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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 70% probability that the firm will have a 20% return and a 30% probability that the firm will have a -30% return. The standard deviation for the return on an portfolio of 20 type S firms is closest to ________.

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Parrain

Answer: 23%

Explanation:

First calculate the expected return:

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

= 5%

Then use that to calculate variance:  

Variance:

= (70% * (20% - 5%)²) + (30% * (-30% - 5%)²)

= 5.25%

Standard Deviation:

= √5.25%

= 23%

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