Principles of Banking - N1577

Seminar 6.

Value at Risk and Bank Capital

Question 1.

A fund manager announces that the fund’s one-month 95% Value at Risk is 6% of the size of the portfolio being managed. You have an investment of £100,000 in the fund managed. How do you interpret the portfolio manager’s announcement?

Question 2.

Suppose that the gain from a portfolio during six months is normally distributed with a mean of £2 million and a standard deviation of £10 million.

Find the portfolio’s 99% six-month VaR. (Use the standard normal distribution table)

What would be the six-month VaR at the 98%, 97%, 95% and 90% levels, respectively?

Question 3.

Suppose that each of two investments has a 4% chance of a loss of $10 million, a 2% chance of a loss of $1 million, and a 94% chance of a profit of $1 million. They are independent of each other.

(a) What is the VaR for one of the investments when the confidence level is 95%? (b) What is the expected shortfall when the confidence level is 95%?

(c) What is the VaR for a portfolio consisting of the two investments when the confidence level is 95%?

(d) What is the expected shortfall for a portfolio consisting of the two investments when the confidence level is 95%?

(e)  Show that, in this example, VaR does not satisfy the subadditivity condition whereas expected shortfall does.