How do you get these answers? 5) We have a portfolio that is invested 70% in Ass

Question

How do you get these answers?

5) We have a portfolio that is invested 70% in Asset A and 30% in Asset B. Assume the following

State of the Econ . Probability Exp.Ret (Asset A) Exp. Ret (Asset B)

Recession 40% -4% 2%

Expansion 60% 16% 6%

Calculate the Return of the portfolio under each of the given states of the economy

State of the Econ. Probability Return of the Portfolio containing 70% in A and 30% in B

Recession 40% _______-2.2% _________%

Expansion 60% _______13% _________%

What is the overall Expected return of the portfolio? Expected Return on the Portfolio = ___________ 6.92% ______________%

What is the standard deviation of the $10,000 portfolio? Standard Deviation of the $10,000 portfolio = _____ 7.446% ___________%

Explanation / Answer

Returns State Probability A B A - Bar B - Bar 1 2 3 1*2 1*3 Recession 40% -4.00% 2.00% -1.60% 0.80% Expansion 60% 16.00% 6.00% 9.60% 3.60% Expected Return 8.00% 4.40% Returns State Probability A B A - Abar B - Bbar Var A Var B a b c d = a - 8% e = b - 4% a*d^2 a*e^2 Recession 40% -4.00% 2.00% -12.00% -2.40% 0.00576000 0.00023040 Expansion 60% 16.00% 6.00% 8.00% 1.60% 0.00384000 0.00015360 Variance 0.00960000 0.00038400 SD = Variance SD - A 0.0980 SD - B 0.0196 Expected Return Stock A 8.00% Stock B 4.40% Standard Deviation Stock A 9.80% Stock B 1.96% Recession = 70% * -4% + 30% * 2% = -2.8% + 0.6% = -2.2% Expansion = 70% * 16% + 30% * 6% = 11.2% + 1.8% = 13% Overall Expected Return = 70% * 8% + 30% * 4.4% = 5.6% + 1.32% = 6.92% Standard Deviation Portfolio = 70% * 9.80% + 30% * 1.96% = 6.859% + 0.588% = 7.446%

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