return reversal, but not return momentum. Conversely, the worst performing NASDAQ securities demonstrate return reversal, whereas the best performing NASDAQ securities demonstrate return momentum. Results are robust to the number of best and worst stocks that are flagged. Results are also robust to other combinations of formation and holding period lengths.     

Active timing decisions of equity mutual funds

In this paper we examine an aspect of professional investment management which has not been adequately documented and studied; the extent to which equity mutual fund managers actively adjust their portfolio's equity risk exposure over time. Estimates of a portfolio's quarter-end beta are developed using the actual stock holdings of the portfolio at the quarter-end. Changes in these beta estimates from one quarter to the next are shown to arise from both passive and active asset allocation. We find that active risk adjustment dominates passive rebalancing and that equity risk exposure is quite variable over time. Thus, individual investors who estimate the equity risk inherent in a portfolio based on a single time series return beta might seriously misestimate the portfolio's current equity risk. We also test whether active risk management is better characterized as anticipatory of future market events or reactive to past market events.