Bond Price Sensitivity and Default Risk Premium Analysis
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Bond Price Sensitivity
7.7 Interest rate sensitivity. An investor purchased the following 5 bonds. Each bond had a par value of $1,000 and an 8% yield to maturity on the purchase date. Immediately after the investor purchased them, interest rates fell, and each of them had a new YTM of 7%. What is the percentage change in price for each bond after the decline in interest rates? Fill in the following table:
| BOND | PRICE @8% | PRICE @7% | PERCENTAGE CHANGE |
|---|---|---|---|
| 10 year 10% annual coupon | 1,134.20 | 1,210.71 | 6.75% |
| 10 year zero | 463.19 | 508.35 | 9.75% |
| 5 year zero | 680.58 | 721.99 | 4.76% |
| 30 year zero | 99.38 | 131.37 | 32.19% |
| $100 perpetuity (100/0.8 or 0.7) | 1,250.00 | 1,428.57 | 14.29% |
N=10 Y=8 or 7 PV=? FV=1000 PTM=0 except coupon=100
Default Risk Premium
6.4 Default risk premium. A treasury bond that matures in 10 years has a yield of 5.75%. A 10 year corporate bond has a yield of 8.75%. Assume that the liquidity premium on the corporate bond is 0.35%. What is the default risk premium on the corporate bond?
1. Calculation Method: 5.75 + 0.35 = 6.10; 8.75 - 6.10 = 2.65
2. Calculation Method: rt10= 5.75%; rc10=8.75%; LP=0.35%; DRP=?
r= r*+IP+DRP+LP+MRP FORMULA
rt10=5.75%=r*+IP10+MRP10; DRP=LP=0
rc10=8.75%=r*+IP10+DRP+0.35%+MRP10.
Because both bonds are 10-year bonds the inflation premium (IP) and maturity risk premium (MRP) on both bonds are equal. The only difference between them is the liquidity and default risk premium.
Rc10=8.75%=r*+IP10+MRP10+0.35%+DRP. But we know from above that r*+IP10+MRP10=5.75%; therefore,
Rc10=8.75%=5.75%+0.35%+DRP
2.65%=DRP
Default Risk Premium Calculation
6.11 Default risk premium. A company’s 5-year bonds are yielding 7% per year. Treasury bonds with the same maturity are yielding 5.2% per year, and the real risk-free rate (r*) is 2.75%. The average inflation premium is 2.05% and the maturity risk premium is estimated to be 0.1x (t-1) where the number t=number of years to maturity. If the liquidity premium is 0.7%, what is the default risk premium on the corporate bonds?
FORMULA rcbond= r* + IP + MRP + LP + DRP
MRP= 0.1%(5-1)=0.4%
7.00%=2.75+2.05+0.4+0.7+DRP
7.00%=5.9+DRP
DRP=1.10%
Default Risk Premium Calculation
6.12 Default risk premium. The real risk-free rate (r*) is 1.7%. Inflation is expected to average 1.5% a year for the next 4 years, after which time inflation is expected to average 4.8% a year. Assume there is no maturity risk premium. An 11-year corporate bond has a yield of 8.7%, which includes a liquidity premium of 0.3%. What is its default risk premium?
FORMULA rcbond= r* + IP + MRP + LP + DRP
8.7%=1.7+ (1.5x4+4.8x7)/11+0+0.3+DRP
8.7%=1.7+3.6+0+0.3+DRP
8.7%=5.6+DRP
DRP= 3.10%