Question

TIPS (inflation protected securities) in 1997. The key The US Treasury started issuing provisions and features of these securities can be found at https://www.treasurydirect.gov/indiv/research/indepth/tips/res_tips_rates.htm, and are reported here The coupon rate which is set at auction, remains fixed throughout the term of the security The principal amount of the security is adjusted for inflation, but the inflation- adjusted principal will not be paid until maturity Semiannual interest payments are based on the inflation-adjusted principal at the time the interest is paid. . The index for measuring the inflation rate is the non-seasonally adjusted U.S. Cit (CPI-U), Average All Items Consumer Price Index for All Urban Consumers published monthly by the Bureau of Labor Statistics (BLS). At maturity, the securities will be redeemed at the greater of their inflation- adjusted principal or par amount at original issue. The main difference from other treasury bills is that the face value is adjusted for used by the Treasury Department, the par value is the value of the principal, which Consider the followings TIPS, issued on 1/1/2007 with maturity of 2 years and yearly inflation, both for the final payments and for the setting of coupons. In the terminology corresponds to the face value for non inflation-indexed bonds. coupon payments (the minimum maturity for TIPS is 5 years and coupon payments occur every six months, but these assumptions simplify the calculations). Assume the face value is 1000$, the coupon rate is 2% and that rate of change in the CPI- U (the inflation measure used for the adjustment) is 1.8% from 1/1/2007 to 1/1/2008 and 2.4% from 1/1/2008 to 1/1/2009 Calculate the coupon payments in 1/1/2008 and 1/1/2009 and the inflation adjusted value of the principal in 1/1/2009. What is the yield to maturity (interest rate) on this bond? Now assume that the CPI-U between 1/1/2008 and 1/1/2009 is-1.4%. Compute the coupon payment in 1/1/2009 and the amount paid out at maturity. What is the yield to maturity for this bond?

Answer 1

(a) Initial Face Value = $1000, Coupon Rate = 2 % , CPI Inflation 2007 (end of 2007) = 1.8 % and CPI Inflation 2008 = 2.4 %

Face Value at the end of 2007 = 1000 x 1.018 = $ 1018 and Face Value at the end of 2008 = 1018 x 1.024 = $ 1042.43

Coupon Payment on 1/1/2008 = 0.02 x 1018 = $ 20.36 and Coupon Payment on 1/1/2009 = 0.02 x 1042.43 = $ 20.85

Inflation Adjusted Principal Value on 1/1/2009 = Face Value at the end of 2008 = $ 1042.43

Let the YTM be R

Therefore, 1000 = 20.36 / (1+R) + 20.85 / (1+R)^(2) + 1042.43 / (1+R)^(2) (assuming that the TIPS are issued at par)

Using trail and error method/EXCEL's Goal Seek Function to solve the above equation we get:

R = 0.04138 or 4.14 %

(b) Face Value at the end of 2007 = $ 1018 and Inflation in 2008 = - 1.4 %

Face Value at the end of 2008 = (1-0.014) x 1018 = $ 1003.748

Coupon at the end of 2008 (payment on 1/1/2009) = 1003.748 x 0.02 = $ 20.075

Let the YTM be R

Therefore, 1000 = 20.36 / (1+R) + 20.075 / (1+R)^(2) + 1003.748 / (1+R)^(2) (assuming that the TIPS are issued at par)

Using trail and error method/EXCEL's Goal Seek Function to solve the above equation we get:

R = 0.02207 or 2.207 %