EVT, when used in the context of operational risk measurement, focuses on tail events and attempts to build a distribution of losses beyond what is covered by VaR. Statements I, II and II are correct. Statement IV describes conditional VaR (CVAR) and not EVT.

Choice 'c' is the correct answer.

Marginal liquidity gap measures the expected net change in liquidity over, say, a day. It is just equal to the liquidity inflow minus liquidity outflow. The cumulative liquidity gap measures the aggregate change in liquidity from a point in time, in other words it is just the summation of the marginal liquidity gap for each of the days included in the period under consideration. The residual liquidity gap goes one step further and adds available 'opening balance' of liquidity to the cumulative liquidity gap to reveal the days or times when the net liquidity is most at risk.

Liquidity at Risk measures the expected time to survival at a certain confidence level applied to the firm's cash flows - and is not a measure of the liquidity gap.

Therefore Choice 'a' is the correct answer.

Explantion:

Changing leverage does not affect the Sharpe ratio or the Information ratio. However, leverage magnifies both risk and return. Therefore Choice 'b' is the correct answer. Recall that Sharpe ratio is the ratio of the excess returns (over the risk free rate) of an investment to its standard deviation, and the information ratio is the ratio of the 'alpha' returns to the standard deviation of such returns.

Be wary of questions asking you to calculate VaR where the mean or expected returns are different from zero. The VaR formula of z-value times standard deviation needs to have an adjustment for the expected return [ie use VaR = z-value times standard deviation minus expected return]. In this case, the standard deviation for 1 day for the portfolio is =SQRT(1/250)*20%*$10m = $126,491. The VaR is therefore (2.326 * $126,491) - ($10,000,000 * 10% * 1/250) = $290,218.

I, III and IV represent situations where Monte Carlo simulations can be employed. I is not a situation where Monte Carlo can be used, as there is no basis available to simulate the returns. When no distribution assumption is possible, it may be advisable to use historical simulations. Therefore Choice 'd' is the correct answer, and the others are incorrect.

When a derivative transaction is entered into, its value generally is close to zero. Over time, as the value of the underlying changes, the transaction acquires a positive or negative value. It is not possible to predict the future value of the transaction in advance, however distributional assumptions can be made and potential exposure can be measured in multiple ways. Of all the possible future exposures, it is generally positive exposures that are relevant to credit risk because that is the only situation where the bank may lose money from a default of the counterparty.

The maximum (generally a quantile eg, the 97.5th quantile) exposure possible over the time of the transaction is the 'Potential Future Exposure', or PFE.

The average of the distribution of positive exposures at a specified date before the longest trade in the portfolio is called 'Expected Exposure', or EE.

The expected positive exposure calculated as the weighted average of the future positive Expected Exposure across a time horize is called the EPE, or the 'Expected Positive Exposure'.

The price that would be received to sell an asset or paid to transfer a liability in an orderly transaction between market participants at the measurement date - is the 'fair value', as defined under FAS 157.

Therefore the corect answer is that EPE is the weighted average of the future positive expected exposure across a time horizon.

Note that events of default under the ISDA MA are caused by one of the parties that is considered 'at fault'. In contrast, "termination events" are events for which no one is at fault, for example changes in legislation, illegality etc that still justify termination of the transactions under the contract.

The ISDA MA describes the following 8 types of events of default:

1. failure of pay or deliver

2. breach of agreement

credit support default

4. misrepresentation

5. default under specified transaction

6. cross default

7. bankruptcy

8. merger without assumption

All of the options presented in the question are events of default.