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Application Problem Set

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)

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
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 $10.34 M in after-tax savings each year due to the automation. If the company’s cost of
capital is 12%, should it automate the processes? Support your recommendation. (6 points)
2
A commercial bank has provided the balance sheet below. It has no off-balance sheet activities.
Corporate bonds have a 100% loan-to-value risk weight and residential mortgages have a 50% loanto-value risk weight.
Assets ($ 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)
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)

Full Answer Section

c. Equity:

Use the inverse normal function to find the 99th percentile value considering the standard deviation and confidence level.
Multiply the percentile value by the standard deviation to get daily earnings at risk.

d. 9-day Value at Risk (VAR):

Multiply the daily VAR by the square root of 9 (assuming a normal distribution).

e. Portfolio VAR:

Use the individual VARs and correlation coefficients to calculate the portfolio VAR using a variance-covariance approach.

2. Contingent Liabilities

Contingent assets and liabilities become actual assets and liabilities when the contingencies occur.
To reflect the changes, add contingent assets to total assets and subtract contingent liabilities from total equity.
Analyze the impact on the bank's capital ratios (e.g., capital adequacy ratio) due to the changes.

3. Automation Cost-Benefit Analysis

Calculate the net present value (NPV) of the after-tax savings using the cost of capital as the discount rate.
If the NPV is positive, automation is recommended due to cost savings outweighing the initial investment.

4. Risk-Based Capital Ratios

Calculate risk-weighted assets by multiplying each asset class by its risk weight.
Divide risk-weighted assets by Tier 1 capital, Tier 1 risk-based capital, total capital, and total assets to get the respective ratios.
Compare the ratios to regulatory capital adequacy requirements to determine the capital category zone.

5. Securities Firm Ratios

a. Aggregate indebtedness to net capital ratio:

Calculate the firm's net capital by subtracting subordinated liabilities from equity.
Divide total liabilities by net capital.

b. Highly liquid assets to total liabilities ratio:

Identify highly liquid assets (e.g., cash, marketable securities).
Divide highly liquid assets by total liabilities.

c. Rule 15C 3-1 Compliance:

Compare the calculated ratios to the regulatory limits set by Rule 15C 3-1 (limits may vary).
If either ratio is above the limit, the firm is not in compliance.

Important Note:

It's crucial to consult financial regulations and refer to official sources for specific requirements and calculations.

Sample Answer

1. Value at Risk (VAR) Calculations

a. Bonds:

Calculate the change in bond price due to a 62 basis point yield increase.
Multiply the price change by the face value to get daily earnings at risk.

b. Euros:

Use the delta-normal approach considering the volatility and confidence level.
Delta is the change in the dollar value of the euro position due to a small change in the euro exchange rate.