In this article we test the random walk hypothesis for weekly stock market returns by comparing variance estimators derived from data sampled at different frequencies. The random walk model is strongly rejected for the entire sample period (1962--1985) and for all subperiod for a variety of aggregate returns indexes and size-sorted portofolios. Although the rejections are due largely to the behavior of small stocks, they cannot be attributed completely to the effects of infrequent trading or timevarying volatilities. Moreover, the rejection of the random walk for weekly returns does not support a mean-reverting model of asset prices.

Green and Hollifield (1992) argue that the presence of a dominant factor is why we observe extreme negative weights in mean-variance-efficient portfolios constructed using sample moments. In that case imposing no-shortsale constraints should hurt whereas empirical evidence is often to the contrary. We reconcile this apparent contradiction. We explain why constraining portfolio weights to be nonnegative can reduce the risk in estimated optimal portfolios even when the constraints are wrong. Surprisingly, with no-shortsale constraints in place, the sample covariance matrix performs as well as covariance matrix estimates based on factor models, shrinkage estimators, and daily data.

Mean-variance efficient portfolios constructed using sample moments often involve taking extreme long and short positions. Hence practitioners often impose portfolio weight constraints when constructing efficient portfolios. Green and Hollifield (1992) argue that the presence of a single dominant factor in the covariance matrix of returns is why we observe extreme positive and negative weights. If this were the case then imposing the weight constraint should hurt whereas the empirical evidence is often to the contrary. We reconcile this apparent contradiction. We show that constraining portfolio weights to be nonnegative is equivalent to using the sample covariance matrix after reducing its large elements and then form the optimal portfolio without any restrictions on portfolio weights. This shrinkage helps reduce the risk in estimated optimal portfolios even when they have negative weights in the population. Surprisingly, we also find that once the nonnegativity constraint is imposed, minimum variance and minimum tracking error portfolios constructed using the sample covariance matrix perform as well as

country. It was founded in 1969 through a grant from Oppenheimer & Company in honor of its late partner, Rodney L. White. The Center receives support from its endowment and from annual contributions from its Members. The Center sponsors a wide range of financial research. It publishes a working paper series and a reprint series. It holds an annual seminar, which for the last several years has focused on household financial decision making. The Members of the Center gain the opportunity to participate in innovative research to break new ground in the field of finance. Through their membership, they also gain access to the Wharton School’s faculty and enjoy other special benefits.

Abstract: In this paper, I study the behavior of an investor with unit risk aversion who maximizes a utility function defined over the mean and the variance of a portfolio’s return. Conditioning information is accessible without cost and an unconditionally riskless asset is available in the market. The proposed approach makes it possible to compare the performance of a benchmark tangency portfolio (formed from the set of unrestricted estimates of portfolio weights) to the performance of a restricted tangency portfolio which uses single-index and multi-index asset pricing models to constrain the first moments of asset returns. The main findings of the paper are summarized as follows: i) The estimates of the constant and timevarying tangency portfolio weights are extremely volatile and imprecise. Using an asset pricing model to constrain mean asset returns eliminates extreme short positions in the underlying securities and improves the precision of the estimates of the weights. ii) Partially restricting mean asset returns according to single-index and multi-index asset pricing models improves the out-of-sample performance of the tangency portfolio. iii) Active investment strategies (i.e., strategies that incorporate the role played by conditioning information in investment decisions) strongly dominate passive investment strategies in-sample but do not provide any

This paper examines the hedging effectiveness of German stock index DAX futures and shows that the application of a dynamic hedging strategy based on a GARCH(1,1) covariance structure, combined with an error correction of the mean returns, yields economically significant in- and out-of-sample improvements in welfare over a simple constant hedge and over a dynamic hedge with the error correction but without the GARCH(1,1) covariance structure. A nonparametric test of the model's forecasts shows that it is able to predict both portfolio returns and investor utility significantly better than the simpler alternative models considered.

Constructing a data base that is relatively free of bias, this paper provides measures of the returns of hedge funds as well as the distinctly non-normal characteristics of the data. We provide risk-adjusted measures of performance as well as tests of the degree to which hedge funds live up to their claim of market neutrality. We also examine the substantial attrition of hedge funds and analyze the determinants of hedge fund survival as well as perform tests of return persistence. Finally, we examine the claims of the managers of “funds of funds ” that they can form portfolios of “the best ” hedge funds and that such funds provide useful instruments for individual investors. We conclude that hedge funds are far riskier and provide much lower returns than is commonly supposed. 2 Preliminary Draft: Not for quotation or citation. Hedge funds have become an increasingly popular asset class during the 1990s and early 2000s. Amounts invested in global hedge funds have risen from approximately $50 billion in 1990 to approximately $1 trillion by the end of 2004. Because these funds characteristically employ substantial leverage, they play a far more important role in global securities markets than

The relative merits of forecasting volatility using high-frequency, daily and option data have received much attention. The objective of this paper is to extend this research to the covariance matrix. Forecasts are compared for covariance matrices composed of 17 stocks over 4 horizons, 1-, 30-, 90- and 180-days. Since it is not possible to invert equity option prices to obtain a covariance estimate, a market model assumption is made and forecasts are made based on implied betas and variances. Consequently, these are denoted option-factor-implied forecasts. An additional 6 models are included in the comparisons which can be categrorised into multivariate GARCH models, models estimated directly on the realised covariances (RC) and historical averages. Multiple forecast evaluation criteria are used to obtain a more complete understanding of each model’s performance. These include a statistical loss function, optimlaity tests based on Mincer-Zarnowitz regressions and an economic loss function. On balance, it is very difficult to identify a single model as superior. The option-factor-implied forecasts appear to perform poorly under the statistical loss function whilst they are one of the more informative according to the R 2 from Mincer-Zarnowitz regressions. A persistent positive bias appears to be the source of the conflicting results. However, a simple historical average computed from high-frequency data performs well under all evaluation criteria, bringing into question the benefits of dynamic models in forecasting covariance matrices.

Statistics are developed to test for the presence of an asymptotic discontinuity (or infinite density or peakedness) in a probability density at the median. The approach makes use of work by Knight (1998) on L1 estimation asymptotics in conjunction with non-parametric kernel density estimation methods. The size and power of the tests are assessed, and conditions under which the tests have good performance are explored in simulations. The new methods are applied to stock returns of leading companies across major U.S. industry groups. The results confirm the presence of infinite density at the median as a new significant empirical evidence for stock return distributions.

In markets with trading friction, the incorporation of information into market prices can be substantially delayed through a weakening of the arbitrage process. We re-examine the profitability of relative strength trading strategies (buying past strong performers and selling past weak performers) by testing the predictions of a friction-based explanation. We provide a model of price friction and then use this model to infer trading costs from investor behavior. We find that the execution of standard relative strength strategies requires large trading costs because of the type and frequency of securities traded such that trading costs prevent profitable relative strength investing. In the cross section, we find evidence that trading costs provide binding constraints to relative strength strategy profits. Relative strength returns are localized among low-price, poor performers and are increasing in investor transaction costs. We conclude that the delay in price adjustment for security returns simply reflects the costs of arbitrage--creating an illusion of anomalous price behavior and momentum trading profit opportunity when, in fact, none exists. Lesmond can be reached at 504-865-5665 or dlesmond@mailhost.tcs.tulane.edu. Schill can be reached at