Bayesian Betas and Deception: A Comment

Barry, Christopher B.

doi:10.1111/j.1475-6803.1980.tb00039.x

Cited by 4 publications

(4 citation statements)

References 11 publications

(9 reference statements)

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“…The first one was the parametric Bayes (Bayes) because it is the most used estimator among Bayesian practitioners. Also, this Bayes estimator yielded a similar performance as the most popular estimator, the OLS, in the CAPM if the sample size is large (Barry, 1980;Phuoc, 2018;Zellner, 1971). The second estimator was the non-parametric, Student's t, Bayes (R.Bayes) with three degrees of freedom because the t-distribution is flatter and handles outliers better than the normal distribution or when the variance of stock returns is unknown.…”

Section: The Approach and Estimatorsmentioning

confidence: 65%

“…In corporate practice, this beta is very often estimated using the ordinary least square (OLS) and parametric Bayes (Bayes) estimators because the OLS estimator is the best linear unbiased estimator (BLUE) and the availability of software packages having the OLS estimator algorithm, for example, the Microsoft Excel. Also, the OLS and Bayes estimators yielded similar performance if the sample size of the data is large (Barry, 1980;Phuoc, 2018;Zellner, 1971). In addition, the monthly/quarterly/annual returns data are preferred in the CAPM because of their normality property and availability of data (Ang and Bekaert, 2007;Fama and French, 1992, 1993, 1996a, 1996b, 2004, 2016, 2018Kamara et al, 2016Kamara et al, , 2018Phuoc, 2018;Phuoc et al, 2018;Zhang, 2006).…”

Section: Introductionmentioning

confidence: 95%

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The systematic risk estimation models: A different perspective

Phuoc

Pham

2020

Heliyon

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In practice, the capital asset pricing model (CAPM) using the parametric estimator is almost certainly being used to estimate a firm's systematic risk (beta) and cost of equity as in Eq. (1). However, the parametric estimators, even when data is normal, may not yield better performance compared with the non-parametric estimators when outliers existed. This research argued for the non-parametric Bayes estimator to be employed in the CAPM by applying both advance and basic evaluation criteria such as hypotheses/confidence intervals of the AIC/DIC, model variance, fit, and error, alpha, and beta and its standard deviation. Using all the S&P 500 stocks having monthly data from 07/2007-05/2019 (450 stocks) and the Bayesian inference, we showed the non-parametric Bayes estimator yielded less number of zeroed betas and smaller alpha compared with the parametric Bayes estimator. More importantly, this non-parametric Bayes yielded the statistically significantly smaller AIC/DIC, model variance, and beta standard deviation and higher model fit compared with the parametric Bayes estimator. These findings indicate the CAPM using the non-parametric Bayes estimator is superior compared with the parametric Bayes estimator, a contrast of common practice. Hence, the non-parametric estimator is recommended to be employed in asset pricing work.

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Section: The Approach and Estimatorsmentioning

confidence: 65%

Section: Introductionmentioning

confidence: 95%

The systematic risk estimation models: A different perspective

Phuoc

Pham

2020

Heliyon

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“…The first one was the parametric Bayes (Bayes) using the normal likelihood,

because it is the most used estimator among Bayesian practitioners. Also, this Bayes and the ordinary least square (OLS) estimators performed similarly ( Barry, 1980 ; Phuoc, 2018 ; Zellner, 1971 ). The weakly informative normal priors,

of both Alpha and Beta of this Bayes estimator were chosen to match with the frequentist approach and our past knowledge.…”

Section: Data Approach and Estimator And Evaluation Criteriamentioning

confidence: 77%

Is estimating the Capital Asset Pricing Model using monthly and short-horizon data a good choice?

Pham

Phuoc

2020

Heliyon

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This research argued for estimating the Capital Asset Pricing Model (CAPM) using daily and medium-horizon data over monthly and short horizon-data. Using a Gibbs sample, the Bayesian framework via both parametric and non-parametric Bayes estimators, confidence interval approach, and six data sets (two daily, two weekly, and two monthly data) from a sample of 150 randomly selected S&P 500 stocks from 2007 – 2019, the empirical results showed that the CAPM using daily data yielded a statistically significant higher model fit and smaller Beta standard deviation, model error, and Alpha compared with monthly data. The CAPM using medium-horizon data yielded a statistically significant higher model fit, smaller Beta standard deviation and Alpha, and much less zeroed Betas compared with short-horizon data. These findings show 1) daily data is more reliable and efficient, has higher forecasting power, and fits better with the assumption of market efficiency compared with monthly data. 2) Medium-horizon data is more reliable and efficient, has more explanatory power, and fits better with the assumption of market efficiency compared with monthly data. Therefore, these findings challenge the common practices of using monthly (quarterly/annually) and short-horizon data among the practitioners and researchers in asset pricing work.

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“…Yet this may not be the correct assumption in our longer-term application. This is pointed out by Johnson, Bennett, and Curcio (1979) and by Barry ((1980), p. 88), who states, "[W]hen beta is suspected to vary over time, a technique that explicitly recognizes the variation (be it systematic or random) should be used. No technique that assumes stationarity should be expected to perform well under nonstationarity.…”

Section: Beta Calculationsmentioning

confidence: 99%

Best Practice for Cost-of-Capital Estimates

Levi¹,

Welch²

2017

J. Financ. Quant. Anal.

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Cost-of-capital assessments with factor models require quantitative forward-looking estimates. We recommend estimating Vasicek-shrunk betas with 1-4 years of daily stock returns and then shrinking betas a second time (and more for smaller stocks and longer-term projects), because the underlying betas are themselves time-varying. Such estimators also work well in other developed countries and for small-minus-big (SMB) and high-minuslow (HML) exposures. If own historical stock returns are not available, peer betas based on market cap should be used. Historical industry averages have almost no predictive power and should never be used.

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Bayesian Betas and Deception: A Comment

Cited by 4 publications

References 11 publications

The systematic risk estimation models: A different perspective

The systematic risk estimation models: A different perspective

Is estimating the Capital Asset Pricing Model using monthly and short-horizon data a good choice?

Best Practice for Cost-of-Capital Estimates

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