Risk Management

Exercises

Exercise

Value at Risk calculations

Problem

Consider a stock S valued at $1 today, which after one period can be worth ST: $2 or $0.50.

Consider also a convertible bond B, which after one period will be worth max(1, ST).

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?

1. 525

2. 775

3. 600

4. 700

Exercise

Hedging

Problem

Consider a stock S valued at $1 today, which after one period can be worth ST: $2 or $0.50.

Consider also a convertible bond B, which after one period will be worth max(1, ST).

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 ST: $2 or $0.50.

Consider also a convertible bond B, which after one period will be worth max(1, ST).

Assume the stock can default, after which event ST=0.

Determine which is the following three portfolios has lower Credit-VaR:

1. B2. B-S3. B+S