Question

Consider an economy with two types of firms, S and I. S firms always move together, but I firms

move independently of each other. For both types of firms there is a 40% probability that the
firm will have a 20% return and a 60% probability that the firm will have a -30% return.
The standard deviation for the return on an individual firm is closest to ________.
A) 24.49%
B) -10.00%
C) 12.25%
D) 9.80%

Answer 1

option (A) 24.49%

Step-by-step explanation:

Data provided in the question:

Return : 20% -30%

Probability : 40% 60%

Now,

Expected return = ∑ (Return × Probability)

= ( 0.20 × 0.40 ) + (-0.30 × 0.60)

= 0.08 - 0.18

= - 0.10 or - 10%

Thus,

Variance = ∑ [ Probability × (Return - Expected return)² ]

= 0.40 × ( 0.20 - ( -0.10))² + 0.60 × ( -0.30 - ( -0.10))²

= ( 0.40 × 0.09 ) + ( 0.60 × 0.04 )

= 0.036 + 0.024

= 0.06

Also,

Standard deviation = √variance

thus,

Standard deviation = √0.06

or

Standard deviation = 0.2449 or 24.49%

Hence,

the correct answer is option (A) 24.49%