CAS Exam 9 Spring 2019, Question 7
Study guide: Exam 9
Given the following bonds with annual coupon payments:
| Bond | Par Value | Time to Maturity (in years) | Annual Coupon Rate | Bond Price |
|---|---|---|---|---|
| 1 | $100 | 1 | 4% | $99.52 |
| 2 | $100 | 2 | 2% | Not Given |
| 3 | $100 | 3 | 2% | Not Given |
| 4 | $100 | 4 | 0% | $81.03 |
The following forward rate agreements, valued as of today, are available for an investor to purchase:
| Forward Rate Agreement | Lending Period Begins | Term | Principal | Annual Effective Interest Rate | Value (to Lender) |
|---|---|---|---|---|---|
| A | in 2 years | 1 year | $700,000 | 6.6% | $6,000 |
| B | in 3 years | 1 year | $1,600,000 | 7.7% | $19,500 |
Part a (2.25 points)
Calculate the price of Bond 3 assuming annually compounding interest.
Part b (0.75 points)
An investor has developed the following probability distribution for future short rates in year 4:
| Scenario | Year 4 Future Short Rate | Probability |
|---|---|---|
| 1 | 6% | 0.25 |
| 2 | 7% | 0.50 |
| 3 | 10% | 0.25 |
The investor is interested in purchasing Bond 4 but requires a liquidity premium of 1% in year 4 to engage in this long-term bond strategy. Based on the investor's expectation of future interest rates and liquidity premium criteria, recommend whether the investor should purchase Bond 4.
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