There is no necessary reason why capital should be equally productive at all times. For example, in agrarian societies, capital could be very productive in summer (and earn a rate of return of 3%), but not in winter (and earn a rate of return of only 1%). This does not mean that investment in summer is a better deal or a worse deal than investment in winter, because cash in winter is not the same—not as valuable—as cash in summer, so the two interest rates are not comparable. You could not invest winter money at the 3% interest rate you will be able to invest it with 6 months later.
But although seasonal effects do influence both prices and rates of return on agricultural com-modities, and although the season example makes it clear that capital can be differently produc- tive at different times, it is not likely that seasonality is the reason why 30-year Treasury bonds in May 2002 paid 5.6% per annum, and 6-month Treasury notes paid only 1.9% per annum. So why is it that the yield curve was so steep? There are essentially three explanations:
1. The 30-year bond is a much better deal than the 1-year bond. This explanation is highly unlikely. The market for Treasury bond investments is close to perfect, in the sense that we have used the definition. It is very competitive and efficient. If there was a great deal to be had, thousands of traders would have already jumped on it. So, more likely, the interest rate differential does not overthrow the old tried-and-true axiom: you get what you pay for. It is just a fact of life that investments for which the interest payments are tied down for 30 years must offer higher interest rates now.
It is important that you recognize that your cash itself is not tied down if you invest in a 30-year bond, because you can of course sell your 30-year bond tomorrow to another investor if you so desire.
2. Investors expect to be able to earn much higher interest rates in the future. For example, if the interest rate r0,1 is 2% and the interest rate r1,2 is 10%, then r0,2 = (1 + 2%) · (1 + 10%) ≈ 1 + 12%, or r2 = 5.9%. If you graph rT against T , you will find a steep yield curve, just as you observed. So, higher future interest rates can cause much steeper yield curves.
However, I am cheating. This explanation is really no different from my “seasons” explanation, because I have given you no good explanation why investment opportunities were expected to be much better in May 2032 than they were in May 2002. I would need to give you an underlying reason. One particular such reason may be that investors believe that money will be worth progressively less. That is, even though they can earn higher interest rates over the long run, they also believe that the price inflation rate will increase. Inflation erodes the value of higher interest rates, so interest rates may have to be higher in the future merely to compensate investors for the lesser value of their money in the future.
However, the empirical evidence suggests that the yield curve is not a good predictor of future interest rates, except on the very shortest horizons (a month or less). So, the expectation of higher interest rates is not the most likely cause for the usually upward sloping curve in the real world.
3. Long-term bonds might somehow be riskier than short-term bonds, so investors only want to buy them if they get an extra rate of return. Although we have yet to cover uncertainty more systematically, you can gain some intuition by considering the effects of changes in economy-wide interest rates on short-term bonds vs. long-term bonds.
The empirical evidence indeed suggests that it is primarily compensation for taking more risk with long-term bonds than short-term bonds that explains why long-term bonds have higher yields than short-term bonds. That is, investors seem to earn higher expected rates of return on average in long-term bonds, because these bonds are riskier (at least in the interim).