Question

An investor owns 12,000 shares of a particular stock. The current market price is R100.
What is the “worst case” value of the portfolio in six months? For the purposes of this
question, define the worst case value of the portfolio as the value which is such that there is only a 1% chance of the actual value being lower. Assume that the expected return and
volatility of the stock price are 8.5% and 23%, respectively.

Answer 1

Assumption : Expected Return is for 6 months

(In case you assume it to be annual take the value as =8.5/2=4.25%)

Step1

Given

No.of shares=12000

CMP= R100

Expected Return =8.5%

Volatility (Standard Deviation)=23%

Confidence Level=99%(1% Chance of actual value being lower)This will be seen in normal distribution table to calculate z value

The above information is provided to calculate VALUE AT Risk

It mean the value of risk, How risky an investment is. Hence worst case scenario can be anlaysed by the following formula

STEP2

Value at risk of A portfolio

VAR=mean+(Zvalue*Standard deviation)

(z value multiplied by Sd denotes volatility)

Mean in this case is Expected return

Z value as per normal distribution table for 1% is -2.33

8.5%-2.33*23%=-45.09%

Step 3 Worst Case Scenario for the portfolio

Value of portfolio=12000*100=R1200000

Value of portfolio*(1+var)

1200000*(1+(-0.4509)

=1200000*(1-0.4509)

=1200000*(0.54910)=R658920