Financial Mathematics Risk Management Flashcards

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.

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.

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?

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.

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?

Answer: 0.8

Formula: Sharpe Ratio = (Rp - Rf) / σ Calculation: Sharpe Ratio = (0.12 - 0.03) / 0.15 = 0.8

Two assets have the following characteristics: Asset A: Return = 10%, Volatility = 20% Asset B: Return = 8%, Volatility = 15% Correlation (𝜌) = 0.5 What is the portfolio’s standard deviation if the weights of Asset A and B are 50% each?

Answer: 19.0%

Formula: Portfolio Std Dev = √[wA^2σA^2 + wB^2σB^2 + 2wAwBσAσBρ] Calculation: wA = wB = 0.5, σA = 0.20, σB = 0.15, ρ = 0.5 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)] Portfolio Std Dev = √[0.01 + 0.005625 + 0.0075] = √0.023125 = 0.191 = 19.0%

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?

Answer: 1,200

Formula: Hedge Shares = Delta × Number of Options Calculation: Hedge Shares = 0.6 × 1,000 = 1,200