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March 8, 2021 Activity 1: Interest RatesProb. 7-3 Expected Interest Rate. What is the yield on 2-year Treasury securities? What is the yield on 3-year Treasury securities?Solution: r = r* + IP + MRP2-year treasury securities rT2 = 3% +( 2% + 4%/2) + 0 = 3% + 3% + 0 = 6%3-year treasury securities rT3...

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March 8, 2021 Activity 1: Interest Rates

Prob. 7-3

Expected Interest Rate. What is the yield on 2-year Treasury securities? What is the yield on 3-year Treasury securities? Solution: r = r* + IP + MRP 2-year treasury securities rT2 = 3% +( 2% + 4%/2) + 0 = 3% + 3% + 0 = 6% 3-year treasury securities rT3 = 3% + (2% + 4% + 4%/ 3) + 0 = 3% + 3.33% + 0 = 6.33%

Prob. 7-6

Inflation Cross-Product What is the yield on a 4-year security with no maturity, default, or liquidity risk? Solution: rRF = r* + IP + (r* x P) rRF = 5% + (16% +16% +16% + 16%/4) + (5% x 16%) = 5% + 16% + (5% x 16%) = 5% + 16% + 0.08 = 21.80%

Prob. 7-10

Inflation What inflation rate is expected after year 1? Solution 1-year yield Treasury bonds r = r* + IP + MRP = 2% + 3% + 0 = 5% 3-year yield Treasury bonds rT3 = 1-year yield Treasury bonds + 2% = 5% + 2% = 7% (1 + 0.07)^3 = (1 + 0.05) x (1 + X)^2 1.225043/ (1 + 0.05) = (1 +X)^2 1.166707619 = (1 +X)^2 (1.166707619)^1/2 = 1 + X 1.080142407 = 1 + X 1.080142407 -1 = X X = 0.080142407 or 8.01%

r (year 2) = r* + IP + MRP 8.01% = 2% + IP + 0

8.01% - 2% = IP IP3 = 0.0601 or 6% Prob. 7-12

Maturity Risk Premium What is the difference in the maturity risk premiums (MRPS) on the two securities? IP 2.5% (YR1)

r* 2.75% (constant)

3.2% (YR2)

Treasury Securities 6.25% (3YR) 6.80% (5YR)

3.6% (each year thereafter) Solution 3-year treasury security 6.25% = 2.75% + (2.5% + 3.2% + 3.6%/3) + MRP5

5-year treasury security 6.80% = 2.75% + (2.5% + 3.2% + 3.6% + 3.6% + 3.6%/5) + MRP5

6.25% = 2.75%+ 3.1% + MRP5

6.80% = 2.75% + 3.3% + MRP5

6.25% - 5.85% = MRP5

6.80% - 6.05% = MRP5

MRP5 = 0.4%

MRP3 = 0.75%

Difference = MRP5 - MRP3 = 0.75% - 0.40% = 0.35% Prob. 7-13

Default Risk Premium What is the default risk premium? r = r* + IP + DRP + LP + MRP Solution 8.3% = 2.5% + (2.8% + 3.75%/2) + DRP8 + 0.75% + 0 8.3% = 2.5% + 3.275% + DRP8 + 0.75% + 0 8.3% = 6.525% + DRP8 8.3% - 6.525% = DRP8 DRP8 = 1.775%

Prob. 7-14

Expectations Theory and Inflation a. What is the yield on a 1-year bond 1 year from now? b. What is the expected inflation rate in Year 1?

a.) Solution 2-year Treasury bonds = 4.5% 1 Year bonds = 3% r* = 1% MRP = 0 (1 + 0.045)^2 = (1 + 0.03)(1 + X) 1.092025 / (1 + 0.03)= 1 + X 1.060218447 = 1 + X 1.060218447 - 1 = X X = 0.060218447 or 6.02% or 6%...