Question

Consider a 3 TIPS maturing 7/15/02 (settlement on 7/15/00). Assume the TIPS is trading at par. What is the real yield to maturity on the TIPS? Also, what is the price of the TIPS, if the CPI has increased 12% from the time the TIPS has been issued (Assume an initial par value of M=100,000). Assume that the semi-annual inflation rate for the next two years equals 1.5%.

Calculate the semi-annual coupon payments on the TIPS. Also calculate the par value on the maturity date 7/15/02.

Answer 1

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Answer:

We are given with a par Value of M =100000

Coupon rate = 3 + (5/8) = 3.625%

Also given that the semi annual inflation rate is 1.5 % for next 2 years

=> First Semi Annual Coupon payment = 0.03625 X (1 + 1.5%) X 100000= $3679.38

=> Second Semi Annual Coupon payment = 0.03625  X 1.015² X 100000 = $3716.17

=> Third Semi Annual Coupon payment = 0.03625  X 1.015³  X 100000 = $3790.58

=> Fourth Semi Annual Coupon payment = 0.03625  X 1.015_⁴  X 100000 = = $3847.44

Now the price of TIPS = 100000 X 1.12 = $1,12,000 (Since CPI rised to 12% )

100000*1.12 = $1,12,000

=> Real YTM = (3679.38+3716.17+3790.58+3847.44)/4 = 3758.39

and Real yield = (3758.39/100000)*100 = 3.76%