First, let us recall a standard result from linear algebra: "real symmetric matrices are diagonalizable by orthogonal matrices". Thus, any variance-covariance matrix can be written since a variance-covariance matrix is also definite positive. In ... [Read more...]

Some pictures to explore the reality of the theory that stocks with higher beta should have higher expected returns. Figure 2 of “The effect of beta equal 1″ shows the return-beta relationship as downward sloping.  That’s a sample of size 1.  In this post we add six more datapoints. Data The exact ... [Read more...]

Data The data are daily returns starting at the beginning of 2007.  There are 477 stocks for which there is full and seemingly reliable data. Estimation The betas are all estimated on one year of data. The times that identify the betas mark the point at which the estimate would become available.  ... [Read more...]

What does beta look like in the out-of-sample period for the portfolios generated to have beta equal to 1? In the comments Ian Priest wonders if the results in “The effect of beta equal 1″ are due to a shift in beta from the estimation period to the out-of-sample period.  (The current ... [Read more...]

Investment Performance Guy had a post about beta equal 1.  It made me wonder about the properties of portfolios with beta equal 1.  When I looked, I got a bigger answer than I expected. Data I have some S&P 500 data lying about from the post ‘On “Stock correlation has been rising”‘.  ... [Read more...]

Much of what has been said and thought about beta in finance is untrue. Myth 1: beta is about volatility This myth is pervasive. Beta is associated with the stock’s volatility but there is more involved.  Beta is the ratio of the volatility of the stock to the volatility of ... [Read more...]