In this advanced problem, let's look at the behavior of ordinary Treasury bonds and inflation-indexed bonds, or TIPS. We will simplify by assuming annual interest payments rather than semiannual. Suppose over the next five years, investors expect 3 percent inflation each year. The Treasury issues a 5-year ordinary bond that pays $55 interest each year.
The Treasury issues a 5-year TIPS that pays a coupon rate of 2 percent. With TIPS, the coupon payment is determined by multiplying the coupon rate times the inflation-adjusted principal value.
Like ordinary bonds, TIPS begin with a par value or principal value of $1,000.
However, that principal increases over time as inflation occurs. Assuming that inflation is in fact equal to 3 percent in each of the next five years, then the cash flows associated with each bond would look like this:
|
Year
|
T-bond Pays
|
TIPS Pays
|
Inflation-adjusted
Prindpal (TIPS)
|
Coupon pymt calculation
|
|
0 (cost)
|
-1,000.00
|
-1,000.00
|
-1,000.00
|
NA
|
|
1
|
55.00
|
20.60
|
1,030.00
|
1,000.00(1.03) x 2%
|
|
2
|
55.00
|
21.22
|
1,060.90
|
1,030.00(1.03) x 2%
|
|
3
|
55.00
|
21.85
|
1,092.73
|
1,060.90(1.03) x 2%
|
|
4
|
55.00
|
22.51
|
1,125.51
|
1,092.73(1.03) x 2%
|
|
5
|
1,055.00
|
1,182.46
|
1,159.27
|
1,125.51(1.03) x 2%
|
In the last row of the table, notice the final TIPS payment includes the return of the inflation-adjusted principal ($1,159.27), plus the final coupon payment.
a. Calculate the yield to maturity (YTM) of each bond. Why is one higher than the other? Show that the TIPS YTM equals the product of the real interest rate and the inflation rate.
b. What is the real return on the T-bond?
c. Suppose the real return on the T-bond stays constant, but investors expect 4 percent inflation rather than 3 percent. What happens to the required return on the T-bond in nominal terms?
d. Imagine that during the first year, the inflation that actually occurred was 3 percent, as expected. However, suppose that by the end of the first year, investors had come to expect 4 percent inflation for the next four years. Fill out the remaining cash flows for each bond in the table below
|
Year
|
T-bond Pays
|
TIPS Pays
|
Inflation-adjusted
Principal (TIPS)
|
Coupon pymt
calculation
|
|
0(cost)
|
-1,000.00
|
-1,000.00
|
-1,000.00
|
NA
|
| 1 |
55.00 |
20.60 |
1,030.00 |
1,000.00(1.03) X 2%
|
| 2 |
|
|
|
|
| 3 |
|
|
|
|
| 4 |
|
|
|
|
| 5 |
|
|
|
|
e. Now calculate the market price of the Treasury bond as of the end of the first year. Remember to discount the bond's remaining cash flows, using the nominal required return that you calculated in part (c). Given this new market price, what is the total return offered by the T-bond the first year? \
f. Next, calculate the market price of the TIPS bond. Remember, at the end of the first year, the YTM on the TIPS will equal the product of one plus the real return (2%) and one plus the inflation rate (4%). What is the total nominal return offered by TIPS the first year?