Today is 1 January. You buy $100,000 par value of TIPS (Treasury Inflation Prote

Question

Today is 1 January. You buy $100,000 par value of TIPS (Treasury Inflation Protected Securities) that pay a coupon of 3.5% and mature one year from now. The coupons are paid semi-annually at the end of June and December. The par value of the TIPS is adjusted for inflation using the CPI-U. a) Over the first six months, the inflation rate turns out to be 3% pa. What is the coupon payment you will receive at the end of June? b) Over the second six months, the inflation rate drops to -1% pa. What will be your total holding period return when the TIPS mature at the end of December, assuming that you did reinvest the coupons received at the end of June in the same TIPS security?

Explanation / Answer

The sole purpose of Inflation protected bonds is to insulate an investor from inflation. How they do this is buy assuring the investor of inflation + X interest. So the investor always makes more than the inflation.

Here we have been given that the the nominal coupon is 3.5% and that the previous inflation was 3%. So we simply add 3.5% to 3% and divide it by 2 <<< it is 3.5% / 2 as the coupon is paid semi annually and the inflation is 3% pa but we have only 6 months to calculate for. hence division by 2

So the coupon that will be paid will be calculated on (3.5+3)% / 2 = 3.25%

So for $100,000 after 6 months you will get

$100,000 * (1 + 3.25/100) = $103,250 So return = $3250

Similarly for the second half year we can calculate the effective coupon rate. But this time the inflation is negative

So (-1 + 3.5)% / 2 = 1.25%

Again the return for these 6 months will be (100,000+$3250) * (1+1.25/100) = $104,540.625

Return = $104,540.625-$100,000 = $4,540.625 or 4.540625% return (absolute)

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