Suppose that $10,000 is invested into an index fund. After a period of 5 years t

Question

Suppose that $10,000 is invested into an index fund. After a period of 5 years the value of the stock is expected to follow a normal distribution with a mean vale of $20,000 and a standard deviation of 5,000. questions: a) Find the value at risk for this investment by finding the 5th percentile; i.e, the bottom 5% of outcomes. b) What is the best case range? That is, what range of values represents the top 20% of outcomes? Do not find the entire percentile profile, only the best case range of values. c) What is the average case range? That is, what range of values represents the middle 20% of outcomes? Do not find the entire percentile profile, only the average case range of values.

Explanation / Answer

Let X be normal =20000,=5000

Find a such that

P(x>a)=.95

P(0<z<(20000-a)/5000)=.475

(20000-a)/5000=1.645

a=20000-5000(1.96)

a=10200

b)Top 20% of values=b

P(X>b)=.2

P((1000<x<(b-20000)/5000)=.2

P(0<z<(b-20000)/5000)=.0525

b=20000+.0525(5000)=202625

c =distance from mean to top of middle 20%

P(20000-c<x<20000+c)=.2

P(20000<x<20000+c)=.1

P(0<z<c/5000)=0.25

c=5000(.25)=1250

(1875,21250) contains middle 20%

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