## Value at risk

mayankmundhra30
Good Student
Posts: 23
Joined: Sat Jun 25, 2016 8:13 am

### Value at risk

You are hired as the credit risk manager for a large bank. You find that the bank’s credits are poorly diversified. The bank has an extremely large exposure to one firm with a BB rating. All its other loans have the equivalent of an AAA rating. You recommend that the bank diversify its credit exposures. After the bank follows your advice, you are summoned to the CEO’s office and fired. The CEO says that they followed your advice, acquired many small exposures to firms with BB ratings to replace the large exposure, and all it did was to make the bank riskier because its credit VaR increased. The bank measures its credit VaR as the maximum loss of principal over one year at the 1% level. You seek advice from a consultant to make sure not to repeat the mistake you made. Which of the following explanations provided by the consultant is correct?
a. VaR necessarily falls as diversification increases. Consequently, the bank’s software to compute VaR must be flawed. Incorrect
b. The VaR would not have increased had the bank measured it as a shortfall relative to the expected value of the banking book. Correct
c. The bank did not diversify since it replaced one exposure with a BB rating with multiple exposures with a BB rating. Incorrect
d. The VaR would not have increased had the bank not used the normal distribution for the portfolio return. Incorrect
Why the answer is B and not C?

2) ortfolio A has a 1-day, 95% VaR of \$5 million. Portfolio B has a 1-day, 95% VaR of \$7 million. Is it possible for the 1-day, 95% VaR of the combined portfolio (A + B) to be greater than \$12 million?
a. No, never Incorrect
b. Yes, but only if the positions in the two portfolios are perfectly correlated Incorrect
c. Yes, but only if the tails of the loss distributions for A and B are not monotonically decreasing Correct
d. Yes, but only if the loss distribution for one portfolio is skewed to the right, and the loss distribution for the other is skewed to the left

edupristine
Finance Junkie
Posts: 981
Joined: Wed Apr 09, 2014 6:28 am

### Re: Value at risk

a) The reason for By diversifying, the bank swaps the small probability of a large loss for the certainty of a small loss. Yet, the expected value of the banking book is unchanged and the volatility of the terminal value of the banking book has fallen.

b) This is possible but unusual. It does remind us that we usually need the whole distribution and not just a single point to aggregate VARs.