Suppose a portfolio of risky assets has an expected return of 5.57% [E(r) = 0.05

Question

Suppose a portfolio of risky assets has an expected return of 5.57% [E(r) = 0.0557] and a standard deviation of 20.33% [sigma = 0.2033]. For the questions below assume normal distribution. Use the "Standard Normal Distribution Table" provided in CROPS under "Excel Files" to answer the questions. (a) What is the probability that the portfolio will fall by more than 15% this year? (b) What is the probability that the portfolio will rise by more than 30% this year? (c) What is the 5% Value of Risk (VaR) of this portfolio?

Explanation / Answer

a. mean = 0.0557

sigma = 0.2033

P(return<-0.15) = P((return-mean)/sigma<(-0.15-0.0557)/0.2033)

=P(z<-1.012) =0.1557

b. P(return>0.3) = P((return-mean)/sigma>(0.3-0.0557)/0.2033)

=P(z>1.202) =0.885

c. For 5%VaR, we want 5% of the times worst loss.

So, return = mean + Z0.05*sigma = 0.0557 + 1.645*0.2033 = 0.3901

As VAR is expressed as positive for loss, VAR here is -0.3901 = -39.01%

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