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Richard has two investment opportunities, He can invest in The Sunglasses Company or The Umbrella Company
Richard has two investment opportunities, He can invest in The Sunglasses Company or The Umbrella Company. If he diversifies his investment by putting 50% of his money into each company, what is the expected return and standard deviation of his portfolio? State of the Probability of the Expected Return Sunglasses Expected Return Economy State Company Umbrella Company Sunny .50 25% 0% Rainy .50 25% A) The expected return for the portfolio is 12.50% and the standard deviation 0.00%. B) The expected return for the portfolio is 25.00% and the standard deviation 0.00%. C) The expected return for the portfolio is 12.50% and the standard deviation 12.50%. D) The expected return for the portfolio is 25.00% and the standard deviation 25.00%. 0%
Expert Solution
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To determine we will calculate portfolio return and portfolio standard deviation.
Scenario Probability S U S*P U*P (S-S Bar)^2 * P (U- U bar )^2 * P (S - S bar) (U -U Bar )*P Sunny 0.5 25 0 12.50 0.00 78.125 78.125 -78.125 Rainy 0.5 0 25 0.00 12.50 78.125 78.125 -78.125 Total 12.50 12.50 156.250 156.250 -156.250 Standard Deviation - 12.500 12.500 Return of S = ∑S*P = 12.50%
Return U + ∑U*P = 12.50 %
SD S = √∑((S-S Bar)^2 * P) = 12.50 %
SD U = √∑ ((U- U bar )^2 * P) = 12.50%
Corelation Coefficent = ∑(S - S bar) (U -U Bar )*P / SD S * SD U = -156.25/12.50*12.50 = -1
Portfolio Return = ∑R*P = 12.50 *0.50 + 12.50 *0.50 = 12.50%
Portfolio Risk = √(SD S * WS )2 +(SD U * WU)2 + 2*SD S * SD U * WS * WU * r(S,U)
= √(12.50*0.50)2 + (12.50*0.50)2 + 2*12.50*12.50*0.50 *0.50 * (-1)
=0
Therefore Correct answer is A
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