The beta reported for a stock [finance]

Three presumably easy questions about stocks’ betas, possibly answerable with a single citation:

  • When a page like MSFT reports beta (1.01 for MSFT as of this post), over what time period are the (co)variances taken? (The past year? Five years?) I’m guessing is just reporting numbers from someone else.

  • Relatedly: What size time window is used for the data (e.g., daily returns? monthly returns?)

  • Why don’t short ETFs have negative betas? For example, I would have expected SDS to have beta=-2.00, but it shows up as having beta=1.00.

There is no one right answer on how to do this, and different services do it differently. Five years of monthly data is somewhat of a standard – or at least used to be before teh wide availablility of daily data. I suspect most are now calcualted with daily data though.

I’ll also point out that there are other ways to do this with daily data. One common correction is the Scholes-Williams adjustment. I’d give you a link but most are through JStor which many won’t have access to and most othes are pdfs, but a google search will show up some I’m sure.

The Scholes (same guy as in Black-Scholes options) Williams adjustment accounts for nonsimultaneous trading and is fairly important for thinly traded assets. It’s a bit more complicated than the expanation I’ll give, but this is the basic idea.

Suppose a stock trades just a couple of times a day on average. The time line below shows an example. x’s mark trades and | marks end of day


Note that the reported return from the first day close to the second close includes all of the second day (since a trade occured just at close) but also part of teh first day (the part after the last trade). Similarly the reported return from the second day to the third day includes only part of the third day.

The Scholes Williams correction in simplest form regresses

R_t = a + b_1M_t-1 + b_2M_t + b_3*M_t+1 and reports as beta the sum of the three b’s. This will be correct if the market return has no serial correlation. But there are adjustments for that as well.

That certainly seems wrong. I suspect the “1.00” is a default value and for some reason they were unable to calculate a meaningful beta for this fund.

Here’s Value Line’s definition, and a brief summary of how they find the number.