Ken Solow is the Chief Investment Officer of Pinnacle Advisory Group, and Sauro Locatelli is the Quantitative Analyst.
Ken: Sauro, we need to have a clear and understandable way to explain “Beta” to our clients, since we use the term all the time. Can we simply say that if a fund has a Beta of 0.5 that means that the fund will get 50% of the benchmark performance, and if it has a Beta of 1.0 it will gather 100% of the benchmark performance?
Sauro: Well… no.
Ken: Why not?
Sauro: Because Beta doesn’t really measure the percent of return versus the benchmark. It actually measures the amount of volatility attributable to the benchmark.
Ken: That’s what I said.
Sauro: No, you said the percentage of return. A fund can have a Beta of 0.5 and actually have much higher or lower returns than the benchmark. Beta only measures how much of the volatility is attributable to the benchmark. The rest of the return in attributable to something else.
Ken: So the Beta of the fund tells you how the fund will move versus the benchmark?
Sauro: Well… sort of. Now you’re talking about correlation, which is part of the calculation of Beta.
Ken: Right, I knew that. The correlation of the portfolio to the benchmark tells you the direction of the portfolio performance relative to the benchmark. So a correlation of 100% means that the fund will move in the same direction as the benchmark 100% of the time, and a negative correlation of 100% means it will move in the opposite direction of the benchmark 100% of the time. A 50% correlation means it moves in the direction of the benchmark 50% of the time.
Sauro: Correct, but we don’t use correlation in the calculation. We use correlation- squared, or R-Squared.
Ken: Aw, come on! What’s wrong with correlation?
Sauro: Well, we’re trying to determine the impact of Beta on portfolio returns. So, R-Squared is measured from 0% to 100%, where we’re trying to determine what percentage of the fund’s volatility is explained by Beta. Correlation is measured from -100% to +100%, so it gives you the direction of the fund versus the benchmark. R-Squared tells you the explanatory power of the benchmark versus portfolio returns.
Ken: So if the portfolio has an R-Squared of 85%, that means that Beta will explain 85% of the portfolio’s volatility, and something else will explain the rest?
Ken: So what happens if we have a portfolio with a low R-Squared? What does that tell us about the Beta?
Sauro: Ken – seriously — why are you doing this to yourself?
Ken: Just answer the question, please.
Sauro: Well, we wouldn’t pay too much attention to the results of that analysis. In this case, the low R-Squared means that the Beta only explains a small portion of the portfolio volatility.
Can I go back to work now?
Ken: No, not yet. I want to know what explains the rest of the portfolio performance.
Sauro: Yes, of course you do. If the Beta is telling us how much the market, or the benchmark, is responsible for portfolio returns, then the “something else” that’s responsible for the rest of the returns is the skill of the portfolio manager. We call the remaining return, over and above the Beta, Alpha.
Ken: So if a portfolio has a positive Alpha, it means that it had a positive return?
Sauro: Well… no.
Ken: You are now officially trying my patience.
Sauro: A portfolio can have a positive return without having a positive Alpha. If the Alpha is negative, it just means that the return is less than we would have expected considering the portfolio’s Beta and the benchmark’s return. On the other hand, a portfolio with a poor absolute return can have a positive Alpha, meaning the manager earned returns higher than we would expect based on the Beta and the benchmark return.
Ken: So let me get this right… If the benchmark earns 10%, and my portfolio earns 7%, and the R-Squared of the portfolio is 90%, and the Beta of the portfolio is 0.5, then do I have any Alpha or not? And by the way, its lunch time and I’m getting a little cranky.
Sauro: Please pay attention. If the benchmark earns 10%, then the Beta of 0.5 implies that the portfolio should have earned 5% just from its exposure to market risk. The R-Squared of 90% tells us that the exposure to market risk explains 90% of the portfolio’s return. Since the portfolio actually earned 7%, then the manager earned 2% more than we would have expected based on the movement of the benchmark, so he or she would have earned a positive Alpha of 2%.
Ken: So I guess that explains it perfectly to our clients. Thanks for everything, Sauro.
Sauro: Uh, Ken?
Sauro: The positive Alpha might not mean that the manager was skilled. It might just mean that they were using the wrong benchmark.
Ken: I’m going to lunch!