Pricing a risk Free Bond 6. Pricing a Risk-Free Bond You are thinking about inve

Question

Pricing a risk Free Bond

6. Pricing a Risk-Free Bond You are thinking about investing in a bond issued by the U.S. Government. It is a one year, zero coupon bond with a face value of $100. There is no default risk, but there is inflation risk. For the remainder of the problem, assume that the real interest rate is 1% per year. (a) Compute the expected value of the inflation rate, are pi^e. (b) At this expected inflation rate, what is the present value of the bond? Use the exact Fisher equation. (c) Let's account for the risk a different way. For each possible value of inflation, compute the corresponding nominal interest rate using the exact Fisher equation. (d) Price the bond at each of the interest rates you computed in part (c). Treating these prices as the random variable, what is the expected value of the price of the bond? (e) Compare the numbers you computed in part (a) and part (d). Given your answers, do you think it was worth the extra effort to compute the answer in part (d)?

Explanation / Answer

a) Expected Value of Inflation

b) Discount rate for the Bond = (1+real rate)*(1+inflation rate) = 1.01*1.15 =

Nominal Rate = 1.16%

Present Value of the Bond = (1*.9885)+(100*.9885) = $99.8418

c)

d)

e) The comparison reveals that calculating the present value of the bond using the answer (a) 99.8418 and (d) 98.9607 shows the effect of inflation in the discount rates more precisely considering the probability of inflation.

Inflation Probability Expected Value% 1000 0.0001 0.1 5 0.05 0.25 1 0.8 0.8 0 0.1499 0 Total 1.15

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.