A Framework for Understanding Bond Portfolio Performance
Investors are legitimately concerned that interest rates, after falling reliably for decades, are on their way up and that bond portfolio values are on their way down. Investors now seek interest-rate protection. Some regard the bond bear market as having already started: The 10-year Treasury yield has risen from an all-time low of 1.4% on July 24, 2012, to a high of 2.98% on Sept. 5, 2013, before settling slightly to 2.88% as of December 6.
In an earlier article, I recounted the long-term history of the bond market, focusing on the “bond mountain” of 1941-2012 wherein Treasury bond yields rose from 3% to over 15% and then fell back below 2%. Here, I provide a framework for analyzing and, hopefully, predicting the returns on actively managed portfolios of bonds – a task different from analyzing the bond market itself.
Alpha and beta
One of the basic teachings of modern finance is that the return – on any portfolio in any asset class – consists of a market part (beta) and a non-market part (alpha). The “beta” component is the return that would have been achieved through passive exposure to the underlying asset class — say, the bond market. The non-market or “alpha” part is the rest of the return and is attributable to active management. This analytical framework works well for equity portfolios, which usually have betas quite close to 1 (the beta of the market). For example,
|Equity portfolio return:
Market (benchmark) return:
Beta of portfolio*:
Beta component of return:
0.9 x (10% − 0%) = 9%
|Alpha of portfolio:||14% − 9% = 5%*|
*Beta is calculated from a regression of a time series of market returns, in excess of the riskless rate, on portfolio returns, also in excess of the riskless rate.
In the bond market, however, there is an extra wrinkle. The amount of market exposure – the beta or, using bond-market terminology, the duration of a bond portfolio – can vary widely and depart greatly from the bond market’s duration. The choice of duration is up to the portfolio manager. Bonds can have a duration as short as zero as and long as 18 years (based on the longest coupon-paying bond, which has 30 years to maturity). By including leverage or derivatives, the manager can engineer a negative duration, or one beyond 18 years. That’s a lot of flexibility for the bond portfolio manager and a lot of choices from which the investor has to select.
Duration is a type of beta, but the scale is different
So far, I’ve used “duration” and “beta” interchangeably when referring to the bond market. Some readers may find this confusing. Beta is the general term for the sensitivity of a security or portfolio’s value to the change in some variable. In its most common use, beta is the sensitivity of an equity portfolio’s value to changes in the value of the overall equity market – and that is the sense in which I used “beta” in the example above. In that context, beta is scaled so that the market has a beta of one, and betas greater than one reflect risk or sensitivity greater than that of the market, while betas less than one are associated with less risk than the market. In the bond market, however, the sensitivity of the bond’s price to a change in interest rates is scaled in years and is called duration.1
While duration and beta measure exactly the same thing – the sensitivity of a security’s price to a change in some other variable – the scales are different. A bond portfolio with a duration of 5 years, when the market benchmark (usually the Barclays Aggregate index, or AGG) has a duration of 5.6 years, is very much like an equity portfolio with a beta of 0.9: it is nine-tenths as risky as the market. Readers who train themselves to think of duration and beta as functional equivalents – measures of relative risk – will find bond math and bond portfolio performance evaluation much easier to understand.
Alpha and beta cannot be separated for a bond portfolio as simply as I did for an equity portfolio. We must first consider the question of what we mean by alpha and beta in a bond context.
1. The duration of a bond is the present-value-weighted average number of years it takes the bondholder to get his or her money back. Thus, a 30-year bond, bought at par, with a 5% coupon paid semiannually, has a duration of 15.8 years. This is the approximate number of dollars by which a bond with $100 par value will decline in price if the interest rate moves from 5% to 6%. A more accurate estimate is given by the modified duration, D/[1+YTM/n], in which D is the unmodified or Macaulay duration defined above, YTM is the yield to maturity and n is the number of coupon payments per year.