Question

e. Suppose most investors expect the inflation rate to be 5% next year, 6% the following year, and 8% thereafter. The real risk-free rate is 3%. The maturity risk premium is zero for bonds that mature in 1 year or less and 0.1% for 2-year bonds; then the MRP increases by 0.1% per year thereafter for 20 years, after which it is stable. What is the interest rate on 1-, 10-, and 20-year Treasury bonds? Draw a yield curve with these data. What factors can explain why this constructed yield curve is upward sloping?

Answer 1

Step 1 - Finding average expected inflation rate Avg Inflation = Total Inflation for N years/No. of years to maturity Accordingly, Inf 1 = 5%/1 = 5% Inf 10 = (5%+6%+8%(8))/10 = 7.5% Inf 20 = (5% +6% +8%(18)}/20 = 7.75% Step 2 - Finding maturity risk premium (MRP). As the MRP for first year is O, MRP for subsequent years would be caluclated as, MRP = 0.1% * (No. of years to maturity - 1) MRP 1 = 0% MRP 10 = 0.1% x(10-1) = 0.9% MRP 20 = 0.1% % (20-1) = 1.9%

Step 3 - Calculating interest rates As we know, interest rate (r) = Risk Free Rate (RFR) + Inf Preminum + Default Risk Premium (DRP) + liquidity premium (LP) + MRP But remember students that the question has specified that these are treasury bonds and hence DRP and LP = 0. Taking the RFR of 3% as given, r1 = 3% +5.0% +0.0% = 8.0% r 10 = 3% + 7.5% +0.9% = 11.4% r 20 = 3% +7.75% +1.9% = 12.65% 13% 12% 11% 10% Step 4 - Yield Curve Interest Rate Maturity 10% Interest Rate 8% 11.40% 12.65% 6% 10 | 20 - 10 Maturity 20 Step 5- Reasons for upward sloping curv 1 increase in expected inflation 2 increasing maturity risk premium