Beta and Bonds

Yesterday's post was all about Alpha. A commenter asked me about leverage in bond portfolios, which got me thinking about the other half of the CAPM equation: Beta.

For those who didn't major in finance, the CAPM theory proffers that the return on an asset or portfolio is based on three components: the risk-free return, the general market return (beta), and a residual (alpha). Its fairly easy to understand if you think of a stock portfolio. Let's say you have created a portfolio of 50 stocks all of which are in the S&P 500. Any day in which the S&P 500 is up, you're portfolio is most likely up as well, and vice versa. This sort of general market effect is the beta.

Now let's say that your portfolio seems to be consistently more volatile than the market. I.e., if the market is up 1%, you are usually up 1.2%. We'd say you have a beta of 1.2. If at the end of the year, the S&P is up 20% and you have a beta of 1.2, we'd expect you to be up 24%. Same if the market is down, we'd expect you to be down more. Notice that if the beta concept really holds, then someone with a higher beta only outperforms or underperforms because they've taken more risk. Not because of any skill on the manager's part.

This is why a lot of people in the business focus on alpha, which is the residual return after accounting for market movement and portfolio volatility. Again, if the beta concept holds, then someone with a positive alpha is producing returns over and above the risk taken. That's obviously what everyone wants.

The beta concept is fairly easy for stocks, but more complicated for bonds. We know that over the long-term, stocks tend to rise in price, which compensates investors for their risk. So generally investors want a positive beta to the stock market, to capture this long-run price appreciation tendency.

Ignoring income, bonds do not have a long-term appreciation tendency. For a general bond portfolio to experience price appreciation, interest rates must fall. While we can agree that over the next 50-years, stock prices are highly likely to rise, we can't say that interest rates are highly likely to fall persistently. So it follows that investors would generally want a positive beta to stocks, but would be ambivalent about the beta to rates. If we assume that there is no long-run tendency for rates to rise or fall, then the desired beta is unknown.

In fact, if we assume that you could enjoy the income regardless, you'd probably want a beta of zero. Why be exposed to movements in rates at all?

Getting back to the real world, you can't get the income without taking interest rate risk. Today's yield curve is unusual; in most environments you would be giving up a large chunk of income by eliminating duration risk, whether through hedging or buying short-term bonds. Most of the time, there is a large increase in yield as you move from 0 to 5 years in maturity. Then there is a smaller yield advantage to increasing duration from 5 to 10 years. From 10 to 30 years, the yield pickup is usually relatively small. So you can get most of the income by sticking to 5-10 year maturities, and avoid the volatility of holding longer bonds.