On the Cross-sectional Relation between Expected Returns and Betas

There is an exact linear relation between expected returns and true “betas” when the market portfolio is on the ex ante mean-variance efficient frontier, but empirical research has found little relation between sample mean returns and estimated betas. A possible explanation is that market portfolio proxies are mean-variance inefficient. We categorize proxies that produce particular relations between expected returns and true betas. For the special case of a zero relation, a market portfolio proxy must lie inside the efficient frontier, but it may be close to the frontier.     

Return,Risk, and Yield: Evidence from Ex Ante Data

The purpose of this study is to investigate the relationship between return and yield in the context of ex ante data from The Value Line Investment Survey and by examining the role of dividends as a proxy for risk. The use of ex ante data should substantially reduce the confounding of tax and information effects that has affected earlier studies. Heteroscedasticity is detected in the after-tax CAPM and found to be negatively related to yield and positively related to beta. Maximum likelihood methods are used to correct for heteroscedasticity and generate efficient coefficient estimates. Using data for each of the years 1973 through 1983, there is an overall positive relationship between expected return and yield. However, coefficient estimates of yield are highly variable from year to year.     

Underpricing and Ex Post Value Uncertainty

As documented by a vast empirical literature, initial public offerings (IPOs) are characterized by underpricing. A number of papers have shown that underpricing is directly related to the amount of ex ante uncertainty concerning the IPOs valuation. Recent theoretical papers propose that not all value uncertainty is resolved prior to the start of trading, but rather continues to be resolved in the beginning of the after market. We term this type of uncertainty as ex post value uncertainty and develop proxies for it. We find strong support for the existence of ex post value uncertainty and find that including a proxy for it more than doubles the explanatory power of previous models.     

Return spread and liquidity: Evidence from Hong Kong ADRs

Fifteen Chinese H-shares listed on the Stock Exchange of Hong Kong are cross listed as ADRs on the NYSE. We empirically determine the role of security specific liquidity associated with those ADRs and their underlying H-shares on return spreads, differences between the returns on ADRs and their corresponding H-shares after controlling for ADRs and H-shares excess market returns and their respective price inverses denoting conditional betas. We use three proxies for liquidity, trading volume, turnover, and illiquidity (Amihud, 2002) and find that only trading volume and turnover are consistent determinants of return spread for the majority of Chinese ADRs with primary listing in Hong Kong Stock Exchange (SEHK). We use a switching regression model and find that the model parameter estimates are not stationary and change, often drastically between pre and post 2000 and 2003. Further tests using Bai Perron indicate return spreads data as non-stationary with multiple regime changes during the sample period. Further the causes of non-stationarity seem to be largely security specific and not driven by broad market swings in either market.     

Designing proxies for stock market indices is computationally hard*

In this paper, we study the problem of designing proxies (or portfolios) for various stock market indices based on historical data. We use four different methods for computing market indices, all of which are formulae used in actual stock market analysis. For each index, we consider three criteria for designing the proxy: the proxy must either track the market index, outperform the market index, or perform within a margin of error of the index while maintaining a low volatility. In eleven of the twelve cases (all combinations of four indices with three criteria except the problem of sacrificing return for less volatility using the price-relative index) we show that the problem is NP-hard, and hence most likely intractable.     

THE UNDERPRICING OF INITIAL PUBLIC OFFERINGS,EX ANTE UNCERTAINTY,AND PROXY SELECTION

This paper reconsiders the prediction that the underpricing of IPOs is increasing in ex ante uncertainty by objectively establishing proxies for ex ante uncertainty on definitional grounds rather than by appealing to intuitive arguments. Based on a sample of 420 U.S. IPOs from the period 1976–1985, the results suggest that there is a hierarchy of proxies. The results also support the prediction of a positive relation between underpricing and ex ante uncertainty. Finally, the results suggest that as the effectiveness of a selected proxy as a measure of ex ante uncertainty increases, so does the strength of the relation between the degree of underpricing and ex ante uncertainty as measured by that proxy.     

The use of domestic and world market indexes in the estimation of time-varying betas

This paper generates time-varying estimates of Australian industry betas relative to an Australian market index and a world market index using the Kalman filter approach. As a means of comparison, these conditional estimated betas are used to forecast each industry’s return in-sample. The forecast error metrics suggest that the estimates of conditional risk relative to the domestic market index are preferred to estimates generated using the world market index, irrespective of the industry concerned. While not to suggest time-varying betas estimated relative to a domestic index are universally superior, these results suggest that they are preferable in certain circumstances.     

Using Cointegration Restrictions to Improve Inference in Vector Autoregressive Systems

An improved way of dealing with uncertain prior information in the context of vector autoregressive systems of equations is proposed. The procedure is appropriate when inference about parameters of a cointegrated system is the aim of the analysis. The estimator uses uncertain prior information about the existence of trends and co-trends in the time series to improve parameter estimation within these systems. The improved estimator eliminates the need to carry out the unit root, cointegration, and parameter restriction pretests and is shown in our Monte Carlo experiments to have good statistical properties in small samples. The pretest, maximum likelihood, and restricted maximum likelihood estimators are compared to the proposed estimator based on squared error risk, mean square error of prediction risk, and out-of-sample root-mean-square forecast error. The Monte Carlo simulations are based on actual economic data collected for eurodollar futures contracts. The evidence suggests that the parameters of vector autoregressive systems can be estimated with lower mean square error with the new estimator even when prior guesses about the nature of the cointegrating vector(s) are incorrect. In-sample prediction is likewise improved. The Monte Carlo simulations are based on eurodollar spot and futures market data that has been used to test the unbiased expectations hypothesis.Marjory B. Ourso Center for Excellence in Teaching Professor     

Unbiased estimation of expected return using CAPM

Estimation of expected return is required for many financial decisions. For example, an estimate for cost of capital is required for capital budgeting and cost of equity estimates are needed for performance evaluation based on measures such as EVA. Estimates for expected return are often based on the Capital Asset Pricing Model (CAPM), which states that expected excess return (expected return minus the risk-free rate) is equal to the asset's sensitivity to the world market portfolio (β) times the risk premium on the “world market portfolio” (the market risk premium). Since the world market portfolio, by definition, contains all assets in the world, it is not observable. As a result, an estimate for expected return is commonly obtained by taking an estimate for β based on some index (as a proxy for the world market portfolio) and an estimate for the market risk premium based on a potentially different index and multiplying them together. In this paper, it is shown that this results in a biased estimate for expected return. This is undesirable since biased estimates lead to misallocation of funds and biased performance measures. It is also shown in this paper that the straightforward procedure suggested by Fama and MacBeth [J. Financ. Econ. 1 (1974) 43] results in an unbiased estimate for expected return. Further from the analysis done, it follows that, for an unbiased estimate, it does not matter what proxy is used, as long as it is used correctly an unbiased estimate for expected return results.     

Time‐Varying Risk–Return Trade‐off in the Stock Market

We uncover a strong comovement of the stock market risk–return trade‐off with the consumption–wealth ratio (CAY). The finding reflects time‐varying investment opportunities rather than countercyclical aggregate relative risk aversion. Specifically, the partial risk–return trade‐off is positive and constant when we control for CAY as a proxy for investment opportunities. Moreover, conditional market variance scaled by CAY is negatively priced in the cross‐section of stock returns. Our results are consistent with a limited stock market participation model, in which shareholders require an illiquidity premium that increases with CAY, in addition to the risk premium that is proportional to conditional market variance.     

A Simulation-Based Investigation of Errors in Accounting-Based Surrogates for Internal Rate of Return

Accounting-based measures of a firm's ex post performance represent accessible, albeit imperfect, surrogates for its internal rate of return (IRR). Using a cross-sectional data set obtained via computer simulation, this study calculated the error with which the accounting rate of return (ARR) and conditional estimate of internal rate of return (CIRR) estimate IRR. The study compared the error with which both surrogates measure IRR, as well as the ability of growth in unit demand (gD), inventory cost flow assumption (INV) and depreciation method (DEP) to explain the measurement error in both surrogates.     

Benchmark Portfolio Inefficiency and Deviations from the Security Market Line

This paper theoretically evaluates the robustness of the Security Market Line relationship when the market proxy employed is not mean-variance efficient. The analysis focuses on the behavior of the “benchmark errors,” the deviations of assets and portfolios from the Security Market Line. First, we characterize how the location of an asset in mean-variance space determines its benchmark error. Then the continuity properties of the benchmark errors are studied. The results indicate that the magnitudes of the errors exhibit continuous but not uniformly continuous behaviors. The relative rankings based on deviations from the Security Market Line, however, exhibit some severe discontinuities. In fact, these can be exactly reversed for two proxies arbitrarily close in mean-variance space.     

Agency costs of free cash flow and conditional conservatism

This study investigates whether agency costs of free cash flow (FCF) are associated with conditional conservatism. Prior research documents that conditional conservatism improves ex ante efficient investment decisions and facilitates ex post monitoring of managers’ investment decisions. As conditional conservatism can provide protection from possible managerial expropriation, the demand for conditional conservatism should increase with the agency costs of FCF. Using excess cash as a proxy for the agency costs of FCF, I provide evidence that firms with higher agency costs of FCF incorporate losses in a timelier manner relative to gains compared to their counterparts. Additionally, the association between excess cash and conditional conservatism predictably varies with the presence of alternative monitoring mechanisms that mitigate FCF problems, such as debt or dividend payouts or repurchases. Further investigation suggests that greater conservatism is associated with a lower likelihood of overinvestment among firms bearing high agency costs of FCF, demonstrating the ability of conservatism to reduce agency costs of FCF.     

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 role of autoregressive conditional skewness and kurtosis in the estimation of conditional VaR

This paper investigates the role of high-order moments in the estimation of conditional value at risk (VaR). We use the skewed generalized t distribution (SGT) with time-varying parameters to provide an accurate characterization of the tails of the standardized return distribution. We allow the high-order moments of the SGT density to depend on the past information set, and hence relax the conventional assumption in conditional VaR calculation that the distribution of standardized returns is iid. The maximum likelihood estimates show that the time-varying conditional volatility, skewness, tail-thickness, and peakedness parameters of the SGT density are statistically significant. The in-sample and out-of-sample performance results indicate that the conditional SGT-GARCH approach with autoregressive conditional skewness and kurtosis provides very accurate and robust estimates of the actual VaR thresholds.     

Are the Latent Variables in Time-Varying Expected Returns Compensation for Consumption Risk?

Multibeta asset pricing models are examined using proxies for economic state variables in a framework which exploits time-varying expected returns to estimate conditional betas. Examples include multiple consumption-beta models and models where asset returns proxy for the state variables. When the state variables are not specified, the tests indicate two or three time-varying expected risk premiums in the sample of quarterly asset returns. Conditional betas relative to consumption generate less striking evidence against the model than betas relative to asset returns, but both the consumption and the market variables fail to proxy for the state variables.     

Covariance complexity and rates of return on assets

This paper considers the estimation of the expected rate of return on a set of risky assets. The approach to estimation focuses on the covariance matrix for the returns. The structure in the covariance matrix determines shared information which is useful in estimating the mean return for each asset. An empirical Bayes estimator is developed using the covariance structure of the returns distribution. The estimator is an improvement on the maximum likelihood and Bayes–Stein estimators in terms of mean squared error. The effect of reduced estimation error on accumulated wealth is analyzed for the portfolio choice model with constant relative risk aversion utility.     

Cross-holdings: estimation issues, biases, and distortions

Cross-bolding occurs when listed corporations own securitiesissued by other corporations. We analyze the effect of cross-holdingson market capitalization and return measures as well as implicationsfor econometric testing of asset pricing theories. We show thatcross-holdings generally distort standard market return andrisk measures. The magnitudes of such distortions are calculatedfor simulated economies by using a variety of crossholding patterns.In addition, cross-holdings are shown to induce non-stationarityin the covariance matrix of security returns. We examine theeffect of this nonstationarity for estimating efficient frontiersand factor structures. We also discuss the implications forrisk-return estimates in equilibrium asset pricing models.     

The Conditional CAPM and the Cross-Section of Expected Returns

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.     

EXCESS RETURNS AND RISK AT THE LONG END OF THE TREASURY MARKET: AN EGARCH-M APPROACH

In this paper we model weekly excess returns of ten-year Treasury notes and long-term Treasury bonds from 1968 through 1993 using an exponential generalized autoregressive conditional heteroskedasticity in mean (EGARCH-M) approach. The results indicate the presence of conditional heteroskedasticity and a strong tendency for the ex-ante volatility of excess returns to increase more following negative excess return innovations compared with positive innovations of equal magnitude. In addition, increases in ex-ante volatility are associated in some subperiods with rising excess returns on longer-term instruments, although the slope of the yield curve and lagged excess returns generally remain significant predictors of excess returns.