Explanation:
Cash flow at maturity:
| Notional | Coupon | |
|---|---|---|
| Tranche 1 | 100 | 0.75 |
| Tranche 2 | 100 | 1.25 |
| Tranche 3 | 100 | 1.50 |
Based on the law of one price, if we can construct a portfolio (using tranches 1 and 3) that has the same cash flow as Tranche 2, then both should have the same price.
Suppose we invest x% in Tranche 1 and (100-x)% in Tranche 3. In order to ensure the same cash flow x, the formula is the following:
x \times 0.75 + (1 - x) \times 1.5 = 1.25 \rightarrow x = 33.33\% $`$33.33`% invested in Tranche 1 and 66.67% invested in Tranche 3 will cost: $`$33.33`\% \times \text{USD } 97.54 + 66.67\% \times \text{USD } 103.72 = \text{USD } 101.66Ultimate access to all questions.
Q.18 The Treasury Department of a regional bank recently got additional liquidity, amounting to USD 10,000,000. Gayane Gag, head of the treasury department, is interested in a T-Bond that is maturing at the end of September 2017. The tranche is paying a coupon rate of 2.5%. Although the tranche is not actively traded on the market, Gayane manages to collect the following information:
| Maturity | Coupon Rate | Price (per USD 100 face value) | Coupon frequency | |
|---|---|---|---|---|
| Tranche 1 | 30/09/2018 | 1.5% | USD 97.54 | Semiannual |
| Tranche 2 | 30/09/2018 | 2.5% | n/a | Semiannual |
| Tranche 3 | 30/09/2018 | 3% | USD 103.72 | Semiannual |
All three tranches have a semiannual frequency of coupon payments. Based on the above information, what is the price of Tranche 2?
A
USD 101.527
B
USD 101.887
C
USD 103.028
D
USD 101.66
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