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BETA Calculation Method

In order to calculate BETA of a stock for a filter in my algorithm, I'm taking the covariance of the average of the last year of daily close-prices for my asset and SPY, then dividing by the variance of SPY. This is similar to the method found on StackOverflow:

covariance = numpy.cov(asset , SPY)[0][1]  
variance = numpy.var(asset)

beta = covariance / variance  

Does using the last year of daily close-prices as historical data work for finding covariance and variance? Or does this affect these values, and what alternative methods for calculating BETA exist?

2 responses

You can use anything you want! I think it is important to take a step back and realize what we mean when we talk about "beta." When we think of "beta" to the market we are really asking how sensitive is this security to market movement, or how much of this security's returns can be explained by the market. There is a fundamentally more basic understanding of "beta" is though. In short when we regress (linearly) some data against something else we model that regression as y = alpha + beta*x_1 + beta*x_2 + .... So "x" and "y" can be any sort of data, e.g. regress daily AAPL returns to the daily temperature in Cupertino, and find the "beta" of that relationship. So yes, using daily closing prices is totally acceptable. For a waaaaaaay better explanation see Delaney's lecture on Beta hedging from the lectures page.

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After using the described method, I received this error:

RuntimeWarning: Degrees of freedom <= 0 for slice  

Where does my issue occur? The related excerpt of the source code can be found below.

priceFrom1yearAgo = history(bar_count=365, frequency='1d', field='price')

if (np.cov(np.mean(priceFrom1yearAgo[stock]), np.mean(priceFrom1yearAgo[sid(8554)]))[0][1])/(np.mean(priceFrom1yearAgo[sid(8554)])) < 3:  

The purpose of the code is to average the prices of the asset and the index, SPY, from the last year and find the beta, which must be less than 3 for the stock to be selected. Where is the error occurring, and how do I solve it?