Question

You have bought a stock for a $250. You are expecting to get a return of 12/% while the volatility of your stock is 22%. if you intend to sell the stock after one year.

a-      What is the stock price range (upper and lower bound) assuming that the stock returns are normally distributed, and a two-tailed confidence interval of 90%? explain your answer.

b-      What is the Value at Risk of this investment at a confidence interval of 90%? explain your answer.

c-      What are the similarities and differences in calculating the above questions (a and b)? Please support your answer by drawing the needed figures showing each case.

Answer 1

a.

for two-tailed confidence interval of 90%:

$z=\pm 1.645$

then, for stock return:

$\frac{x-\mu}{\sigma}=\pm 1.645$

we have:

$\mu=0.12,\sigma=0.22$

then return:

$0.12-1.645\cdot0.22<x<0.12+1.645\cdot0.22$

$-0.24<x<0.48$

price range:

$250(1-0.24)<p<250(1+0.48)$

$\$190<p<\$370$

b.

VAR is a probability-based measure of loss potential. It is an estimate of the minimum loss that is expected to be exceeded in a specified time period with a given level of probability.

 Value at Risk:

$VAR=(\mu-z\sigma)p=250(0.12-1.645\cdot0.22)=-\$60$

c.

similarities: both calculations founded on normal distribution

differences: in first case we use both negative and positive values of z score for confidence interval of 90%; in second case we use only positive value of z score for confidence interval of 90%