Commentary

28 Jan 2011 by Jim Fickett.

*Looking at the long-term rate of change in bond yields, and using the concept of duration to estimate corresponding price changes, it is possible to make an educated guess about which bonds or bond funds are likely to give positive real returns.*

There is a good chance that bond yields have bottomed, and we have begun a long period (perhaps decades) of rising rates. Rising yields mean falling bond prices. How can one think about this in a pragmatic way, to evaluate whether yields on bonds are high enough to compensate for the negative environment?

The first question is, how fast are rates likely to rise? While no one really knows the answer to that question, it is interesting that, over the last 60 years, the medium-term trend rate of change (first in rising, then in falling rates), though hardly a constant, tended to be in the neighborhood of 0.35 percentage points per year:

(Constant maturity Treasury yields from the Federal Reserve H.15 release. Click for larger image.)

I'm not suggesting any law of nature here, and I'm open to other suggestions on how to think about what rate of change is likely, but thinking of rates rising at about 0.35 percentage points per year is a reasonable starting point for some quantitative thinking.

The tool for relating changes in yield to changes in price is duration. The duration of a bond is defined as the average length of time, in years, one waits to receive each of the dollars due, including both principal and interest. A rule of thumb is that, for a bond with duration D, a 1% change in interest rates changes the price of the bond by D percent. The same concept applies to bond funds, which always report the average duration of the bonds in the fund. A moment's thought and some simple algebra show that taking a weighted average of the duration of the bonds gives the same result as calculating duration directly on all payments due on all bonds in the fund. So the rule of thumb on yield and price should work for bond funds as well.

So let's look at how some specific investments are likely to fare under rising rates. Since Vanguard is famous for low expense ratios, let's look at some Vanguard bond funds.

- The short-term bond index fund, VBISX, is paying 1.1% and has an average duration of 2.6 years. With that duration, and rates rising at 0.35 pts/yr, one expects a capital loss of about 2.6*0.35 = 0.9%/yr. In addition, we currently have inflation of 0.8%/yr. So 1.1% - 0.9% - 0.8% gives a total expected loss of 0.6%/yr.
- The intermediate-term bond index fund, VBIIX is paying 3.2% and has an average duration of 6.3 years. Here the expected capital loss is 6.3 * 0.35 = 2.2%/yr, so the expected real yield is 3.2% - 2.2% - 0.8% = 0.2% (as long as inflation holds at 0.8%). Not much, but at least it is positive.
- The long-term bond index fund, VBLTX is paying 5.0% and has an average duration of 12.9 years. Here the expected real yield is 5.0% - 0.8% - (12.9*0.35)% = -0.3%. Back to negative returns.

Duration is also useful for thinking about risk of a sudden price move. Here is a history of the month-to-month change in yield on the 10-year Treasury from 1953 on.

If you take a monthly look at your investments, you are unlikely to suffer more than a 0.5 percentage point move in yield before noticing. With the short-term fund above, a 0.5% rise in yield gives a loss of 1.3%. With the intermediate term fund, the loss would be 3.2%, and with the long-term, 6.5%. A very rough rule for all three cases is that your risk from a sudden change in yield is about one year's nominal interest. Note that the real yield (assuming the background of rising rates) is quite similar for the short-term and the long-term fund, while the risk for the latter is much greater.

There are many caveats to this analysis. Most importantly,

- The 0.35 point/yr rule is helpful for a multi-year perspective, but not so much for shorter terms
- Inflation, rates, and the composition of a bond fund can all change in unpredictable ways

Still, one has to make educated guesses in investing, and this is one reasonable way to think about the environment and make an intelligent choice of bonds or bond funds.

Given this analysis, if I were choosing between the three particular funds above, I would choose the intermediate term. The likely real yield is positive, and the risk is manageable.