Richard has two investment opportunities. He can invest in The Sunglasses Company or The Umbrella Company. What is the expected return and standard deviation of each company?
State of the Economy Probability of the State Expected Return Sunglasses Company Expected Return
Umbrella Company
Sunny .50 25% 0%
Rainy .50 0% 25%
A) The expected return for each company is 12.50% and the standard deviation for each company is 0.00%.
B) The expected return for each company is 12.50% and the standard deviation for each company is 12.50%.
C) The expected return for each company is 12.50% and the standard deviation for each company is 156.25%.
D) The expected return for each company is 12.50% and the standard deviation for each company is 25.00%.
Answer: B
Explanation: B) Expected payoff = Σ payoffi × probabilityi = .50 ∗ 25% + .50 ∗ 0% = 12.50%.
Standard deviation = Σ[(rs - E(r))2 ∗ probs]1/2
= [(25% - 12.5%)2 ∗ .50 + (0% - 12.5%)2 ∗ .50]1/2 = 12.50%.
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