# Beta question

I’m doing some performance analysis on our portfolio vs the S&P. I’ve calculated our portfolio’s beta to be slightly less than 1. However, our portfolio has slightly outperformed the S&P. How is this possible?

What time period are you looking at? If you started in Oct 2007, S&P is still down like 15%. A beta slightly less than 1 would indicate that you are down slightly less than that. Also, what time increments are you using to calculate your beta?

Looking at 2011 YTD returns, so both my port and the S&P are positive. I’m calculating beta on daily returns. Basically COVAR(myport,S&P)/VAR(S&P) = beta. I’m getting like 0.94 for the beta, but my portfolio has like 0.42% of alpha. Not sure how I can be outperforming the S&P with a lower beta in an uptrending market… its pretty close to 1 and the alpha is small so perhaps there is some noise that allows for a bit of leeway on that? Idk how to explain it though and I’m pretty sure I’m not f-ing up my calcs.

Unless you are running an index portfolio, there will be tracking risk. So expected the return on your portfolio to be different than the benchmark.

I’m not a statistical or beta expert, but I suspect using daily is reducing the beta. Not sure what you can do about it though, since you would have so few data points if you go with weekly instead.

Portfolio performance = RFR + (Portfolio Beta) * (R_mkt - RFR) + (ex post Alpha) Market Performance = RFR + (Market Beta = 1) * (R_mkt - RFR) so… (Port_R - Mkt_R) = (Port Beta - 1) * (R_mkt - RFR) + (ex post Alpha) Congratulations, it looks like you have some (ex post) Alpha. (however, it may or may not be statistically significant). Additionally, assuming that the market was up over the time period and beta was < 1, you actually produced even more alpha than you might guess from the simple difference in portfolio - market returns.

Yeah I figure the alpha is possible because I have some unsystematic risk in the portfolio. I went and tested the r^2 and it came to like 90%. So with 10% unsystematic risk I guess its possible to outperform considering my beta is close to 1 and alpha is small. Its YTD so I’m not popping champagne just yet.

Maybe you are exposed to risk factors in higher proportions that the S&P. Maybe your portfolio is biased towards value or growth. Have to make sure that the S&P is the true benchmark.

Is there a software to find portfolio beta automatically? I don’t really feel like putting my CFA-learned wisdom to use, when I can press a button.

Palantir Wrote: ------------------------------------------------------- > Is there a software to find portfolio beta > automatically? I don’t really feel like putting my > CFA-learned wisdom to use, when I can press a > button. If you have BB, I believe you can save your portfolio there and it will track all the metrics for you, assuming everything in your portfolio is quoted.

Alpha.

You should be using the function varp, not var, for the denominator.