Question

On January 1, 2017 you bought a new, two-year U.S. government bond with a principal (face value) of $1000 and a coupon rate of 8% with coupons paid on December 31, 2017 and December 31, 2018. The principal will be repaid on December 31, 2018.   The Consumer Price Index (CPI) was 240 on January 1, 2017 and 250 on January 1, 2018. You decide to sell your bond on January 1, 2018 when the interest rate on brand-new U.S. government one-year bonds is 5%. What was the actual (ex post) nominal one-year return on your bond for your one-year holding period? What was the actual (ex post) real return?

Answer 1

Computation of actual (ex post) nominal one-year return:
Formula for Ex post Nominal return (R) = C/P+(P_t+1– P) / P
here, C = Coupon = $1,000*8% = $80
P = Face of the bond = $1,000
P_t+1 = Present value of the bond (i.e., the amount the bond that promises to pay = $1,000+ coupon = $1,080) = PV of $1,080 = $1,080 / (1+interest 5%) = $1,080 / 1.05 = $1,028.57
Therefore, Your actual ex post nominal return (R)= C/P+(P_t+1– P) / P
= 80/1,000+ (1028.57 – 1,000) / 1,000 = 0.08 + 0.02857 = 10.86%

Now, let us calculate the Actual (ex post) real rate:
Ex post real rate = Nominal rate -inflation rate
here. Inflation from January 1, 2017 to January 1, 2018 = (250 – 240) / 240 = .04167 = 4.17%
Thus, Actual (ex post) real rate = 10.86% - 4.17% = 6.69%