3. Problem on Inflation Risk The US Treasury started issuing TIPS (inflation protected securities) in 1997....

(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 %