MANG 6020 Financial Risk Management
Seminar 5
Question 1
Explain the difference between value at risk and expected shortfall.
Question 2
Explain the historical simulation method for calculating VaR.
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 (ES) 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.
Question 4
The change in the value of a portfolio in three months is normally distributed, with a mean of
$500,000 and a standard deviation of $3 million. Calculate the VaR and ES for a confidence
level of 99.5% and a time horizon of three months.
Question 5
Consider a position consisting of a $100,000 investment in asset A and a $100,000 investment in
asset B. Assume that the daily volatilities of both assets are 1% and that the coefficient of
correlation between their returns is 0.3. What is the 5-day 99% value at risk and expected
shortfall for the portfolio?
Seminar 5
Question 1
Explain the difference between value at risk and expected shortfall.
Question 2
Explain the historical simulation method for calculating VaR.
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 (ES) 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.
Question 4
The change in the value of a portfolio in three months is normally distributed, with a mean of
$500,000 and a standard deviation of $3 million. Calculate the VaR and ES for a confidence
level of 99.5% and a time horizon of three months.
Question 5
Consider a position consisting of a $100,000 investment in asset A and a $100,000 investment in
asset B. Assume that the daily volatilities of both assets are 1% and that the coefficient of
correlation between their returns is 0.3. What is the 5-day 99% value at risk and expected
shortfall for the portfolio?
