FINM3404 Final Exam (Practice) - Solutions Semester 1, 2022
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FINM3404 Final Exam (Practice) - Solutions
Semester 1, 2022
Question 1. (10 marks)
WQF Bank has assets of $3 million invested in a 30-year, 10 percent semi-annual coupon Treasury Bond selling at par. The duration of this bond has been estimated at 7 years. The assets are financed with equity and a $750000, two-year, 8 percent semi-annual coupon capital note selling at par.
a. What is the leverage adjusted duration gap of WQF Bank? (3 marks)
b. What is the impact on equity value if the relative change in all market interest rates is a decrease of 25 basis points? Note: The relative change in interest rates is ΔR/(1+R/2) = –0.0025. (2 marks)
c. Using the information calculated in parts (a) and (b), what can be said about the desired duration gap for a financial institution if interest rates are expected to increase or decrease? (2 marks)
d. Verify your answer to part (c) by calculating the change in the market value of equity assuming that the relative change in all market interest rates is an increase of 20 basis points. (2 marks)
e. What would the duration of the assets need to be to immunise the equity from changes in market interest rates? (1 mark)
ANSWER (a)
Calculate the duration of liabilities:
Par value (in 000) = $750, Coupon rate = 8%, Semi-annual payments R = 8%, Maturity = 2 years
T |
CF |
PV of CF |
PV of CF × t |
0.5 |
30.0 |
28.84615385 |
14.42307692 |
1 |
30 |
27.73668639 |
27.73668639 |
1.5 |
30 |
26.66989076 |
40.00483614 |
2 |
780 |
666.747269 |
1333.494538 |
|
Total = |
750 |
1415.6591 |
Duration = $1415.6591/$750.00 = 1.8875
The leverage-adjusted duration gap can be found as follows: Leverage − adjusted duration gap = [ − ] = 7 − 1.8875 = 6.5281 years
ANSWER (b)
The change in net worth using leverage adjusted duration gap is given by:
= −[ − ] ∗ ∗ = − 7 − (1.8875) 7.530 (3 000 000)(− .0025)
= $48,960.94
ANSWER (c)
If the FI wishes to be immune from the effects of interest rate risk (either positive or negative changes in interest rates), a desirable leverage-adjusted duration gap (DGAP) is zero. If the FI is confident that interest rates will fall, a positive DGAP will provide the greatest benefit. If the FI is confident that rates will increase, then a negative DGAP would be beneficial.
ANSWER (d)
= −[ − ] ∗ ∗ = − 7 − (1.8875) 7.530 (3 000 000)(0.002)
= − $39, 168.75
ANSWER (e)
Immunising the equity from changes in interest rates requires that the DGAP be 0. Thus, (DA – DLk) = 0 ⇒ DA = DLk, or DA = 1.8875 × (750/3000) = 0.4719 years.
Question 2.
(10 marks)
a. Using regression analysis on historical loan losses, a bank has estimated the following:
XC = 0.005 + 0.7XL and
XH = 0.008 + 1.9XL
where XC = loss rate in the business sector
XH = loss rate in the consumer (household) sector
XL = loss rate for its total loan portfolio
i. If the bank’s total loan loss rates increase by 20 percent, what are the increases in the expected loss rates in the business and consumer sectors? (1 mark)
ii. In which sector should the bank limit its loans, and why? (2 marks)
ANSWER (a) (i)
Business loan loss rates will increase by 0.005 + 0.7(0.20) = 14.50 percent. Consumer loan loss rates will increase by 0.008 + 1.9(0.20) = 38.80 percent.
ANSWER (a) (ii)
The bank should limit its loans to the consumer sector because the loss rates are systematically higher than the loss rates for the total loan portfolio. Loss rates are lower for the business sector. For a 20 percent increase in the total loan portfolio, the consumer loss rate is expected to increase by 38.80 percent, as opposed to only 14.50 percent for the business sector.
b. The following table shows the allocation of the loan portfolio to different sectors for BNM Bank and LRT Bank:
Sector |
(1) National |
(2) BNM Bank |
(3) LRT Bank |
Real estate |
35% |
55% |
20% |
Business |
25% |
30% |
15% |
Individuals |
20% |
10% |
55% |
Others |
20% |
5% |
10% |
|
100% |
100% |
100% |
Calculate loan allocation deviation from national benchmark both for BNM Bank and LRT Bank. Explain which bank deviates significantly from the national benchmark. (7 marks)
ANSWER (b)
BNM Bank’s deviation on loan portfolio allocation:
Real estate |
(0.55 – 0.35)2 = |
0.0400 |
Business |
(0.30 – 0.25)2 = |
0.0025 |
Individuals |
(0. 10 – 0.20)2 = |
0.0100 |
Others |
(0.05 – 0.20)2 = |
0.0225 |
|
Total = |
0.0750 |
σBNM = = 0.1369 or 13.69%
LRT Bank’s deviation on loan portfolio allocation:
Real estate |
(0.20 – 0.35)2 = |
0.0225 |
Business |
(0. 15 – 0.25)2 = |
0.0100 |
Individuals |
(0.55 – 0.20)2 = |
0.1225 |
Others |
(0. 10 – 0.20)2 = |
0.0100 |
|
Total = |
0.1650 |
σLRT = = 0.2031 or 20.31%
Comments:
LRT Bank deviates significantly from the national benchmark than BNM Bank because LRT Bank’s standard deviation on loan portfolio allocation (20.31%) is higher than that of BNM Bank (13.69%).
Question 3.
(10 marks)
You can obtain a loan of $200000 at a rate of 15 percent for two years. You have a choice of (i) paying the interest (15 percent) each year and the total principal at the end of the second year or (ii) amortising the loan, that is, paying interest (15 percent) and principal in equal payments each year. The loan is priced at par.
a. What is the duration of the loan under both methods of payment? (8 marks)
b. Explain the difference in the two results. (2 marks)
2022-06-16