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Beta Definitions by Database


Bloomberg defaults to a 2 year historical weekly price and then calculates the beta based on this.

The adjusted beta calculation is: (0.67 * Raw Beta) + (0.33 * 1.0)

Center for Research in Security Prices (CRSP)

"Beta is a statistical measurement of the relationship between two time series, and has been used to compare security data with benchmark data to measure risk in financial data analysis. CRSP provides annual betas computed using the methods developed by Scholes and Williams (Myron Scholes and Joseph Williams, “Estimating Betas from Nonsynchronous Data,” Journal of Financial Economics, vol 5, 1977, 309-327).

Beta is calculated each year as follows:

reti,t = log of ( 1 + return for security i on day t)
mret t = log of (1 + value-weighted market return on day t)
mret3t = mret t-1 + mret t + mret t+1 (a 3 day moving average market window)
n = number of observations for the year where summations over t are over all days on which security i traded, beginning with the first trading day of the year and ending with the last trading day of the year.

Image source: Chicago Booth Center for Research in Security Prices. (2012). CRSP Data Descriptions Guide - CRSP US Stock and US Index Databases

There are two portfolio types based on ScholesWilliams Beta calculations: NYSE/NYSE MKT and NASDAQ-only. In the NYSE/NYSE MKT portfolios, only trading prices are considered in the beta calculation, and a security must have traded half the days in a year to be given a non-missing beta for that year. The index used in the calculation is the total returns on the Trade-only NYSE/NYSE MKT Value-Weighted Market Index.

Thomson ONE

The beta coefficient indicates how a stock's daily changes compare to the daily changes of the S&P500. [It] is computed from data over the past 7 years, more than 1300 observations of daily stock changes are used. The abbreviation N/A is displayed for stocks trading for less than a year, and for betas less than 0.4 and greater than 2.5.

Toronto Stock Exchange Database - CFMRC

Beta- the rolling average beta from the CAPM.

Given Rf(t) and Rm(t) the T-bill return and return on the TSX 300 Total Return Index (see above) and the security return, R(t), beta is calculated as:

log[R(t) - Rf(t)] = a + Beta*log[Rm(t) - Rf(t)]

When there is no valid return due to missing prices, the mean of the bid and ask is used as a proxy (-1 times the monthly closing price, if valid). A minimum of 24 months of returns over the past 60 months are required before a beta is calculated.

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