Value-At-Risk and Expected Short Fall [14 marks]

a) Consider stocks A and B whose annualised rate of return following normal distribution having the following characteristics:

Stock	Expected Value	Standard Deviation
A	5%	12%
B	8%	15%

The market risk free rate is 2%. Coefficient of correlation ( ) between the two stocks is 0.3.

i) What is the daily 99% VaR of a 10 million investment in the optimal portfolio consist of A and B? Given the 99% normal percentile is 2.33. Assume there are 252 trading days in a year. [6 marks]

ii) What is the 10-day 99% Expected Shortfall of the above portfolio? [2 marks]

b) The following shows the historical 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	-10.0%		18	1.0%
4	0.5%		19	7.0%
5	2.0%		20	19.0%
6	4.0%		21	4.0%
7	0.0%		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%

i) What is the 90% daily Value-at-Risk of an $1million investment in stock C? [1 mark]

ii) What is the 90% daily Expected Shortfall of an $1million investment in stock C? [1 mark]

iii) Using the results in part ii) and iii), explain why expected shortfall is more desirable than value-at-risk when used in regulatory requirement. [4 marks]