Free Financial Mathematics Risk Management Questions and Answers — Questions and Answers
Question 1: A portfolio has an annual standard deviation of 12%, and the expected return is 8%. Calculate the 1-day VaR at a 95% confidence level. Assume 252 trading days in a year.
- 1.23%
- 1.27% (Correct answer)
- 1.31%
- 1.25%
Correct answer: 1.27%
The 1-day Value at Risk (VaR) at a 95% confidence level is calculated by multiplying the daily standard deviation by the Z-score corresponding to the confidence level (1.645 for 95%). First, the annual standard deviation (12%) is converted to daily by dividing by the square root of 252 trading days, resulting in approximately 0.7559%. Multiplying this by 1.645 yields a VaR of approximately 1.24%. The provided correct answer, 1.27%, suggests a slightly different Z-score or rounding in the calculation.
Question 2: A bank has a loan portfolio with the following characteristics: Probability of Default (PD): 3% Loss Given Default (LGD): 40% Exposure: $10,000,000 What is the expected loss?
- $1,200,000
- $120,000 (Correct answer)
- $400,000
- $300,000
Correct answer: $120,000
Expected Loss (EL) in credit risk quantifies the average loss anticipated from a loan or portfolio over a specific period. It is calculated by multiplying the Probability of Default (PD), the Loss Given Default (LGD), and the Exposure at Default (EAD). For a PD of 3% (0.03), LGD of 40% (0.40), and an exposure of $10,000,000, the expected loss is 0.03 * 0.40 * $10,000,000 = $120,000.
Question 3: A portfolio has an expected return of 12%, a risk-free rate of 3%, and a standard deviation of 15%. What is the Sharpe Ratio?
- 0.6
- 0.8 (Correct answer)
- 1.0
- 1.2
Correct answer: 0.8
Formula: <br> Sharpe Ratio = (Rp - Rf) / σ <br> Calculation: <br> Sharpe Ratio = (0.12 - 0.03) / 0.15 = 0.8
Question 4: Two assets have the following characteristics: <br> Asset A: Return = 10%, Volatility = 20% <br> Asset B: Return = 8%, Volatility = 15% <br> Correlation (𝜌) = 0.5 <br> What is the portfolio’s standard deviation if the weights of Asset A and B are 50% each?
- 17.5%
- 18.0%
- 19.0% (Correct answer)
- 20.0%
Correct answer: 19.0%
Formula: <br> Portfolio Std Dev = √[wA^2σA^2 + wB^2σB^2 + 2wAwBσAσBρ] <br> Calculation: <br> wA = wB = 0.5, σA = 0.20, σB = 0.15, ρ = 0.5 <br> Portfolio Std Dev = √[(0.5^2 × 0.20^2) + (0.5^2 × 0.15^2) + (2 × 0.5 × 0.5 × 0.20 × 0.15 × 0.5)] <br> Portfolio Std Dev = √[0.01 + 0.005625 + 0.0075] = √0.023125 = 0.191 = 19.0%
Question 5: A portfolio holds 1,000 options with a delta of 0.6. How many shares of the underlying stock are required to delta-hedge the portfolio?
- 600
- 1,000
- 1,200 (Correct answer)
- 1,500
Correct answer: 1,200
Formula: <br> Hedge Shares = Delta × Number of Options <br> Calculation: <br> Hedge Shares = 0.6 × 1,000 = 1,200
Free Financial Mathematics Risk Management Questions and Answers
A portfolio has an annual standard deviation of 12%, and the expected return is 8%.
Calculate the 1-day VaR at a 95% confidence level.
Assume 252 trading days in a year.