Case 1. A treasury bond that matures in 10 years has a yield of 6%. A 10-year corporate bond has a yield
of 8%. Assume that the liquidity risk premium on the corporate bond is 0.5%. What is the default risk
premium on the corporate bond?
Corporate Bond Yield= Risk-Free Rate + Default Risk Premium + Liquidity Risk Premium
Rearrange formula to solve for the default risk premium:
Default Risk Premium=Corporate Bond Yield−Risk-Free Rate−Liquidity Risk
Corporate Bond Yield = 8%
Risk-Free Rate (Treasury Bond Yield) = 6%
r10 = 6%
rc10 = 8%
LP = 0.5%
DRP = 8% - 6% -0.5% = 1.5%
Case 2. Due to a recession, expected inflation this year is only 3%. However, the inflation rate in Year 2
and thereafter is expected to be constant at some level above 3%. Assume that the expectations theory
holds and the real risk-free rate (r*) is 2%. If the yield on 3-year Treasury bonds is equal to 1-year yield
plus 2%, what inflation rate is expected after Year 1?
Given : Expected inflation this year = 3%
Real risk-free rate (r*) = 2%
Solution:
𝑟 𝑡 = 𝑟 *+𝐼𝑃𝑡 + 𝐷𝑅𝑃𝑡 + 𝑀𝑅𝑃𝑡
𝑟 1 = r* + 𝐼𝑃1
r1 = 2% + 3%
r1 =5%
r3 = r1+ 2%
r3 = 5% + 2%
r3 =7%
Formula for r3:
r3= r* +𝐼𝑃3
7%= r* +𝐼𝑃3
7% = 2% +𝐼𝑃3
𝐼𝑃3 = 7% - 2%
𝐼𝑃3 =5%
𝐼𝑃3 =
(𝐼1 + 𝐼2 + 𝐼3)
3
5% =
(3% + 2𝐼)
3
3𝑥(5% =
(3% + 2𝐼)
)
3
15% = 3% + 2I
2I = 15% - 3%
2I = 12%
2𝐼 12%
=
2
2
I = 6%
Case 3. A company’s 5-year bonds are yielding 7.75% per year. Treasury bonds with the same maturity
are yielding 5.2% per year, and the real risk-free rate (r*) is 2.3%. The average inflation premium is 2.5%;
and the maturity risk premium is estimated to be 0.1 x (t – 1) %, where t = number of years to maturity.
If the liquidity premium is 1%, what is the default risk premium on the corporate bonds?
rc5 = 7.75%
r5 = 5.2%
LP= 1%
DRP = 7.75% - 5.2% - 1% = 1.55%
Case 4. An investor in Treasury Securities expects inflation to be 2.5% in Year 1, 3.2% in year 2, and 3.6%
each year thereafter. Assume that the real risk-free rate is 2.75% and that this rate will remain constant.
Three-year Treasury securities yield 6.25%, while 5-year treasury securities yield 6.80%. what is the
difference in maturity risk premiums (MRPs) on the two securities, that is, MRP5 – MRP3?
R* = 2.75%
2.5% + 3.2% + 3.6%
𝐼𝑃3 =
= 3.1%
3
2.5% + 3.2% + 3.6%(3)
𝐼𝑃5 =
= 3.3%
5
R3 = 6.25%
MRP3 = 6.25% - 2.75% - 3.1% = 0.40%
R5 = 6.80%
MRP5 = 6.80% -2.75% -3.3% =0.75%
MRP5- MRP3 = 0.75%-0.40% = 0.35%