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ACFI 450 Application Problem Set 5 Spring 2024

Due by 11:59 PM on Monday, April 29, 2024

Record your responses to the questions in a Word or PDF file named YourLastName_APS5. If you choose

to perform your calculations in Excel, you may also submit your calculations in an Excel file also named

YourLastName_APS5. Your Excel file SHOULD NOT CONTAIN WRITTEN RESPONSES; it should ONLY

CONTAIN CALCULATIONS. Your responses should be free of grammar, spelling, and punctuation errors.

Upload and submit your file using the Application Problem Set 5 drop box by the deadline.

1. A financial institution has the following assets:

• A portfolio of 18-year zero-coupon bonds with a face value of $22 million and currently yielding

7.3%

• A €9 million trading position in spot euros, with the current exchange rate of $1.05/€

• A $14 million trading position in equities

a. Calculate the daily earnings at risk (DEAR) for the bonds, assuming a 62 basis point potential

adverse move in yields. (8 points)

b. Calculate the dollar DEAR for the position in euros, assuming a volatility of the daily percentage

changes in the €/$ of 43 basis points and 99% confidence that an adverse move will not exceed

this amount. (6 points)

c. Calculate the DEAR for the equity position, assuming the standard deviation of daily returns on

the equities is 342 basis points and 99% confidence that an adverse move will not exceed this

amount. (4 points)

d. Calculate the 9-day value at risk (VAR) for (i) the bonds, (ii) the euro position and (iii) the equity

position. (6 points)

e. Calculate the DEAR for a portfolio of these three assets. The correlation coefficients are 0.24 for

the bonds and the euros, -0.29 for the bonds and the equities, and 0.43 for the equities and the

euros. (8 points)

2. A commercial bank has the following balance sheet (market value, millions). It also has $89 M in

contingent assets and $125 M in contingent liabilities. Should these contingencies take place and

these items move onto the balance sheet, what is the effect on the bank’s equity? Reflect these

changes on its balance sheet. (6 points)

Assets Liabilities and Equity

Cash $ 24 Deposits $204

Loans 285 Borrowed funds 182

Securities 135 Equity 58

Total Assets $444 Total Liabilities and Equity $444

3. A securities firm is considering automating some of its portfolio maintenance activities. The cost to

install the system is $34.65 M. Until the system needs to be replaced in 5 years, the securities firm

expects $10.34 M in after-tax savings each year due to the automation. If the company’s cost of

capital is 12%, should it automate the processes? Support your recommendation. (6 points)

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4. A commercial bank has provided the balance sheet below. It has no off-balance sheet activities.

Corporate bonds have a 100% loan-to-value risk weight and residential mortgages have a 50% loan-

to-value risk weight.

Assets ($ millions) Liabilities and Equity ($ millions)

Cash $ 170 Deposits $ 1,328

U.S. Treasury securities 325 Subordinated debentures 146

Corporate bonds 753 Common stock 41

Residential mortgages 284 Retained earnings 17

Total Assets $ 1,532 Total Liabilities and Equity $ 1,532

a. Calculate each of the following ratios. For each ratio, also explain which capital category zone

the bank falls into. (4 points each)

i. CET1 risk-based capital ratio

ii. Tier I risk-based capital ratio

iii. Total risk-based capital ratio

iv. Tier I leverage ratio

b. Given your calculations and the capital categories in a., what prompt corrective actions will be

required of the bank by its regulators? Explain. (4 points)

5. A securities firm has provided the balance sheet below.

Assets ($ millions) Liabilities and Equity ($ millions)

Cash $ 46 Short-term funding $ 65

Debt securities 680 Bonds 593

Equity securities 1,045 Debentures 1,145

Other assets 56 Equity 24

Total Assets $ 1,827 Total Liabilities and Equity $ 1,827

The debt securities have an annual 6.42% coupon rate, 15 years to maturity and a yield to maturity

of 7.43%. The market value of the equity securities and the other assets is equal to their book value.

The firm has 1,750,000 shares outstanding and the price per share is $12.68.

a. Calculate the firm’s aggregate indebtedness to net capital ratio. (5 points)

b. Calculate the firm’s highly liquid assets to total liabilities ratio. (5 points)

c. Based on the firm’s ratios from a and b, is it in compliance with Rule 15C 3-1? Why or why not?

(3 points)

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6. The risk-based capital charges for a life insurance company are provided below. The insurer has total

capital and surplus of $65.32 M.

Risk RBC Charge (millions)

Asset risk–affiliate (C0) $ 5.22

Asset risk–other investments (C1o) 3.87

Asset risk–common stock (C1cs) 12.56

Insurance risk (C2) 16.43

Interest rate risk (C3a) 10.76

Health credit risk (C3b) 4.32

Market risk (C3c) 7.93

Business risk (C4a) 8.15

Health business risk (C4b) 1.42

a. Calculate the (i) risk-based capital (RBC) charge and (ii) RBC level for the insurance company. (7

points)

b. What supervisory action level applies to this insurer? Support your response with the calculation

results from a. (3 points)

c. How much capital, if any, must the insurer raise to comply with the regulatory requirement? (3

points)

7. The risk-based capital charges for a property-casualty insurance company are provided below. The

insurer has total capital and surplus of $265.43 M.

Risk RBC Charge (millions)

Asset risk–OBS and affiliated P&C (R0) $ 6.43

Asset risk–fixed income (R1) 6.72

Asset risk–equity (R2) 12.87

Credit risk (R3) 9.35

Underwriting risk–premium (R4) 95.43

Underwriting risk–reserve (R5) 50.46

Catastrophe risk (Rcat) 78.92

a. Calculate the (i) risk-based capital (RBC) charge and (ii) RBC level for the insurance company. (7

points)

b. What supervisory action level applies to this insurer? Support your response with the calculation

results from a. (3 points)

c. How much capital, if any, must the insurer raise to comply with the regulatory requirement? (3

points)