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 firm there is a 70% probability that the firm will have a 20% return and a 30% probability that the firm will have a -30% return.(a) What is the expected return for an individual firm?
(1) 14% (2) 3% (3) 5% (4) -5%
(b) The standard deviation for the return on an individual firm is closest to:
(1) 23% (2) 5.25% (3) 15% (4) 10%

Answer 1

Answer:

a. (3) 5%

b. (1) 23%

Explanation:

The computation is shown below:

a. Expected return is

= 70% ×  20% + 30% × (-30%)

= 5%

We simply multiplied the probability with its return

b. And for computing the standard deviation first we have to find out the variance which is shown below:

Variance = 70% × (0.20 - 0.05)^2 + 30% ×  (-0.30 - 0.05)^2

= 0.0525

Now

Standard Deviation is

= (0.0525)^(1 ÷ 2)

= 23%

Answer 2

Based on the probabilities and returns, the following are true:

• Expected return = 5%
• Standard deviation = 23%

Expected return is the weighted average of probabilities and returns:

= (Probability of payoff x Payoff) + (Probability of second payoff x Second payoff)

= (70% x 20%) + (30% x -30%)

= 5%

Standard deviation requires that variance is calculated first:

Variance = ∑((Probability x Difference between return and expected return) )²

= ((70% x (0.2 - 0.05)) + ( 30% x (-30% -0.05)))²

= 0.0525

Standard deviation:

= √Variance

= √0.0525

= 0.023

= 23%

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