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.
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%
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