Question

you have been given this probability distribution for the holding for the holding-period return for GM stock. what is the expected standard deviation for GM stock

Answer 1

Answer:

14.86%

Explanation:

For computing the standard deviation, first we have to determine the expected return and then variance which is shown below:

= (Expected return of the boom × probability of boom) + (expected return of the normal growth × probability of normal growth) + (expected return of the recession × probability of recession)

= (0.30 × 0.40) + (0.11 × 0.40) + (-0.10 × 0.20)  

= 0.12 + 0.044 - 0.02

= 0.144

Now the variance would equal to the

= Probability × (Return - Expected Return) ^2

For boom:

= 0.40 × (0.30 - 0.144) ^2

= 0.0097344

For normal growth:

= 0.40 × (0.11 - 0.144) ^2

= 0.0004624

For recession:

= 0.20 × (-0.10 - 0.144) ^2

= 0.0119072

So, the total variance would be

= 0.0097344  + 0.0004624  + 0.0119072

= 0.022104

Now as we know that

Standard deviation is

$\sqrt{variance} \\\\ = \sqrt{0.022104}$

= 14.86%