Question

4. Suppose that a mean of asset price is $50 and standard-deviation would be $1.51. If we assume that the change in the asset price is normally distributed, we can be 90% certain that the asset price will be between?

5. Suppose that we back-test a value at risk model using 1,000 days of data. The value at risk confidence level is 99% and we observe 15 exceptions. Should we reject the model at the 5% confidence level?

Answer 1

4. Given u-50, 5 = 1.51 since the data is normally distributed have to lind values betwees goes of ted Anda Pla< x < b) = 0.90 qol 250 b Praca < b = oogo scenarios peber and p(xra) are a d. As from graph i-peber = 0.05 And on 1-Plata) = 0.05 consider 1-pc box) = 0.05 => pcbs x) = 0-05 => pcxzb) =0.05 p( 2 b ) =0.05 Plze b- l = 0.05 As xu az ( re

:. 4- plzs b) = 005- • pizsb-) = 0.95 using Inverse - Normal table the value boll at 6.95 is b- l = 1.645 b- utcl.645) * - b= 50+ (1.645) 4.50 (b= 52.487 Now I-plara -0.05 P(xsa) =005 PCV <-4)= vos Plzs am) -0.05 osing Inverse Norssical ane = -1.645 a= -(1.645) a= 5) - C1.645) a.si a So-2.48 (a = 47.527 got certain that the asset price Es between C47.52, 52.44) will be

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