To: Smooth Drive who wrote (130 ) 5/31/1998 8:49:00 PM From: ftth Respond to of 237
Hi Eric, I won't go into a ton of detail because it requires equations that aren't easily typed in with this text-based entry. There are probably 50 pages devoted to the alpha, beta, r-squared calculations in Sharpe's book (Ch 8,17,25). You start with a market model in that familiar y=mx+b form. In our case b is alpha, m is beta, and x is the return on the market index. y is the return on the security of interest. There's also an error term added that accounts for the fact that the model doesn't explain the returns perfectly. The procedure to find alpha, beta, and the other MPT (modern portfolio theory) variables is to plot the returns of the market index versus the returns of the security (market on x-axis, security on y). So, for example, if the market return on day 1 is .5% and the security return is 1%, you plot a point at .5 on x and 1 on y. After you plot a bunch of points, you get a scatter plot that you apply a least-squares regression to. This spits out alpha, beta, and standard deviation of the random error term. From this you can calculate the standard error of alpha and beta, the correlation coefficient, and the coefficient of determination (r-squared). This can be done easily in Excel and probably in some of the more advanced stock charting packages. What Navellier is calculating is called the Reward-to-Variability (RVAR) ratio in Sharpe's book. There is also a Reward-to-Volatility ratio (RVOL) that has the same numerator (alpha or excess return) but divides by beta (whereas the Reward-to-Variability divides by the standard deviation of returns). It is possible for RVOL to indicate the security outperformed the market, while RVAR doesn't. This happens when there is unique risk (i.e. non-market). RVOL only accounts for market risk; RVAR accounts for total risk (i.e. market and non-market (stock-specific)). A portfolio of stocks with low market risk could have high total risk, so the "conventional wisdom" that more stocks=more diversified=lower risk isn't necessarily true. I'd like to run a screen based on RVAR, but it would have to be something automated that I could do with my stock database directly. Otherwise, it's not realistic to use because of all the format conversions. I'll put it on the list (that never seems to get smaller) of stuff to try. dh