Practic:

1. Suppose returns are uncorrelated over time. You are given that the volatility over five days is 3.20%. What is the volatility over 60 days? 

2. Assume the possible one-year returns of a stock are normally distributed, with mean 15% and volatility 20%. What are the 95 percent confidence limits for the returns of the stock? 

3. A trader has made a profit of $15 million in foreign exchange. Assume that the face value of the contracts was $100 million, and the volatility of the JPY/$ rate is 16 percent per annum. The bank needs to hold enough capital to cover 99 percent of possible losses. What is the capital requirement to sustain this position? What is the risk-adjusted return on capital for the trader?

 4. If the one-year arithmetic rate of return for a stock is 20%, what is the geometric rate of return for the same period?

 5. A portfolio of $2 million has a daily expected return of 0% and a daily standard deviation of 1.33%. What is the annual standard deviation of this portfolio? (Assume 260 trading days in a year.)

 6. Using the same information from Q.8, what is the one-day VAR at 99 percent confidence level by using the analytical method? 

7. If costs follow a normal distribution with an expected value of $1 million and standard deviation of $0.2 million, what is the maximum probable cost with a 99 percent accuracy?

 8. Imagine a situation where there is a 40% chance of a $100 loss, a 40% chance of a $50 gain, and a 20% chance of a $350 gain. What is the expected value of this risky situation? 

9. If the one-day VAR at 95% confidence level of ABC Bank is $3 million, what is the 10-day VAR at 99% confidence level? 

10. The one-day 99% VAR of positions of ABC stock and XYZ stock are $365,000 and $207,000, respectively. Given that the correlation of returns of the two stocks is 0.6, what is the benefit of diversification by combining the two positions into a portfolio?

 11. The prices of an asset in Week 1 and Week 2 are $1500 and $1570, respectively. If the asset price changes at the same geometric rate of return of Week 2, what would be the asset price in Week 3? 

12. Currently your portfolio value is $200,000. According to your estimation, the expected profit for your portfolio in the next year will be $15,000. If the yearly VAR(mean) at 99% confidence level is $95,000, then you have 99% confidence your portfolio value in the next year will not be lower than ___________.