Question

Consider the following two stocks. Probabilities Stock ky) FA" Recession1=35% 9% Normal 2=33% 8% Boom B=32% 15% Stock "B" 3% 2% 28% The portfolio weights for stocks "A" and "B" are 0.2 and 0.8, respectively. What are the expected returns of stock "A" and "B"? Enter your answers as a percentage. Do not put the percent sign in your answers. Round your answers to 2 DECIMAL PLACES. Evo = 4.29 Correct response: 4.29 E (16) = 9.35 Correct response: 9.35 Click "Verify" to proceed to the next part of the question. Using the correct answers from the previous question, what are the standard deviations of stocks "A" and "B"? Enter your answers as a percentage. Do not put the percent sign in your answers. Round your answers to 2 DECIMAL PLACES. Sid=10.15 Correct response: 10.1510.01 Si= 12.96 → Correct response: 12.9610.01 Click "Verify" to proceed to the next part of the question. Using the correct answers from the previous questions, what is the

Answer 1

As all the answer are computed and are correct. I'm calculating standard deviation of portfolio.

First, we will calculate the Co-variance of Stock A & B:-

Probability(P)	Stock A (RA)	P*RA	Stock B (RB)	P*RB​​​​​	Deviation of RA (RA-ERA)	Deviation of RB (RB-ERB)	Deviation of RA*Deviation of RB	(Deviation of RA*Deviation of RB)*p
0.35	-9	-3.15	3	1.05	-13.29	-6.35	84.3915	29.537
0.33	8	2.64	-2	-0.66	3.71	-11.35	-42.1085	-13.8958
0.32	15	4.8	28	8.96	10.71	18.65	199.7415	63.917
		ERA=4.29		ERB=9.35				COVAB= 79.5582

So, Cov_AB = 79.5582

-- Coefficient of Corrrelation(ρ) = Cov_AB/σ_Aσ_B

= 79.5582/(10.15*12.96)

= 0.60

So, now we will calculate Standard deviation of portfolio:-

Op = V(WA)(A)2 + (WB)2(B)2 + 2WAWBOABPAB

$\sigma_{P} =\sqrt{(0.2)^{2}(10.15)^{2}+(0.8)^{2}(12.96)^{2}+2*0.2*0.8*10.15*12.96*0.6}$

$\sigma_{P} =\sqrt{4.1209+107.4954+25.2564}$

$\sigma_{P} =\sqrt{136.8727}$

$\sigma_{P} =11.70$

So, Standard deviation of Portfolio is 11.70%

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