Free Financial Mathematics Risk Management 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.

Accepted Answer

1.27%

Answer

1.23%

Answer

1.31%

Answer

1.25%

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?

Accepted Answer

$120,000

Answer

$1,200,000

Answer

$400,000

Answer

$300,000

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?

Accepted Answer

0.8

Answer

0.6

Answer

1.0

Answer

1.2

Question 4

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?

Accepted Answer

19.0%

Answer

17.5%

Answer

18.0%

Answer

20.0%

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?

Accepted Answer

1,200

Answer

600

Answer

1,000

Answer

1,500