RISK5009
Risk Management Strategy
Assignment 2
Instructions:
• The full mark is 100. “Your mark (between 0 - 100) * 15%” will be included in your final grade.
• Due time: 23:00, Monday, 18 November 2024
• All answers must be combined into one single PDF, in the exact order of the questions, submit this single PDF to Turnitin on Moodle (Risk5009).
• Assignment Name: Your Student Number + assignment 2 e.g., z1234567_assignment 2.pdf
1. A portfolio is composed of three stocks (stock A, B and C). Each valued at $3m. Their expected returns and covariance matrix over the next 3 months are estimated at:
Note: the numbers are in annualized terms.
Assuming normal distributions for the returns, the portfolio variance is calculated to be 5%.
a. Find the 1-week 95% VaR for stock A.
b. Find the 1-week 95% VaR for stock B.
c. Find the 1-week 95% VaR for stock C.
d. What is the undiversified VaR for the portfolio?
e. Find the 1-week 95% VaR for this portfolio (diversified VaR).
2. An estimated linear probability model has been developed to predict business loan applicant default probabilities by Bank XYZ. The model is given by
PD = 0.03X1 + 0.02X2 − 0.05X3 + error,
where X1 is the borrower's debt/equity ratio, X2 is the volatility of borrower earnings, and X3 is the borrower’s profit ratio.
The bank receives a particular loan applicant, X1 = 0.65, X2 = 0.25, and X3 = 0.10,
a. What is the projected probability of default for the borrower?
b. What is the projected probability of default if the debt/equity ratio is 2?
c. What are major weaknesses of the linear probability model?
3. A bank charges a base lending rate of 10% for a loan. The expected probability of default for the loan is 5%.
a. Assume no recovery if the loan is defaulted, what is the expected return on this loan?
b. If the loan is defaulted, the bank expects to recover 50% of its money through the sale of its collateral. What is the expected return on this loan?
4. The Bank BBB has two loans of $1m each: loan 1 has an expected return of 8% and a standard deviation of return of 10%; loan 2 has an expected return of 12% and a standard deviation of return of 18%, respectively. All information is annualized.
a. If the correlation coefficient between loan 1 and loan 2 is 0.2, what are the expected return and standard deviation of this loan portfolio?
b. What is the standard deviation of the portfolio if the correlation is 0?
c. What is the standard deviation of the portfolio if the correlation is -0.2?
5. For a given planning period, the balance sheet information of Bank AAA is given by:
Rate-sensitive assets (RSA) = $200m, Rate-sensitive liabilities (RSL) = $150m.
a. Calculate the net interest income of a 0.8% decrease in interest rates on both assets and liabilities.
b. Calculate the net interest income if interest rates on RSAs decrease by 1% but interest rates on RSLs decrease by 1.5%.
6. Bank KKK’s balance sheet information is listed (amounts in thousands of dollars and duration in years) as following:
Assets Liabilities and Equity
|
T-bills
|
90
|
Duration (0.60)
|
Deposits
|
2,092
|
Duration (1.00)
|
|
T-notes
|
55
|
Duration (0.90)
|
Federal funds
|
238
|
Duration (0.02)
|
|
T-bonds
|
176
|
Duration (4.39)
|
|
|
|
|
Loans
|
2,724
|
Duration (7.00)
|
|
|
|
Total assets $3045 Total liabilities 2330
Equity 715
Total liabilities & equity $3045
a. What is the duration of all the assets?
b. What is the duration of all the liabilities?
c. What is the leverage adjusted duration gap?
d. What is the impact on the market value of equity caused by interest rate shock of 0.5% (i.e., ΔR/(1+R) = 0.5%)?
e. If the interest rate shock was downward by 0.2% (i.e., ΔR/(1+R) = -0.2%), what is the impact on the market value of equity?