On estimating beta – The non-diversifiable, systematic risk

One of the trickiest components when calculating a cost of capital is the beta, reflecting the volatility of the valued company with the overall market.  In theory beta is simple: when the market moves up/down by one, what happens to the company’s stock? Does it move more than the market, (indicating a beta over 1) or less (indicating a beta under 1)? Could it even move against the market (indicating a negative beta)?

Usually, the beta is calculated by regressing the stock return of the company against market returns, typically a local market index. In practice, the results of time-series regressions are sensitive to many factors and many questions should be addressed in the estimation of the beta factor. In this blog, I will reflect on two of them: the estimation interval and period.

In Valuation Corner Finland, the beta factor is derived using the weekly returns over a three-year time period (giving 157 data points) calculated from the last price of the day. 

Regarding the frequency of the estimation period, the benefit with weekly data is the somewhat higher number of observations, having 157 data points compared to for instance 60 when computing with monthly data over a five-year-period. Daily data is often criticized for being affected by potential noise in the data. 

An interesting point of view related to the weekly data frequency is the “day of the week” anomaly. Researchers have found that there tend to be a bias towards positive market performance on Friday compared to Monday. This anomaly also shows up when estimating betas. We had a recent client project, in which we saw a clear pattern of higher betas on Fridays compared to Mondays for the chosen peer groups. In this specific case, these two “extreme days” were finally concluded to better be avoided in the estimation of the beta factor. To my knowledge, there has been very little, if any, empirical research on the “day of the week effect” for beta. In Valuation Corner Finland, we have chosen to use weekly returns and to solve the potential day of the week anomaly by retrieving the data always on the last Tuesday of the month.

Regarding the estimation period, one can find suggestions of everything between one to nine years. On one hand, a longer time period will bring more data points into the regression leading to results that are more reliable from a statistical point of view. On the other hand, the longer time period increases the risks of bias due to a potential changes in the beta over the longer time period. Structural changes in the company or its capital structure would speak for a use of a shorter time period. One study on this issue found that “an estimation period of three years captures most of the maximum reduction in the standard error of the estimated beta from a one-year estimation period to an eight-year estimation period.” (Daves et al. 2000.)

^{Source: Daves, p. Ehrhardt, M., Kunkel R. (2000). Estimating systematic risk: The Choice of Return Interval and Estimation Period. Journal of Financial and Strategic Decisions, Vol. 13, No. 1, p. 7-13.}