Value-At-Risk and Expected Shortfall

1. Consider stocks A and B whose annualised rate of return having the following characteristics

Stock	Standard Deviation
A	12%
B	15%

• Coefficient of correlation (r) between the two stocks is 0.3

1. What is the daily 99% VaR of a portfolio consisting of $5 million of Stock A and $10 million of stock B? Given the 99% normal percentile is 2.33. Assume there are 252 trading days in a year
2. What assumptions on the statistic model have you made in the calculation (i)?
3. The following shows the return series of Stock C

Day	Daily return of Stock C		Day	Daily Return of Stock C
1	12.0%		16	9.0%
2	12.0%		17	16.0%
3	-8.0%		18	-1.0%
4	-2.0%		19	7.0%
5	2.0%		20	19.0%
6	4.0%		21	4.0%
7	-2.0%		22	14.0%
8	5.0%		23	11.0%
9	9.0%		24	6.0%
10	28.0%		25	11.0%
11	-50.0%		26	-1.0%
12	10.0%		27	-2.0%
13	6.0%		28	2.0%
14	4.5%		29	6.5%
15	1.0%		30	3.2%

1. What are the procedures required to find the 90% daily Value-at-Risk (VaR) of stock C using historical simulation?
2. What is the 90% daily Value-at-Risk of $1million investment in Stock C?
3. What is the 90% daily Expected Shortfall of an $1million investment in stock C?
4. Using the results in part ii) and iii), explain why the expected shortfall is more desirable than value-at-risk when used in regulatory requirement

Please note this is a practice question for final exam of AFIN352