Explaining the Term Structure of Interest Rates

The term structure that we showed in Figure 3.4 was upward-sloping. Long-term rates of interest in December 2017 were more than 2.5%; short-term rates were about 1.8%. Why then didn’t everyone rush to buy long-term bonds? Who were the (foolish?) investors who put their money into the short end of the term structure?

Suppose that you held a portfolio of one-year U.S. Treasuries in December 2017. Here are three possible reasons you might decide to hold on to them, despite their low rate of return:

1. You believe that short-term interest rates will be higher in the future.
2. You worry about the greater exposure of long-term bonds to changes in interest rates.
3. You worry about the risk of higher future inflation.

We review each of these reasons now.

1. Expectations Theory of the Term Structure

Recall that you own a portfolio of one-year Treasuries. A year from now, when these Treasuries mature, you can reinvest the proceeds for another one-year period and enjoy whatever interest rate the bond market offers then. The interest rate for the second year may be high enough to offset a low return in the first year. You often see an upward-sloping term structure when future interest rates are expected to rise.

Example 3.3 • Expectations and the Term Structure

Suppose that the one-year interest rate, r_b is 5%, and the two-year rate, r₂, is 7%. If you invest $100 for one year, your investment grows to 100 X 1.05 = $105; if you invest for two years, it grows to 100 X 1.07² = $114.49. The extra return that you earn for that second year is 1.07²/1.05 – 1 = .090, or 9.0%.

Would you be happy to earn that extra 9% for investing for two years rather than one? The answer depends on how you expect interest rates to change over the coming year. If you are confident that in 12 months’ time one-year bonds will yield more than 9.0%, you would do better to invest in a one-year bond and, when that matured, reinvest the cash for the next year at the higher rate. If you forecast that the future one-year rate is exactly 9.0%, then you will be indifferent between buying a two-year bond or investing for one year and then rolling the investment forward at next year’s short-term interest rate.

If everyone is thinking as you just did, then the two-year interest rate has to adjust so that everyone is equally happy to invest for one year or two. Thus the two-year rate will incorporate both today’s one-year rate and the consensus forecast of next year’s one-year rate.

If short-term interest rates are significantly lower than long-term rates, it is tempting to borrow short term rather than long term. The expectations theory implies that such naive strategies won’t work. If short-term rates are lower than long-term rates, then investors must be expecting interest rates to rise. When the term structure is upward-sloping, you are likely to make money by borrowing short only if investors are overestimating future increases in interest rates.

Even at a casual glance, the expectations theory does not seem to be the complete explanation of term structure. For example, if we look back over the period 1900-2017, we find that the return on long-term U.S. Treasury bonds was on average 1.5 percentage points higher than the return on short-term Treasury bills. Perhaps short-term interest rates stayed lower than investors expected, but it seems more likely that investors wanted some extra return for holding long bonds and that on average they got it. If so, the expectations theory is only a first step.

These days, the expectations theory has few strict adherents. Nevertheless, most economists believe that expectations about future interest rates have an important effect on the term structure. For example, you often hear market commentators remark that since the six-month interest rate is higher than the three-month rate, the market must be expecting the Federal Reserve Board to raise interest rates.

1. Introducing Risk

What does the expectations theory leave out? The most obvious answer is “risk.” If you are confident about the future level of interest rates, you will simply choose the strategy that offers the highest return. But, if you are not sure of your forecasts, you may well opt for a less risky strategy even if it means giving up some return.

Remember that the prices of long-duration bonds are more volatile than prices of short-duration bonds. A sharp increase in interest rates can knock 30% or 40% off the price of long-term bonds.

For some investors, this extra volatility of long-duration bonds may not be a concern. For example, pension funds and life insurance companies have fixed long-term l iabilities and may prefer to lock in future returns by investing in long-term bonds. However, the volatility of long-term bonds does create extra risk for investors who do not have such long-term obligations. These investors will be prepared to hold long bonds only if they offer the compensation of a higher return. In this case, the term structure will be upward-sloping more often than not. Of course, if interest rates are expected to fall, the term structure could be downward-sloping and still reward investors for lending long. But the additional reward for risk offered by long bonds would result in a less dramatic downward slope.

2. Inflation and Term Structure

Suppose you are saving for your retirement 20 years from now. Which of the following strat­egies is more risky? Invest in a succession of one-year Treasuries, rolled over annually, or invest once in 20-year strips? The answer depends on how confident you are about future inflation.

If you buy the 20-year strips, you know exactly how much money you will have at year 20, but you don’t know what that money will buy. Inflation may seem benign now, but who knows what it will be in 10 or 15 years? This uncertainty about inflation may make it uncom­fortably risky for you to lock in one 20-year interest rate by buying the strips.

You can reduce exposure to inflation risk by investing short-term and rolling over the investment. You do not know future short-term interest rates, but you do know that future interest rates will adapt to inflation. If inflation takes off, you will probably be able to roll over your investment at higher interest rates.

If inflation is an important source of risk for long-term investors, borrowers must offer some extra incentive if they want investors to lend long. That is why we often see a steeply upward-sloping term structure when inflation is particularly uncertain.

Source:  Brealey Richard A., Myers Stewart C., Allen Franklin (2020), Principles of Corporate Finance, McGraw-Hill Education; 13th edition.