Greg Mankiw on Bond Returns

Greg Mankiw had an interesting post today pointing out that bond returns calculated by the economist were incorrect.

Mankiw wrote:

Here is a question for students who are learning about compounding.  What is wrong with the following passage from The Economist magazine?

Investors who bought Treasury bonds in 1946, when yields were around current levels, did not suffer a formal default. But over the following 35 years they lost money in real terms at a rate of 2% a year. The cumulative real loss was 91%. By that standard, Greek creditors, who recently suffered a 50% loss via default, were lucky.

Answer: The second number is inconsistent with the first.  Note that .98^35=.49, so we get only a 51 percent cumulative loss.

In fact, the price level from 1946 to 1981 rose by a factor of about 5, so holding currency with a zero nominal return led to a real loss of only about 80 percent.

But Mankiw forgot one important element of calculating bond market returns.  Much of the total return for bonds is the interest on the annual interest payments and in a period of rising rates the returns will rise  as the interest payments  are reinvested at higher yields.  It is a bond market convention to assume that all the interest payments will be reinvested at the current yield.  They do that so they can actually calculate a valid price for the bond. But that is just a convention, and in a period of rising rates the returns will be higher than Mankiw calculates.

By omitting this point Mankiw is making just as serious an error as he is accusing the Economist of making.