Financial Risk Manager Part 1

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Explanation:

Since all three bonds mature on the exact same date (30/09/2018) and have identical coupon frequencies (semiannual), we can price Tranche 2 using a no-arbitrage linear combination (replicating portfolio) of Tranche 1 and Tranche 3.

Let $w_1$ be the weight of Tranche 1 and $w_3$ be the weight of Tranche 3. We set up a system of equations for the principal and coupon rates:

$w_1 + w_3 = 1`$ 2) $1.5`\% \times w_1 + 3.0\% \times w_3 = 2.5\%$

Substitute $w_1 = 1 - w_3$ into the second equation: $1.5(1 - w_3) + 3.0w_3 = 2.5 $`$ 1.5- 1.5w_3 + 3.0w_3 = 2.5$ $1.5`w_3 = 1.0 \Rightarrow w_3 = \frac{2}{3}$

Then, $w_1 = 1 - \frac{2}{3} = \frac{1}{3}$ .

The price of Tranche 2 is the weighted average of the prices of Tranche 1 and Tranche 3: Price = $(\frac{1}{3} \times 97.54) + (\frac{2}{3} \times 103.72)$ Price = $32.5133 + 69.1467 = 101.66$

The price of Tranche 2 is USD 101.66.

Explanation:

Let $w_1$ be the weight of Tranche 1 and $w_3$ be the weight of Tranche 3. We set up a system of equations for the principal and coupon rates:

$w_1 + w_3 = 1`$ 2) $1.5`\% \times w_1 + 3.0\% \times w_3 = 2.5\%$

Substitute $w_1 = 1 - w_3$ into the second equation: $1.5(1 - w_3) + 3.0w_3 = 2.5 $`$ 1.5- 1.5w_3 + 3.0w_3 = 2.5$ $1.5`w_3 = 1.0 \Rightarrow w_3 = \frac{2}{3}$

Then, $w_1 = 1 - \frac{2}{3} = \frac{1}{3}$ .

The price of Tranche 2 is the weighted average of the prices of Tranche 1 and Tranche 3: Price = $(\frac{1}{3} \times 97.54) + (\frac{2}{3} \times 103.72)$ Price = $32.5133 + 69.1467 = 101.66$

The price of Tranche 2 is USD 101.66.

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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?

	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

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TTitan

Last updated: May 18, 2026 at 04:39

USD 101.527

50.0%

USD 101.887

50.0%

USD 103.028

USD 101.66