We develop a jackknife estimator for the conditional variance of a minimum-tracking-error-variance portfolio constructed using estimated covariances. We empirically evaluate the performance of our estimator using an optimal portfolio of 200 stocks that has the lowest tracking error with respect to the S&P500 benchmark when three years of daily return data are used for estimating covariances. We find that our jackknife estimator provides more precise estimates and suffers less from in-sample optimism when compared to conventional estimators.

Green and Hollifield (1992) argue that the presence of a dominant factor would result in extreme negative weights in mean-variance efficient portfolios even in the absence of estimation errors. In that case, imposing no-short-sale 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-short-sale constraints in place, the sample covariance matrix performs as well as covariance matrix estimates based on factor models, shrinkage estimators, and daily data.

We illustrate the use of return-based style analysis in practice using several examples. We demonstrate the importance of selecting the right style benchmarks and how the use of inappropriate style benchmarks may lead to wrong conclusions. We show how asset turnover and style graphs over time can be used to ensure right inference about the effective style of a fund, and how to extend return-based style analysis to analyze hedge fund styles. In the examples we consider, return-based style analysis provides insights not available through commonly used peer evaluation alone.

A key input to the capital budgeting process is the cost of capital. Financial managers most often use the CAPM to estimate the cost of capital for which they need to know the market risk premium. Textbooks advocate using the historical value for the US equity premium as the market risk premium. The CAPM as a model has been seriously challenged in the academic literature. In addition, recent research indicates that the true market risk premium might have been as low as half the historical US equity premium during the last two decades. If business finance courses have been teaching the use of the wrong model along with wrong inputs for 20 years, why has no one complained? We provide an answer to this puzzle.

The stochastic discount factor (SDF) method provides a unified general framework for econometric analysis of asset–pricing models. There have been concerns that, compared to the classical beta method, the generality of the SDF method comes at the cost of efficiency in parameter estimation and power in specification tests. We establish the correct framework for comparing the two methods and show that the SDF method is as efficient as the beta method for estimating risk premiums. Also, the specification test based on the SDF method is as powerful as the one based on the beta method.

We provide a brief overview of applications of generalized method of moments in finance. The models examined in the empirical finance literature, especially in the asset pricing area, often imply moment conditions that can be used in a straight forward way to estimate the model parameters without making strong assumptions regarding the stochastic properties of variables observed by the econometrician. Typically the number of moment conditions available to the econometrician would exceed the number of model parameters. This gives rise to overidentifying restrictions that can be used to test the validity of the model specifications. These advantages have led to the widespread use of the generalized method of moments in the empirical finance literature.

This study demonstrates that the U.S. equity premium has declined significantly during the last three decades. The study calculates the equity premium using a variation of a formula in the classic Gordon stock valuation model. The calculation includes the bond yield, the stock dividend yield, and the expected dividend growth rate, which in this formulation can change over time. The study calculates the premium for several measures of the aggregate U.S. stock portfolio and several assumptions about bond yields and stock dividends and gets basically the same result. The premium averaged about 7 percentage points during 1926 70 and only about 0.7 of a percentage point after that. This result is shown to be reasonable by demonstrating the roughly equal returns that investments in stocks and consol bonds of the same duration would have earned between 1982 and 1999, years when the equity premium is estimated to have been zero.

In this paper, we argue that for a sizable fraction of the modern day joint stock companies within an industry, competitive forces may be acting as a disciplining device. For such firms, the inefficiencies that arise due to the agency problem may be of second order importance. We empirically demonstrate that competition in the product market acts as a disciplining device. We provide empirical support for our arguments using data for single business joint stock companies for the period 1973 to 1990.

For options with a reload feature, the holder is automatically entitled to new options when the initial option is exercised. Under Statement of Financial Accounting Standards No. 123, the grant date value of executive stock options excludes the value of a reload feature because the Financial Accounting Standards Board believes it is not feasible to value a reload feature at the grant date. We show how the Binomial Option Pricing Model can be used to value options and the reload feature at the grant date. Ignoring the reload can substantially understate the value of the option. Accordingly, the Financial Accounting Standards Board may wish to reconsider the accounting for reload features.

This note corrects an error in the derivation of a theorem in "The Conditional CAPM and the Cross-Section of Expected Returns," published in the March 1996 issue of the Journal of Finance.

Without the assumption of conditional homoskedasticity, a general asymptotic distribution theory for the two-stage cross-sectional regression method shows that the standard errors produced by the Fama–MacBeth procedure do not necessarily overstate the precision of the risk premium estimates. When factors are misspecified, estimators for risk premiums can be biased, and the t-value of a premium may converge to infinity in probability even when the true premium is zero. However, when a beta-pricing model is misspecified, the t-values for firm characteristics generally converge to infinity in probability, which supports the use of firm characteristics in cross-sectional regressions for detecting model misspecification.

In Japan as in the United States, stocks that are more sensitive to changes in the monthly growth rate of labor income earn a higher return on average. Whereas the stock-index beta can only explain 2% of the cross-sectional variation in the average return on stock portfolios, the stock-index beta and the labor beta together explain 75% of the variation. We find that the labor beta drives out the size effect but not the book-to-market-price effect that is documented in the literature.

It is well documented that stock prices on ex-dividend days drop by less than the value of the dividend, on average. This has commonly been attributed to the effect of tax clienteles. We examine data from the Hong Kong stock market, where neither dividends nor capital gains are taxed. As in the U.S., the average stock price drop is less than the value of the dividend; specifically, the average dividend for the period 1980-1993 is HK $0.12 and the average price drop is HK $0.06. We are able to account for this both theoretically and empirically through market microstructure arguments.

In this article we develop alternative ways to compare asset pricing models when it is understood that their implied stochastic discount factors do not price all portfolios correctly. Unlike comparisons based on χ sup2/sup statistics associated with null hypotheses that models are correct, our measures of model performance do not reward variability of discount factor proxies. One of our measures is designed to exploit fully the implications of arbitrage-free pricing of derivative claims. We demonstrate empirically the usefulness of our methods in assessing some alternative stochastic factor models that have been proposed in asset pricing literature.

Most empirical studies of the static CAPM assume that betas remain constant over time and that the return on the value-weighted portfolio of all stocks is a proxy for the return on aggregate wealth. The general consensus is that the static CAPM is unable to explain satisfactorily the cross-section of average returns on stocks. We assume that the CAPM holds in a conditional sense, i.e., betas and the market risk premium vary over time. We include the return on human capital when measuring the return on aggregate wealth. Our specification performs well in explaining the cross-section of average returns.

Financial planners typically advise people to shift investments away from stocks and toward bonds as they age. The planners commonly justify this advice in three ways. They argue that stocks are less risky over a young person’s long investment horizon, that stocks are often necessary for young people to meet large financial obligations (like college tuition for their children), and that younger people have more years of labor income ahead with which to recover from the potential losses associated with stock ownership. This article uses economic reasoning to evaluate these three different justifications. It finds that the first two arguments do not make economic sense. The last argument is valid—but only for people with labor income that is relatively uncorrelated with stock returns. If a person’s labor income is highly correlated with stock returns, then that investor is better off shifting investments toward stocks over time.

This article describes the academic debate about the usefulness of the capital asset pricing model (the CAPM) developed by Sharpe and Lintner. First the article describes the data the model is meant to explain—the historical average returns for various types of assets over long time periods. Then the article develops a version of the CAPM and describes how it measures the risk of investing in particular assets. Finally the article describes the results of competing studies of the model's validity. Included are studies that support the CAPM (Black; Black, Jensen, and Scholes; Fama and MacBeth), studies that challenge it (Banz; Fama and French), and studies that challenge those challenges (Amihud, Christensen, and Mendelson; Black; Breen and Korajczyk; Jagannathan and Wang; Kothari, Shanken, and Sloan). The article concludes by suggesting that, while academic debate continues, the CAPM may still be useful for those interested in the long run.

We show that valuing performance is equivalent to valuing a particular contingent claim on an index portfolio. In general the form of the contingent claim is not known and must be estimated. We suggest approximating the contingent claim by a series of options. We illustrate the use of our method by evaluating the performance of 130 mutual funds during the period 1968–82. We find that the relative performance rank of a fund is rather insensitive to the choice of the index, even though the actual value of the services of the portfolio manager depends on the choice of the index.

This study examines common stock prices around ex-dividend dates. Such price data usually contain a mixture of observations - some with and some without arbitrageurs and/or dividend capturers active. Our theory predicts that such mixing will result in a nonlinear relation between percentage price drop and dividend yield - not the commonly assumed linear relation. This prediction and another important prediction of theory are supported empirically. In a variety of tests, marginal price drop is not significantly different from the dividend amount. Thus, over the last several decades, one-for-one marginal price drop has been an excellent (average) rule of thumb.

We find support for a negative relation between conditional expected monthly return and conditional variance of monthly return, using a GARCH-M model modified by allowing (1) seasonal patterns in volatility, (2) positive and negative innovations to returns having different impacts on conditional volatility, and (3) nominal interest rates to predict conditional variance. Using the modified GARCH-M model, we also show that monthly conditional volatility may not be as persistent as was thought. Positive unanticipated returns appear to result in a downward revision of the conditional volatility whereas negative unanticipated returns result in an upward revision of conditional volatility.

In empirical studies of the CAPM, it is commonly assumed that, (a) the return to the value-weighted portfolio of all stocks is a reasonable proxy for the return on the market portfolio of all assets in the economy, and (b) betas of assets remain constant over time. Under these assumptions, Fama and French (1992) find that the relation between average return and beta is flat. We argue that these two auxiliary assumptions are not reasonable. We demonstrate that when these assumptions are relaxed, the empirical support for the CAPM is very strong. When human capital is also included in measuring wealth, the CAPM is able to explain 28\% of the cross sectional variation in average returns in the 100 portfolio studied by Fama and French. When, in addition, betas are allowed to vary over the business cycle, the CAPM is able to explain 57\%. More important, relative size does not explain what is left unexplained after taking sampling errors into account.

We show how to use security market data to restrict the admissible region for means and standard deviations of intertemporal marginal rates of substitution (IMRSs) of consumers. Our approach (i) is nonparametric and applies to a rich class of models of dynamic economies, (ii) characterizes the duality between the mean--standard deviation frontier for IMRSs and the familiear mean- standard deviation frontier for asset returns, and (iii) exploits the restriction that IMRSs are positive random variables. The region provides a convenient summary of the sense in which asset market data are anaomalous from the vantage point of intertemporal asset pricing theory.

We study the ex-dividend day behavior of Japanese stock prices for the period 1983-87. We find that, contrary to previous findings, prices of exday stocks drop by nearly the full amount of the dividend. However, ex-day stocks shows an abnormal return. Also, for the many ex-dividend day stocks that also go ex-rights on the same ex-day, we find that the return is on average higher than that for stocks without rights issues. We thus conclude that the ex-day behavior of Japanese stocks are qualitatively similar to that of U. S. stocks.

This paper uses a simple, graphical approach to analyze what happens to commodity prices and economic welfare when futures markets are introduced into an economy. It concludes that these markets do not necessarily make prices more or less stable. It also concludes that, contrary to common belief, whatever happens to commodity prices is not necessarily related to what happens to the economic welfare of market participants: even when futures markets reduce the volatility of prices, some people can be made worse off. These conclusions come from a series of models that differ in their assumptions about the primary function of futures markets, the structure of the industries involved, and the tastes and technologies of the market participants.

We provide a rationale for the presence of points in mortgage loan contracts. Our analysis builds on two key features. First, insurance markets are unavailable for labor income. Second, the "due-on-sale" clause allows banks to offer loan contracts which partially insure against fluctuations in labor income. If explicit prepayment penalties are prohibited by law, points serve effectively as prepayment penalties. We also examine environments where such penalties are not prohibited and show that points will be used if interest rates cannot depend on the size of the loan.

Knowledge of the one-month interest rate is useful in forecasting the sign as well as the variance of the excess return on stocks. The services of a portfolio manager who makes use of the forecasting model to shift funds between bills and stocks would be worth an annual management fee of 2% of the value of the assets managed. During 1954:4 to 1986:12, the variance of monthly returns on the managed portfolio was about 60% of the variance of the returns on the value weighted index, whereas the average return was two basis points higher.

This paper explores a simple model of the effects of requiring public disclosure of insider trading activity in future markets. These disclosures are found to stimulate speculator activity and generate greater volatility, and lead to greater informational efficiency in the sense that futures prices are less biased predictors of future spot prices.

This paper shows that bank runs can be modeled as an equilibrium phenomenon. We demonstrate that some aspects of the intuitive "story" that bank runs start with fears of insolvency of banks can be rigorously modeled. If individuals observe long "lines" at the bank, they correctly infer that there is a possibility that the bank is about to fail and precipitate a bank run. However, bank runs occur even when no one has any adverse information. Extra market constraints such as suspension of convertibility can prevent bank runs and result in superior allocations.

We document a seasonal pattern in stock returns around quarterly earnings announcement dates: small firms show large positive abnormal returns and a sizable increase in the variability of returns around these dates. Only part of the large abnormal returns can be accounted for by the tendency of firms with good news to announce early. Large firms show no abnormal returns around announcement dates and a much smaller increase in variability.

A number of techniques have been proposed to measure portfolio performance and to distinguish between performance due to forecasting security-specific returns and performance due to forecasting market-wide events. We show theoretically and empirically that it is possible to construct portfolios that show artificial timing ability when no true timing ability exists. In particular, investing in options or levered securities will show spurious market timing. These types of securities will also induce the negative correlation between measured selectivity and timing ability found by others. We suggest specification tests to help distinguish between spurious and true timing ability. In addition, the tests can be used to distinguish between different models of the manager's reaction function.

In this paper we examine the parametric test proposed by Henriksson and Merton for evaluating the market timing ability of portfolio managers. Using simulation techniques we show that correction for heteroscedasticity can significantly affect the conclusions. We find that the heteroscedasticity corrections suggested by Hansen and by White are particularly effective.

In this paper we extend the multigood futures pricing model of Grauer and Litzenberger [9] to a dynamic discrete time setting. We then test the model using data on futures prices for corn, wheat, and soybeans. The parameter estimates we obtain are similar to those obtained by other researchers using stock return data. The model itself is rejected and we offer some suggestions as to which assumption may be violated. We also give an interpretation to the Hansen-Singleton nonlinear instrumental variables estimation technique used in our empirical work.

Merton (1973) in his seminal article ‘Theory of Rational Option Pricing’ showed that the rationally determined price of a call option is a non-decreasing function of the ‘riskness’ of its associated common stock. In deriving his results, Merton made restrictive assumptions about the way the market prices payoff distributions, and used the Rothschild-Stiglitz (1970) measure to compare the riskiness of securities. I show by means of an example that the Merton result will not in general be true. I then derive a sufficient condition for the option on one stock to have higher market value than the option on another stock, when both the stocks have the same price, and explain why the Merton result is valid in the Black-Scholes environment.

The authors make a nice case for modifying the utility function of the representative investor in the standard model to incorporate two research findings that characterize individual decision making in experimental settings: Loss Aversion and Narrow Framing (LANF). The authors show how this can be done in a parsimonious way so that the investor's optimization problem can be solved in a rational expectations general equilibrium framework. With this modification alone, they are able to reconcile the low risk free rate with the high equity risk premium at moderate levels of risk aversion. In addition they are able to explain limited participation in the stock market. This is an achievement and the authors must be complemented. I have just one observation to make. LANF, possibly an inherited trait, might have been a desirable characteristic in primitive societies. Those who were willing to fight for avoiding a potential loss, however small when taken in a broader context, in equilibrium probably most often ended up avoiding the loss without actually fighting. However, LANF, probably because it makes individuals react instinctively to situations, can lead to potentially inferior decisions in the modern world. In those situations where LANF leads to high social costs, I expect institutions to develop endogenously to train and educate individuals to minimize the undesirable impact of LANF on their decisions. Smith, Dickhaut, MacCabe and Pardo compared risk versus ambiguity in gain and loss situations on subjects. They found that choice under risk/loss generates more use of the calculational part of the brain (neocortical dorsomedial system), i.e., the more developed part of the brain takes over. Ventromedial system (that arose phylogenetically earlier supporting decision making in animals) plays more of a role in risk/gain, ambiguity/gain and ambiguity/loss situations. Their findings suggest that individuals are likely to react instinctively when they encounter unfamiliar situations that they do not understand well, with the less developed part of the brain playing a more important role. With education individuals are likely to process alternatives in a more calculated manner instead of relying on intuition, with the more developed part of the brain taking over. Therefore the degree of LANF exhibited by an individual may not remain constant over time and is likely to decline with the level of education and experience. In order to fully understand the implications of narrow framing and risk aversion on security prices, it is necessary to allow for heterogeneity in investors' preference parameters, with some investors having standard preferences not subject to the influence of LANF.

We conjecture that an active mutual fund manager with superior ability to analyze value-relevant information affecting a stock is more likely to utilize that skill when there are more information events. We provide empirical support for our conjecture by using the Probability of Informed Trading (PIN, Easley et. al., 1996) as a measure of the density of information events affecting a stock, and inferring mutual fund trades from their reported quarterly holdings data for the period 1983 to 2004. Our conclusions are robust to alternative measures for the density of information events affecting a stock, and unrelated to price momentum in stocks. We further decompose the selection ability of a mutual fund manager to identify the value added from impatient "informed trading" and "liquidity provision." We find that the former is more likely among stocks associated with more information events whereas the latter is more common among stocks affected by fewer information events.

Stylized facts suggest that most investors pay more attention to their asset holdings at the end of the tax year. The tax year ends in December in Japan and April in U.K. August is a relatively quiet period. Therefore we should expect more support for the consumption based capital asset pricing model during the period surrounding the end of the tax year, i.e., fourth and first quarters in Japan; first and second quarters in U.K. We should find least support in the third quarter in both countries. Our findings are consistent with those expectations as well as the patterns in the U.S. documented in the literature. The need to take into account deterministic seasonal patterns in investor behavior provides another rationale for the use of long horizon returns when measuring the consumption risk exposure of stocks.

We examine whether hot hands exist among hedge fund managers. In measuring performance, we use hedge fund style benchmarks. This allows us to control for option-like features inherent in returns from hedge fund strategies. We take into account the possibility that reported asset values may be based on stale prices. We develop a statistical model that relates a hedge fund's performance to its decision to liquidate or close in order to infer the performance of a hedge fund that left the database. While we find significant performance persistence among superior funds we find little evidence of persistence among inferior funds.

We empirically demonstrate that those IPO firms that have reliable comparable firms with at least three years of trading history are priced right at the offer. Those who invested in an IPO firm’s shares at the offering price and those who invested in corresponding Comparable firm’s shares would have earned the same return on average over the five years following the IPO date. In our sample IPO firms had higher expected as well as realized five growth rates than comparable firms. The offering price of an IPO was on average the same as its intrinsic value computed using the Residual Income Model that takes these differences into account; but substantially higher than its intrinsic value based on the P/E multiple of its Comparable firm. The first day return on an IPO is positively related to the absolute value of the difference between its offer price and intrinsic value computed using publicly available information, a proxy for the valuation uncertainty associated with that IPO.

Late in the afternoon on Friday, October 22, 2004, the trading floor at First Convergence Inc. was relatively quiet, as most traders had left for the weekend. However, Mary Lucas, a junior trader, was still sitting in front of her Bloomberg terminal, browsing through the recent trading activities of a few convertible bonds the firm held. First Convergence Inc. was a hedge fund specializing in convertible arbitrage that had been founded by three Wall Street traders in 2002. Lucas had joined the firm only recently after getting her MBA. Prior to starting at the firm, she had known little about convertible bonds. Now she stayed late almost every day in order to learn as much about the business as possible. Suddenly, she noticed something unusual about the trading of a convertible bond issued by Countrywide Financial Corporation (NYSE:CFC). Although the average daily trading volume on this bond had been only three thousand during the previous month, it had shot up to fifty thousand in the last three days. Lucas remembered this particular bond. In fact, First Convergence was actually holding a slightly different convertible bond (known as the liquid yield option note or LYON) issued by the same company. On August 20, Countrywide had offered to exchange the new convertible bond for the original LYON. First Convergence had accepted the exchange offer, thus ending up with the new convertible bond. At that time, Lucas was asked to help evaluate the offer, so she was familiar with the features of both bonds. "What's happening?" she asked herself. She quickly checked the recent price movement on Countrywide's stock. The stock had plunged 11.5 percent on Wednesday, October 20, after the company announced an earning below analysts' expectations. On the same day, trading on the convertible shot up. These two events must be related. But how? Is there a potential investment opportunity?

Sun Charities has an endowment of $100 million. Parker, the Chief Investment Officer of Sun Charities, has an opportunity to invest in Extraordinary Value Partners (EVP), a hedge fund. He is considering investing $10 million in EVP. How should he evaluate the investment opportunity? Learning Objective: Application of return-based style analysis to evaluate the performance of a long-short equities hedge fund. Use of mean-variance portfolio optimization for deciding how much to invest in the long-short fund.