The going public decision and the structure of equity markets

The industries in which listed firms are concentrated in less developed equity markets are not random, nor entirely explained by the underlying composition of production. Listed firms and market capitalization are disproportionately concentrated in industries with low beta (measured with their beta with the market portfolio in the U.S.). We document a strong positive relationship between the industry-weighted country beta and the degree of market development across countries. Recent IPO activity confirms the result since new listings have higher betas than the average firm already in the market.     

RETURN INTERVAL,FIRM SIZE AND SYSTEMATIC RISK ON THE DUTCH STOCK MARKET

In this paper we investigate the behavior of betas of 50 Dutch firms as a function of the return measurement interval. We find beta estimates measured from different intervals differ significantly from each other. As the sample mainly contains stocks that are relatively thin compared to the index, beta estimates from short intervals are on average lower than those obtained from longer intervals. The results further indicate that there exists some variability in the beta coefficients for each interval length. Betas depend on the manner daily prices are juxtaposed to calculate the returns. A way to account for this variability is to average the different betas for each interval length. Asymptotic betas are also computed to show the appropriateness of this method. Finally we show that the size effect is reduced when the interval length is increased, although it remains statistically significant.     

Unconditional Tests of Linear Asset Pricing Models with Time‐Varying Betas

In conditional affine factor models, estimated risk prices should satisfy certain unconditional constraints. Specifically, a cross‐sectional estimate of the unconditional slope associated with a risk factor should equal the average price of risk of the factor. The estimated slope associated with the product of a risk factor and an instrument should be equal to the covariance of the factor risk premium with the instrument. We show that the constraints only apply to the conditional models with time‐varying betas. We identify an unconditional constraint on unconditional betas for time‐varying beta models and incorporate it into model tests. We show that imposing this unconditional constraint changes estimates of unconditional betas and risk prices significantly.     

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.     

Forecasting Beta: How Well Does the 'Five-Year Rule of Thumb' Do?

CAPM betas are generally estimated from historical data and applied to a future period. There is widespread evidence that the CAPM betas vary considerably over time and this raises two questions: can this variation be explained and can it be forecast better than the 'five-year rule of thumb' (i.e using the most recently estimated beta)? We estimate time-varying betas and explain the time-variation in the betas using regression models which we subsequently use for forecasting. We find that forecasting equations have good explanatory power but that their forecasts are dominated, on average, by the five-year rule of thumb.     

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.     

An Adjustment Procedure for Predicting Betas When Thin Trading is Present: Canadian Evidence

We have incorporated effects of the process that generates true betas for TSE stocks, as well as thin trading effects, into the beta adjustment model. We note the Blume and Dimson and Marsh beta adjustment techniques aim at eliminating beta forecast error through regression tendency bias. Effects of other sources of forecast error have been ignored. We show the process generating security betas affects both cross-sectional correlation coefficient and order bias, while thin trading affects only cross-sectional correlation coefficient. We demonstrate that when OLS beta estimates are used to forecast their future risk levels, order bias accounts for 86% of forecast error, while thin trading effects account for 14% of forecast error. A beta regression tendency model which properly accounts for effects of cross-sectional correlation (which is a function of thin trading) and order bias completely abates forecast error. Our results have implications for the use of correlation coefficient to measure stability of betas across time, for beta adjustment models proposed in the literature, and for event study methodologies that rely on prediction errors.     

The size effect in the Mexican stock market

This paper tests for a firm size effect in the Mexican stock market using data from January 1987 to December 1992. Our initial tests indicate that average stock returns are positively related to market betas. We also find, however, that average returns are negatively related to firm size. To measure the effects on average return of betas that are unrelated to firm size, we examine portfolios formed on the basis of size and beta We find that beta is priced in addition to firm size for the Mexican stock market, even after carefully separating the effects of beta and size.     

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.     

Conditional risk and performance evaluation: Volatility timing, overconditioning, and new estimates of momentum alphas

Unconditional alphas are biased when conditional beta covaries with the market risk premium (market timing) or volatility (volatility timing). We demonstrate an additional bias (overconditioning) that can occur any time an empiricist estimates risk using information, such as a realized beta, that is not available to investors ex ante. Calibrating to U.S. equity returns, volatility timing and overconditioning can plausibly impact alphas more than market timing, which has been the focus of prior literature. To correct market- and volatility-timing biases without overconditioning, we show that incorporating realized betas into instrumental variables estimators is effective. Empirically, instrumentation reduces momentum alphas by 20-40%. Overconditioned alphas overstate performance by up to 2.5 times. We explain the sources of both the volatility-timing and overconditioning biases in momentum portfolios.     

CAPM over the long run: 1926–2001

A conditional one-factor model can account for the spread in the average returns of portfolios sorted by book-to-market ratios over the long run from 1926 to 2001. In contrast, earlier studies document strong evidence of a book-to-market effect using OLS regressions over post-1963 data. However, the betas of portfolios sorted by book-to-market ratios vary over time and in the presence of time-varying factor loadings, OLS inference produces inconsistent estimates of conditional alphas and betas. We show that under a conditional CAPM with time-varying betas, predictable market risk premia, and stochastic systematic volatility, there is little evidence that the conditional alpha for a book-to-market trading strategy is different from zero.     

Liquidity risk,leverage and long-run IPO returns

We examine the risk-return characteristics of a rolling portfolio investment strategy where more than 6000 Nasdaq initial public offering (IPO) stocks are bought and held for up to 5 years. The average long-run portfolio return is low, but IPO stocks appear as “longshots”, as 5-year buy-and-hold returns of 1000% or more are somewhat more frequent than for non-issuing Nasdaq firms matched on size and book-to-market ratio. The typical IPO firm is of average Nasdaq market capitalization but has relatively low book-to-market ratio. We also show that IPO firms exhibit relatively high stock turnover and low leverage, which may lower systematic risk exposures. To examine this possibility, we launch an easily constructed “low-minus-high” (LMH) stock turnover portfolio as a liquidity risk factor. The LMH factor produces significant betas for broad-based stock portfolios, as well as for our IPO portfolio and a comparison portfolio of seasoned equity offerings. The factor-model estimation also includes standard characteristic-based risk factors, and we explore mimicking portfolios for leverage-related macroeconomic risks. Because they track macroeconomic aggregates, these mimicking portfolios are relatively immune to market sentiment effects. Overall, we cannot reject the hypothesis that the realized return on the IPO portfolio is commensurable with the portfolio's risk exposures, as defined here.     

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.     

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.     

OLIVE: A SIMPLE METHOD FOR ESTIMATING BETAS WHEN FACTORS ARE MEASURED WITH ERROR

We propose a simple and intuitive method for estimating betas when factors are measured with error: ordinary least squares instrumental variable estimator (OLIVE). OLIVE performs well when the number of instruments becomes large, whereas the performance of conventional instrumental variable methods becomes poor or even infeasible. In an empirical application, OLIVE beta estimates improve R² significantly. More important, our results help resolve two puzzling findings in the prior literature: first, the sign of average risk premium on the beta for market return changes from negative to positive; second, the estimated value of average zero‐beta rate is no longer too high.     

On the County-Level Credit Outcome Beta

In their pioneering work, Musto and Souleles (Journal of Monetary Economics 53(1):59–84, 2006) apply portfolio theory to consumer lending. This paper extends their work by analyzing three county-level credit outcome betas. We use the probability of default calibrated from the credit score, the actual default rate, and the actual bankruptcy rate to compute ‘score’, ‘default’, and ‘bankruptcy’ betas for each U.S. county. The correlation between default and bankruptcy betas is quite low. Counties in states in which a borrower has a right to take action against aggressive collection practices tend to have higher default betas but lower bankruptcy betas. These findings suggest the possibility of an ‘informal bankruptcy’ option for consumers. The effects of county score, default, and bankruptcy betas on the county average revolving credit line per borrower are negative. For small lenders that do not have access to the detailed historical credit files on individual consumers, the county-level beta approach of this paper might be helpful for diversifying portfolios geographically and managing risk on existing accounts.     

Risk characteristics of closed-end stock fund IPOs

We examine 34 closed-end stock fund initial public offerings (IPOs) during the period of January 1, 1986, through June 30, 1987. We find that the funds have low systematic risk during their first trading months, especially the initial month. We also observe that the funds' beta risk tends to increase as the funds season in aftermarket trading. This pattern is in sharp contrast to new issues by nonfinancial corporations, which have very high initial betas that decline over time.     

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.     

Accounting for the Accuracy of Beta Estimates in CAPM Tests on Assets with Time-varying Risks

This paper advocates two ways to make more efficient use of available information in reducing the bias of the risk premium estimate in two-pass tests of the CAPM. First, explicit modelling of the time-variability of betas can improve the accuracy of the beta forecasts. Second, the cross-sectional information available can be exploited more efficiently using individual stocks instead of portfolios provided that noisy beta predictions are given a smaller weight than more accurate ones. This paper proposes an adjustment of the cross-sectional regressions of excess returns against betas to give larger weights to more reliable beta forecasts. A significant positive relationship between returns and the beta forecast is obtained when the proposed approach is applied to data from the Helsinki Stock Exchange, while the traditional Fama–MacBeth approach as such finds no relationship at all.     

U.S. Banking Sector Risk in an Era of Regulatory Change: A Bivariate GARCH Approach

This paper assesses the impact of regulatory change on the risk and returns of the U.S. banking industry. The impact of five major regulatory changes on banking sector risk was assessed using daily data for eighteen major U.S. regional banks, money center banks and savings and loan type depository institutions. Risk in this case was proxied via the use of an M-GARCH model which generates time dependent conditional beta estimates. The evidence obtained suggests that the impact of deregulation and reregulation on banking sector risk is case specific. Further, the results obtained show that the market model incorporating dummy variables, which has proven so popular amongst existing studies, discards important information about the variability of beta which the time varying conditional betas capture.