Homework Answers
Since it is a pure discount bond then there it is no coupon available with this.
YTM and Sport price will be same in this case
Face Value =$1,000
Using the formula
| Maturity | Price | Spot Rate |
| 1 | 952.38 | 5.00% |
| 2 | 898.47 | 5.50% |
| 3 | 847.62 | 5.67% |
| 4 | 799.64 | 5.75% |
| 5 | 754.38 | 5.80% |
Forward rate of interest: 1 + fn = (1 + yn)n/(1 + yn-1)n-1
Where f is spot rate
y is the spot rate of nth period and previous period
Forward rate = Future Interest Rate + liquidity premium
Therefore Future Interest Rate = Forward rate - Liquidity premium
Using the above formula
| Maturity | Price | Spot Rate | Forward Rate | Future Interest Rate |
| 1 | 952.38 | 5.00% | ||
| 2 | 898.47 | 5.50% | 6.00% | 5.00% |
| 3 | 847.62 | 5.67% | 6.00% | 5.00% |
| 4 | 799.64 | 5.75% | 6.00% | 5.00% |
| 5 | 754.38 | 5.80% | 6.00% | 5.00% |
c)
Below table summarize the result
| Maturity | Liquidity premium | Future Interest Rate | Forward rate = Future Interest Rate + liquidity premium | Spot Rate |
| 1 | 5% | 5.00% | 5.00% | |
| 2 | 1% | 4.50% | 5.50% | 5.25% |
| 3 | 1% | 4.50% | 5.50% | 5.33% |
| 4 | 1% | 4.50% | 5.50% | 5.37% |
| 5 | 1% | 4.50% | 5.50% |
5.40% |
(d)
When Liquidity premium increases by 0.5%, below table summarizes the results:
| Maturity | Liquidity premium | Future Interest Rate | Forward rate = Future Interest Rate + liquidity premium | Spot Rate |
| 1 | 5% | 5.00% | 5.00% | |
| 2 | 1.5% | 4.50% | 6.00% | 5.50% |
| 3 | 1.5% | 4.50% | 6.00% | 5.67% |
| 4 | 1.5% | 4.50% | 6.00% | 5.75% |
| 5 | 1.5% | 4.50% | 6.00% |
5.80% |
please comment if you need any further clarification
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