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.     

Estimating Systematic Risk Using Time Varying Distributions

This article proposes a dynamic vector GARCH model for the estimation of time-varying betas. The model allows the conditional variances and the conditional covariance between individual portfolio returns and market portfolio returns to respond asymmetrically to past innovations depending on their sign. Covariances tend to be higher during market declines. There is substantial time variation in betas but the evidence on beta asymmetry is mixed. Specifically, in 50% of the cases betas are higher during market declines and for the remaining 50% the opposite is true. A time series analysis of estimated time varying betas reveals that they follow stationary mean-reverting processes. The average degree of persistence is approximately four days. It is also found that the static market model overstates non-market or, unsystematic risk by more than 10%. On the basis of an array of diagnostics it is confirmed that the vector GARCH model provides a richer framework for the analysis of the dynamics of systematic risk.     

MACROECONOMIC VARIABLES AND SEASONAL MEAN REVERSION IN STOCK RETURNS

In this paper I investigate whether seasonal mean reversion in stock portfolio returns is related to common macroeconomic risk factors. I decompose excess returns into explained and unexplained returns using a multifactor pricing model. The explained excess returns exhibit January mean reversion; the unexplained excess returns do not. The mean reversion can be attributed to the components of return related to unexpected inflation, bond default premium, and market risk. The results do not depend on the time-series properties of the portfolio betas. Bond default premia and excess market returns are mean reverting in January.     

The estimation and determinants of emerging market country risk and the dynamic conditional correlation GARCH model

Country risk assessment is central to the international investment, which recently has increasingly focused on emerging markets (EM). In this paper we proxy for country risk in EM by using time-varying beta. We extend existing literature by applying a dynamic conditional correlation GARCH model. After confirming beta is time varying in twenty EM over the period January 1995 to December 2008 we investigate the GARCH (1,1) model and find the t-distribution generates the lowest forecast errors compared to the normal error distribution and a generalised error distribution. In a comparison of previous modelling techniques the results of our modified Diebold-Mariano test statistics suggest that the Kalman Filter model outperforms the GARCH model and the Schwert and Seguin (1990) model. Using a DCC-GARCH model our evidence suggests that considering dynamic betas can improve beta out-of-sample predicting ability and therefore offers potential gains for investors. Finally, we find dynamic betas across EM are strongly associated with each nation's interest rates, US interest rates and the Consumer Price Index (CPI) and to a lesser extent the exchange rates. Our results have some similarities to those in previous studies of developed markets in the economic determinants of time-varying beta but differences exist in the results on best model to forecast time-varying beta. These findings have implications for estimating country risk for investment and risk management purposes in EM.     

Learning about beta: Time-varying factor loadings, expected returns, and the conditional CAPM

We amend the conditional CAPM to allow for unobservable long-run changes in risk factor loadings. In this environment, investors rationally “learn” the long-run level of factor loadings from the observation of realized returns. As a consequence of this assumption, we model conditional betas using the Kalman filter. Because of its focus on low-frequency variation in betas, our approach circumvents recent criticisms of the conditional CAPM. When tested on portfolios sorted by size and book-to-market, our learning-augmented conditional CAPM passes the specification tests.     

The Estimation of Systematic Risk under Differentiated Risk Aversion: A Mean-Extended Gini Approach

This paper examines a mean-Gini model of systematic risk estimation that resolves some econometric problems with mean-variance beta estimation and allows for heterogeneous risk aversion across investors. Using the mean-extended Gini (MEG) model, we estimate systematic risks for different degrees of risk aversion. MEG betas are shown to be instrumental variable estimators that provide econometric solutions to biases generated by the estimation of mean-variance (MV) betas. When security returns are not normally distributed, MEG betas are proved to differ from MV betas. We design an econometric test that assesses whether these differences are significant. As an application using daily returns, we estimate MEG and MV betas for U.S. securities.     

Index tracking and beta arbitrage effects in comovement

This paper develops a stylised model for S&P 500 index changes with two beta-based styles: index trackers and beta arbitrageurs who trade in both high and low beta event stocks to exploit mean reversion towards one. Arbitrageurs engage in common or contrarian trading patterns relative to index funds depending on whether historical betas are below or above one. Thus, the overall comovement effect has two distinct components. After index additions, pre-event low beta stocks drive the overall beta increases due to common demand – albeit for different reasons - from indexers and arbitrageurs. By contrast, arbitrageur shorting of high beta additions diminishes or sometimes reverses the beta increases for these stocks driven by indexers. Analogous results hold for index deletions.     

AN EMPIRICAL INVESTIGATION OF BETA STABILITY: PORTFOLIOS VS. INDIVIDUAL SECURITIES

The concept that portfolio betas are more stable than betas for individual securities has become the 'conventional wisdom' in finance; statements to this effect may be found in many popular finance textbooks. The objective of this paper is to challenge the conventional wisdom. A random sample of individual stock returns and portfolio returns is used to compare the empirical distribution of beta shifts for individual firms and portfolios. The number of statistically significant changes in beta are no greater for individual securities than for portfolios.     

Die Ermittlung von Risikozuschlägen bei der Zeitwertbewertung von Verpflichtungen aus Schadenversicherungsgeschäften

The IASB proposes fair value accounting of insurance liabilities in the new IFRS on insurance contracts. These liabilities are not systematically traded in markets. Therefore the estimation of a fair value is only possible by simulating a market transaction. This simulation can be carried out by using financial models like the Capital Asset Pricing Model and the Economic Capital Model. In order to determine the fair value it has to be tested if those models can realistically calculate the insurance risk of the liabilities. This includes analysing the nature and extent of risk measurement as well as the assumptions the models are based on. The particular problem of the Capital Asset Pricing Model consists in measuring the risk by betas. An insurance beta can only be determined by relating it to other directly measurable betas. Those relationships can only be developed by putting forward special assumptions which increases the likelihood of a subjective valuation. The Economic Capital Model on the opposite is able to measure the insurance risk. The analysis of the models is carried out under simplified assumptions. Therefore it remains to be proven that the Economic Capital Model can also handle a more specific view of the insurance risk.     

A transactions data analysis of intraday betas

Using a sample of 27 stocks from the Dow Jones Industrial Average for the years 1986–1992, we examine the equality of beta for individual firms during the trading day. Both alphas and betas are found to differ through the trading day. Evidence suggests these changes are systematic for individual stocks. Using the midday beta as the base, the number of rejections of beta equality follow a U-shaped pattern through the trading day, indicating the differing distributions (U-shaped patterns) for intraday returns are reflected in similar changes in beta. These results have implications for further developing and testing market microstructure models.     

Regulator's Determination of Return on Equity in the Absence of Public Firms: The Case of Automobile Insurance in Ontario

In a regulated market, such as automobile insurance (AI), regulators set the return on equity that insurers are allowed to achieve. Most insurers are engaged in a variety of insurance lines of business, and thus the full information beta methodology (FIB) is commonly employed to estimate the AI beta. The FIB uses two steps: first, the beta of each insurer is estimated, and then the beta of each line of business is estimated, as the beta of an insurer is a weighted average of the betas of the lines of business. When there are a sufficient number of public companies, company and market returns are used. Otherwise, researchers have resorted to using accounting data in the FIB. Theoretically, the two steps are not separable and the estimation should be done with one step. We introduce the one‐step methodology in our article. The one‐step and two‐step methodologies are compared empirically for the Ontario market of AI. Insurers in Ontario are predominantly private companies; thus, accounting data are used to estimate the AI beta. We show that a significant bias is introduced by the traditional, two‐step FIB methodology in estimating the betas for different lines of business, while insurers’ betas are very similar under both methods. This has a significant application to the estimation of betas of “pure players” in classic corporate finance. It implies that their betas and hence the resulting, required rates of return used in the net present value calculations should be estimated based on the one‐step method that we develop in this article.     

Galton's Error and the under-representation of systematic risk

Science progresses by improving its measurement apparatus. This holds true in finance too. The new methodology of “complete identification”, using simple algebraic geometry, throws new light on Galton's Error in finance and economics and the resulting misinformation of investors. Mutual funds conventionally advertise their relative systematic market risk, or “betas”, to potential investors based on incomplete measurement by unidirectional bivariate projections: they commit Galton's Error by under-representing their systematic risk. Consequently, far too many mutual funds are marketed as “defensive” and too few as “aggressive”. Using the new methodology it is found that, out of a total of 3217 mutual funds, 2047 funds (63.7%) claimed to be defensive based on the current industry standard methodology, but only 608 (18.9%) actually are. This under-representation of systematic risk leads to inefficiencies in the capital allocation process, since biased betas lead to mispricing of mutual funds. Complete bivariate projections produce a correct representation of the epistemic uncertainty inherent in the bivariate measurement of relative market risk and provide a new CAPM taxonomy. Our conclusions have also serious consequences for the proper “bench-marking” and recent regulatory proposals for the mutual funds industry. Extension of the new methodology to multivariate systematic risk measurement by Asset Pricing Theory (APT) is suggested.     

Bias in estimating the systematic risk of extreme performers: Implications for financial analysis, the leverage effect, and long-run reversals

We show how bias can arise systematically in the beta estimates of extreme performers when long-run return reversals are present and partly, or wholly, due to sign changes in unanticipated factor realizations. Our evidence is consistent with this bias being responsible for the large shifts in the beta estimates of extreme performers, more so than the leverage effect, which has been the predominant explanation in prior literature. Bias in these contemporaneous realized betas, estimated with the same returns that are to be risk adjusted, arises due to the general problem of “overconditioning,” where betas are estimated conditional on information that is not yet known. Several methods for conditioning betas on out-of-sample returns are evaluated and found to be lacking, although some offer improvement under certain circumstances. We also show evidence of this bias in the Fama-French Three-factor loadings of extreme performers. Our findings indicate not only that previous studies of long-run reversals understate contrarian profits but that bias is prevalent in the OLS beta estimates of extreme performers, and this has implications for estimating the cost of capital and measuring long-run performance. We offer recommendations for identifying when this bias is likely present, as well as general methods to correct for it.     

The Regression Tendencies of Betas: A Reappraisal

This paper reexamines the regression tendencies of beta. We show that common assertions in the literature about regression tendencies go well beyond the facts established by Blume. We analyze betas during the 1926–1985 period and examine the tendencies of betas to change. Extreme betas do tend to move toward the mean. However, betas near the mean in one period tend to move away from the mean. As a result, the distribution of betas is approximately stationary over time.     

Derivative Exposure and the Interest Rate and Exchange Rate Risks of U.S. Banks

This article estimates the interest rate and exchange rate risk betas of 59 large U.S. commercial banks for the period of 1975–1992, as well as the bank-specific determinants of these betas. The estimation procedure uses a modified seemingly unrelated simultaneous method that recognizes cross-equation dependencies and adjusts for serial correlation and heteroskedasticity. Overall, the exchange rate risk betas are more significant than the interest rate risk betas. More importantly, we find a link between the scale of a bank's interest rate and currency derivative contracts and the bank's interest rate and exchange rate risks. Particularly noteworthy is the influence of currency derivatives on exchange rate betas.     

Understanding industry betas

This paper models and explains the dynamics of market betas for 30 US industry portfolios between 1970 and 2009. We use DCC–MIDAS and kernel regression techniques as alternatives to the standard ex-post measures. We find betas to exhibit substantial persistence, time variation, ranking variability, and heterogeneity in their business cycle exposure. While we find only a limited amount of structural breaks in the betas of individual industries, we do identify a common structural break in March 1998. We propose two practical applications to understand the economic significance of these results. We find the cross-sectional dispersion in industry betas to be countercyclical and negatively related to future market returns. We also find DCC–MIDAS betas to outperform other beta measures in terms of limiting the downside risk and ex-post market exposure of a market-neutral minimum-variance strategy.     

A model-independent measure of aggregate idiosyncratic risk

This paper introduces a model-independent measure of aggregate idiosyncratic risk, which does not require estimation of market betas or correlations and is based on the concept of gain from portfolio diversification. The statistical results and graphical analyses provide strong evidence that there are significant level and trend differences between the average idiosyncratic volatility measures of Campbell et al. [Campbell, J.Y., Lettau, M., Malkiel, B.G., and Xu, Y., 2001, Have individual stocks become more volatile? An empirical exploration of idiosyncratic risk, Journal of Finance 56, 1–43.] and the new methodology. Although both approaches indicate a noticeable increase in the firm-level idiosyncratic risk, the volatility measure of CLMX is greater and has a stronger upward trend than the new idiosyncratic volatility measure. For both measures of idiosyncratic risk, the upward trend is found to be stronger for smaller, lower-priced, and younger firms. The analytical and empirical results show that the significant upward trend in the differences of the two idiosyncratic volatility measures is related to the increase in the cross-sectional dispersion of the volatility of individual stocks.     

The Role of Stock Size and Trading Intensity in the Magnitude of the "Interval Effect" in Beta Estimation: Empirical Evidence from the Polish Capital Market

In this paper, we present empirical evidence about the "interval effect" in estimation of beta parameters for stocks listed on the Warsaw Stock Exchange. We analyze models constructed for the returns calculated using intervals of different length—that is, 1, 5, 10, and 21 trading days (corresponding to, roughly, 1 day, 1 week, 2 weeks, and 1 month, respectively). In the cases in which heteroskedasticity was present, we estimated ARCH models. The results indicate that the estimates of betas for the same stock differ considerably when various return intervals are used. We further explore the source of differences in betas for every stock by investigating the relations between them and such factors as stock size and its trading intensity. The empirical results provide evidence that a statistically significant relationship exists between these two characteristics of stocks. This finding has important practical implications for beta estimation in practice.     

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.     

Systematic risk and the theory of the firm: A reexamination

A recent microeconomic model of the determinants of equity betas (Subrahmanyam and Thomadakis 1980) is generalized by including risky human capital in the market portfolio and allowing a general covariance structure between the model's sources of uncertainty. This provides an explanation of the ambiguous effect of operating leverage on beta by viewing human capital and equity contributors as risk sharers in the firm's output risk. This explanation may help to clarify the apparent conflict with the previous literature. The relationship between systematic risk and monopoly power is rederived and shown to depend upon a plausible condition on the correlation between wage rate and price uncertainty. Finally, the public policy implications of this analysis are presented.