Question

Consider a newly issued TIPS bond with a three year maturity, par value of $1000, and a coupon rate of 5%. Assume annual coupon payments.

Time	Inflation in year just ended	Par Value	Coupon Payments	Principal Payment	Total Payment
0		$1000.00
1	4.5%
2	3.5%
3	2.0%

1. Fill in the shaded cells with amounts in the above table.
2. What is the nominal rate of return on the TIPS bond in the first year?
3. What is the real rate of return on the TIPS bond in the first year?

Answer 1

Part (a)

In the parenthesis, I have also shown the working for each item. That will help you understand the mathematics behind each calculation.

Time	Inflation in year just ended	Par Value	Coupon Payments	Principal Payment	Total Payment
0		1,000.00
1	4.50%	1,045.00 [=1000 x (1 + 4.5%)]	52.25 [= 5% x 1,045]	-	52.25 [= 52.23 + 0]
2	3.50%	1,081.58 [=1,045 x (1 + 3.5%)]	54.08 [= 5% x 1,081.50]	-	54.08 [=54.08 + 0]
3	2.00%	1,103.21 [1,081.58 x (1 + 2%)]	55.16 [=5% x 1,103.21]	1,103.21	1,158.37 [=55.16 + 1,103.21]

Part (b)

Nominal rate of return in the first year = coupon payment / Face value = 52.25 / 1,000 = 5.225%

Part (c)

Real rate of return in the first year = coupon payment / Par value = 52.25 / 1,045 = 5.00%