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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 Banks 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 Banks 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)