# Question: Suppose that each of two investments has a 4 chance

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.

(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.

**View Solution:**## Answer to relevant Questions

Suppose that daily changes for a portfolio have first-order correlation with correlation parameter 0.12. The 10-day VaR, calculated by multiplying the one-day VaR by , is $2 million. What is a better estimate of the VaR ...Suppose that the portfolio considered in Section 13.1 has (in $000s) 3,000 in DJIA, 3,000 in FTSE, 1,000 in CAC 40, and 3,000 in Nikkei 225. Use the spreadsheet on the authorâ€™s web site to calculate what difference this ...A company has a position in bonds worth $6 million. The modified duration of the portfolio is 5.2 years. Assume that only parallel shifts in the yield curve can take place and that the standard deviation of the daily yield ...Explain one way that the Doddâ€“Frank Act is in conflict with (a) the Basel international regulations (b) the regulations introduced by other national governments. Extend Example 20.3 to calculate CVA when default can happen in the middle of each month. Assume that the default probability during the first year is 0.001667 per month and the default probability during the second year is ...Post your question