Question

What was the increase in real purchasing power associated with both​ 3-month Treasury bills and​ 30-year Treasury​ bonds? Assume that the current​ 3-month Treasury bill rate is

5.665.66

​percent, the​ 30-year Treasury bond rate is

8.778.77

​percent, and the inflation rate is

3.683.68

percent.​ Also, the chief financial officer wants a short explanation should the​ 3-month real rate turn out to be less than the​ 30-year real rate.

Answer 1

According to Fisher equation,

(1 + nominal rate) = (1 + real rate)*(1 + inflation rate), which can be approximated to

nominal rate = real rate + inflation rate

Approximate Real purchasing power for

3 month treasury bill = 5.665.66 - 3.683.68 = 1.982%

30 - year T- Bond = 8.778 - 3.683 = 5.095%

Yes, the 3-month real rate return should be less than that of 30- year bonds. A long duration bond carries a greater risk than a short duration bill. This is basically because the inflation in the future may potentially erode the value of the payments received. There is also the increased credit risk that the payments are not made on time or not made at all