Risk Management Exercises

Exercise Value at Risk calculations

Problem Consider a stock S valued at $1 today, which after one period can be worth S T : $2 or $0.50. Consider also a convertible bond B, which after one period will be worth max(1, S T ). Determine which is the following three portfolios has lower VaR: 1.B 2.B-S 3.B+S

FRM exam 1999 The VaR of one asset is 300, and another one is 500. If the correlation between changes in asset prices is 1/15, what is the combined VaR?

Exercise Hedging

Problem Consider a stock S valued at $1 today, which after one period can be worth S T : $2 or $0.50. Consider also a convertible bond B, which after one period will be worth max(1, S T ). Determine the optimal trading strategy adding a stock portfolio to the bond.

Exercise Credit risk

Problem Consider a stock S valued at $1 today, which after one period can be worth S T : $2 or $0.50. Consider also a convertible bond B, which after one period will be worth max(1, S T ). Assume the stock can default, after which event S T =0. Determine which is the following three portfolios has lower Credit-VaR: 1.B 2.B-S 3.B+S