Finance Assignment 2: Asset-Liability Management and Binomial Trees

This finance assignment focuses on managing interest rate risk within a financial firm's asset and liability portfolio using a duration matching strategy. The assignment provides details on two investments and three bond liabilities, including coupon rates, terms to maturity, and yield to maturity. The solution involves calculating the present values of both assets and liabilities to balance the balance sheet. The calculations include discounted cash flows for the assets and liabilities, determining the market value of the portfolio. Furthermore, the assignment brief includes the construction of a three-year binomial interest rate tree using given spot rates, one-year forward rates, and volatility of the one-year forward rate to model interest rate movements over time. The goal is to balance the market value and duration of the investments to match the liabilities, effectively mitigating interest rate risk within the portfolio. The solution details the steps taken to calculate the bond values and the final market value of the portfolio, indicating a significant negative market value, highlighting the firm's potential exposure to interest rate fluctuations.

Finance

Assignment 2
Investment 1:
Assets
Notes pay-out instrument, coupon rate of 7% payable semi-annually, 15 year term to maturity
and par value is returned to investors at maturity. The current yield to maturity is 4% and a total
face value of $6 million.
Investment 2:
Liabilities
Bond Pay-out
Frequency
Par
Value
Term to
Maturity
Coupon
Rate
YTM Face Value of
Bonds
1 Annual $1000 10 years 8% 6% $2 million
2 Semi-annual $1000 15 years 5% 5.5% $3 million
3 Semi-annual $1000 5 years 2% 1.1% $4 million
Ans.
Assets Discounted Cash Flows
Bond: ($6,000,000*7%/2)/(1+0.02/2) =
202898.55
($6,000,000 + $ 2,10,000)/(1+0.02/2)15 =
3581314.87
37,84,213.42
Assets Value 37,84,213.42

Liabilities Discounted Cash Flows
Bond: ($2,000,000*8%)/(1+0.08) =
$1,60,000/1.08 = $1,48,148
= $21,60,000/(1+0.08)10 = $10,00,509.52
$11,48,657.52
($3,000,000*5%/2)/(1+5%/2) = $75,000/1.025
= $73,170
($3,000,000 +$75,000)/(1.025)15 =
$30,75,000/1.4845 = $20,71,404
$21,44,574
($4,000,000*2%/2)/(1+2%/2) = $40,000/1.01
= $39,603
($4,000,000 + $40,000)/(1+0.01)5 =
$40,40,000/(1.01)5 = $40,40,000/1.0510 =
$38,43,958
$38,83,561
Liabilities value $71,76,792.52
Market Value = $37, 84,213.42 - $$71, 76,792.52 = -$33, 92,579.1