22. Refer to slide 77 of Chl notes. a. Calculate an 85% VaR from the distribution given. b. Repeat part a. for a 30% VaR. 0. Instead of the distribution given on slide 77, suppose the loss distribution is in fact normal with mean 50 and standard deviation 15. Repeat part a. p.77 Loss Distribution Frequency 00 O 0 10 20 30 40 50 60 70 80 90 Loss Amount (in million dollars) N:50+40+30+20+20+30+10=200 200 X 95% = 190 95% VGR : P095 2 70 There is 95% condence that over the next period of time the investment will not lose more than $70 million. A company uses VaR to measure and control the level of risk exposure. VaR T Risk T 200 x 90% = 180 (180 160) 90% VGR : P090 2 60 + m X (70 60) = 66.67 Normal Distribution and Other Statistics VaR (Value-at-Risk) . Suppose an investment has the following historical loss distribution: Loss Distribution 60 50 40 Frequency 30 20 10 10 20 30 40 50 60 70 80 90 Loss Amount (in million dollars) . Thus, the 95% VaR would be 70 million dollars. . What is the practical meaning? . How can we estimate the 90% VaR from the above distribution? C.W. Kwan, Eric Li (SAAS ., , HKU ) STAT1600 Statistics: Ideas and Concepts Ch 1 77 / 80