Question

Consider a portfolio that is constituted by two projects, say A and B. Each project has a 1/10 chance of a loss of $10 million and a 9/10 of a loss $1 million. Moreover, each project has probabilities 1/3 and 2/3 of a loss of $1 million and $10 million respectively, given that the other project had a loss of $1 million, and probabilities 1/4 and 3/4 of a loss of $1 million and $10 million respectively, given that the other project had a loss of $10 million. School of Economics MSc in Applied Economics and Finance & MSc in Finance and Banking Bank Supervision, Risk Management and Derivatives Professor: Plutarchos Sakellaris T.A.: Stelios Giannoulakis 2 (a) What is the 97.5% VaR for each project? (b) What is the 97.5% expected shortfall for each project? (c) What is the 97.5% VaR for the portfolio? (d) What is the 97.5% expected shortfall for the portfolio?

Answer 1

a)

It is defined as the maximum dollar amount expected to be lost over a given time horizon, at a pre-defined confidence level. For example, if the 95% one-month VAR is $1 million, there is 95% confidence that over the next month the portfolio will not lose more than $1 million.

b)

When losses are not normally distributed, an expected shortfall with 97.5% confidence is liable to be quite a bit greater than VAR with 99% confidence. Expected shortfall in the FRTB is actually a stressed ES. It is to be calculated over the worst 250 days for the bank's current portfolio in recent memory