Question

The TIPS bond has an annual coupon rate of 4.5%. The table below shows the history of inflation rates for the first three years of the bond’s life.

Time	Inflation for Yr Just Ended	Par Value
0		$1,000
1	3%
2	4%
3	3%

a. What was the nominal return in year 2?

b. What was the real return in year 2?

c. What was the nominal return in year 3?

d. What was the real return in year 3?

Answer 1

DEFINITION

The rule of thumb in finance is that the value of money today is higher that the value of money in the future because of interest rates and inflation. When calculating investment returns, analysts determine the difference between the nominal rate and the real return, which adjusts to the current purchasing power. If the expected inflation rate is high, investors expect a higher nominal rate. Where nominal rate i the growth rate of money the real rate is basically the growth rate of purchasing power.

FORMULA

Nominal rate of return = Interest + Price Appreciation/ Initial Price .

Real rate of return = (1 + nominal return/ 1 + inflation) − 1

SOLUTION

TIME	INFLATION IN YEAR JUST ENDED	PAR VALUE(Adjust Every Year with Inflation Rate)	COUPON PAYMENT(4.5%*Par Value)	PRINCIPAL REPAYMENT
0		$1000	0
1	3%	$1030	$46.35	0
2	4%	$1071.2	$48.20	0
3	3%	$1103.34	$49.65	$1152.99

The Nominal And Real Return For the bond in each year are as follows:

(a) Nominal Return in Year 2 - 48.20 + 41.2/1030 = 0.08679612

(b) Real Return in Year 2 - (1.08679612/1.04) - 1 = 0.04 or 4%

(c) Nominal Return in Year 3 - 49.65 + 32.14/1071.2 = 0.07635362

(d) Real Return in Year 3 - (1.07635362/1.03) - 1 = 0.04% or 4%