Mean reversion and the forecasting of country betas: a note

In 1971 and 1975, M. E. Blume found individual equity betas to have a “regression” tendency toward the grand mean of unity. His original results have been widely accepted to the extent that a literature has developed on the application of Bayesian techniques to beta estimation so as to adjust for mean reversion. The more recent literature has focused on risk estimation and the applicability of asset pricing models in the international finance setting, where the focus has been on the aggregate country level risk. Given the increasing popularity of country beta models, an interesting but, as yet, unexplored issue is whether aggregate country betas display mean reversion tendencies similar to that found for individual company betas. The examination of this issue is the central aim of the current paper. In short, this analysis reveals strong evidence of mean reversion of country betas, similar to that documented in the single country setting in the existing literature.     

Markov Chains and Regression toward the Mean

Using the theory of stationary Markov chains, we uncover a previously unknown property of the behavior of betas. Specifically, if the cross-sectional distribution of betas is stationary over time, then the set of firms that remain in an arbitrarily chosen beta interval between one period and the next will not regress toward the mean. This surprising result occurs in spite of the well-known fact that the set of all the firms in the interval will exhibit the regression tendency. Our empirical tests indicate that betas behave in remarkable accordance with this prediction.     

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.     

Is value riskier than growth?

We study the relative risk of value and growth stocks. We find that time-varying risk goes in the right direction in explaining the value premium. Value betas tend to covary positively, and growth betas tend to covary negatively with the expected market risk premium. Our inference differs from that of previous studies because we sort betas on the expected market risk premium, instead of on the realized market excess return. However, we also find that this beta-premium covariance is too small to explain the observed magnitude of the value premium within the conditional capital asset pricing model.     

The term structure of euromarket interest rates: An empirical investigation

This paper is an empirical investigation of the predictability and co-movement of risk premia in the term structure of Euromarket interest rates. We present regression results which suggest that risk premia in three Euromarket term structures and on uncovered foreign asset positions move together. We test formally the hypothesis that these risk premia move in proportion to a single latent variable. We are unable to reject this hypothesis. The single latent variable model can be interpreted as in Hansen and Hodrick (1983) and Hodrick and Srivastava (1984) as a specialization of the ICAPM in which assets have constant betas on a single, unobservable benchmark portfolio.     

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.     

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.     

Can unpredictable risk exposure be priced?

We study the link between beta predictability and the price of risk. An investor who desires exposure to a certain risk factor needs to predict what next period’s beta will be. We use a simple model to show that an ambiguity averse agent’s demand is lower when betas are hard to predict, leading to a reduction in risk premiums. We test the implications for downside betas and VIX betas. We find that they have economically and statistically small prices of risk once we account for the fact that an investor cannot observe ex-post realized betas when determining asset demand.     

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.     

The practice of investment valuation in emerging markets: Evidence from Argentina

This paper discusses the challenges of applying traditional valuation techniques to emerging markets, and reports on how CFOs, financial advisors and private equity funds meet those challenges in Argentina, a major Latin American emerging economy. On many fronts, our findings show that there is substantial alignment with U.S. valuation practices. We find that: (a) discounted cashflow techniques like NPV, IRR and payback are very popular among corporations and financial advisors; (b) the CAPM is the most popular asset pricing model, yet it is frequently modified to account for country-specific risk; (c) capital budgeting analyses are performed in U.S. dollars by non-dollar companies; (d) financial advisors tend to apply U.S. betas to the emerging market, yet they rarely adjust betas for cross-border asymmetries; and (e) corporations tend to disregard the effects of small size and illiquidity. We provide tentative explanations for our findings.     

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.     

Semiparametric estimation of a characteristic-based factor model of common stock returns

We introduce an alternative version of the Fama–French three-factor model of stock returns together with a new estimation methodology. We assume that the factor betas in the model are smooth nonlinear functions of observed security characteristics. We develop an estimation procedure that combines nonparametric kernel methods for constructing mimicking portfolios with parametric nonlinear regression to estimate factor returns and factor betas simultaneously. The methodology is applied to US common stocks and the empirical findings compared to those of Fama and French.     

Estimation of conditional asset pricing models with integrated variables in the beta specification

We introduce a methodology which deals with possibly integrated variables in the specification of the betas of conditional asset pricing models. In such a case, any model which is directly derived by a polynomial approximation of the functional form of the conditional beta will inherit a nonstationary right hand side. Our approach uses the cointegrating relationships between the integrated variables in order to maintain the stationarity of the right hand side of the estimated model, thus, avoiding the issues that arise in the case of an unbalanced regression. We present an example where our methodology is applied to the returns of funds-of-funds which are based on the Morningstar mutual fund ranking system. The results provide evidence that the residuals of possible cointegrating relationships between integrated variables in the specification of the conditional betas may reveal significant information concerning the dynamics of the betas.     

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.     

The performance of cross-sectional regression tests of the CAPM with non-zero pricing errors

We show that in the presence of non-zero pricing errors, the Fama–MacBeth (FM) cross-sectional regression test is very likely to either reject the Capital Asset Pricing Model (CAPM) when it (almost) holds or accept the model when it grossly fails. We investigate the case when pricing errors are correlated with betas and demonstrate that the test performance depends crucially on the correlation, cross-sectional distribution of betas, and several other parameter values. Even when the CAPM holds exactly (pricing errors are zero) the FM test is equally likely to either reject or accept the model when typical sample sizes are used.     

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.     

Explaining the default risk anomaly by the two-beta model

This study attempts to explain the anomaly that firms with high-default risk earn low average realized returns. We measure default risk according to Ohlson's (1980) O-score and Campbell, Hilscher, and Szilagyi's (2008) failure probability and further implement Duffie, Saita, and Wang's (2007) doubly-stochastic intensity model to estimate default probabilities that incorporate the dynamics of the changes in covariates. We then employ Campbell and Vuolteenaho's (2004) two-beta model to estimate firms' cash-flow and discount-rate betas according to the default risk. The default risk anomaly persists when using Duffie el al.'s (2007) method. We show that cash-flow and discount-rate betas, respectively, earn a high and low premium and find that high-default firms tend to have relatively high discount-rate and low cash-flow betas. Hence, high-default firms deliver low expected returns. Importantly, 25.5% of the default risk anomaly can be explained by the two-beta model and that, on average, also accounts for 49.2% of the cross-sectional variation across the portfolios formed on default risk. This result implies that investors believe that high-default firms are unlikely to generate significantly extra cash flows when market-wide profitable opportunities improve.     

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.     

The behaviour of the real exchange rate: Evidence from regression quantiles

We test for mean reversion in real exchange rates using a recently developed unit root test for non-normal processes based on quantile autoregression inference in semi-parametric and non-parametric settings. The quantile regression approach allows us to directly capture the impact of different magnitudes of shocks that hit the real exchange rate, conditional on its past history, and can detect asymmetric, dynamic adjustment of the real exchange rate towards its long run equilibrium. It, therefore provides a detailed mapping of the real exchange rate behaviour, while being a robust alternative to previous unit root tests. The latter is confirmed by a simulation analysis comparing the power of the alternative tests. As concerns the real exchange rate, our results suggest that large shocks tend to induce strong mean reverting tendencies in the exchange rate, with half lives less than one year in the extreme quantiles. Mean reversion is faster when large shocks originate at points of large real exchange rate deviations from the long run equilibrium. However, in the absence of shocks no mean reversion is observed. Finally, we report asymmetries in the dynamic adjustment of the RER.