Question

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a. What are her expected returns and the risk from her investment in the three assets? How do they compare with invessing in asset M alone? Hint Find the standard deviations of asset M and of the portiolio equally investe assets M, N, and O b. Could Sally reduce her total risk even more by using assets M and N only, assets M and O only, or assets N and O only? Use a 50/50 spit between the asset pairs, and find the standard deviation of each asset pair Roturm 0% a. What is the expected return of investing equally in all three assets M, N, and 0? %(Round to two decimal places ) What is the expected return of investing in asset M alone? % (Round to two decimal places.) What is the standard deviation of the portfolio that invests equaly in all three assets M. N, and 07 Click to select your answer(s) Recessión | |% (Round to two decimal places) What is the standard deviation of the portfolio that invests equally in all three assets M, N, and O? % (Round to two decimal places) What is the standard deviation of asset M? 1% (Round to two decimal places ) Click to select your answer(s) 11% 12% b. What is the expected return of a portfolio of 50% asset M and 50% asset N? % (Round to two decmai places) What is the expected return of a portfolio of 50% asset M and 50% asset O? % (Round to two decimal places.) NA 50% Normal 2% 20% Recession What is the expected return of a portfolio of 50% asset N and 50% asset O? 96 (Round to two decimal places ) What is the standard deviation of a portfolio of 50% asset M and 50% asset N? 1% (Round to two decimal places) What is the standard deviation of a portfolio of 50% asset M and 50% asset。? Click to select your answer(s) 11% 8% 50% Normal 2% 20% Recession What is the standard deviation of a portfolio of 50% asset N and 50% asset O? (Round to two decimal places.) % Could Sally reduce her total risk even more by using assets M and N only, assets M and O only, or assets N and O only? (Select the best response ) A. Yes, a portfolio of 50% of asset M and 50% of asset O could reduce the risk to 0 50%. O B. There is not enough information to answer this question C. Yes a nn rtinlin nf 5nsh nf asset M and 5n9h nf asset N rnıld reduce the risk tn ( 50% Click to select your answer(s)

Answer 1

	Probability (p)	Asset M (m)	Asset N (n)	Asset O (o)	(p*m)	(p*n)	(p*o)	Portfolio P average(m,n,o)	(P*p)	p*(P-E[r])^2	p*(m-E[r])^2
Boom	30%	12%	19%	2%	3.60%	5.70%	0.60%	11%	3.30%	0.02%	0.05%
Normal	50%	8%	11%	8%	4.00%	5.50%	4.00%	9%	4.50%	0.00%	0.00%
Recession	20%	2%	-2%	12%	0.40%	-0.40%	2.40%	4%	0.80%	0.04%	0.07%
				Expected return E[r]	8.00%	10.80%	7.00%	E[r]	8.60%	0.06%	0.12%
									StDev	2.46%	3.46%

a). Expected return of investing in all 3 assets = 8.60%

Expected return of investing in asset M = 8.00%

Standard deviation for a portfolio equally invested in all 3 assets = 2.46%

Standard deviation of asset M = 3.46%

By investing in the portfolio rather than only in asset M, Sally can increase her return by 0.60% and decrease her risk by 1.01%.

b).

	Probability (p)	Asset M (m)	Asset N (n)	Asset O (o)	Portfolio (P1) of M& N average(m,n)	(P1*p)	p*(P1-E[r])^2	Portfolio (P2) of M& O average(m,n)	(P2*p)	p*(P2-E[r])^2	Portfolio (P3) of N & O average(m,n)	(P3*p)	p*(P3-E[r])^2
Boom	30%	12%	19%	2%	16%	4.65%	0.11%	7%	2.10%	0.0008%	11%	3.15%	0.01%
Normal	50%	8%	11%	8%	10%	4.75%	0.00%	8%	4.00%	0.0013%	10%	4.75%	0.00%
Recession	20%	2%	-2%	12%	0%	0.00%	0.18%	7%	1.40%	0.0005%	5%	1.00%	0.03%
					Expected return E[r]	9.40%	0.29%		7.50%	0.0025%		8.90%	0.04%
						StDev	5.37%		StDev	0.50%		StDev	2.00%

Expected return of a portfolio with 50% M and 50% N = 9.40%; standard deviation for the (M,N) portfolio = 5.37%

Expected return of a portfolio with 50% M and 50% O = 7.50%; standard deviation for the (M,O) portfolio = 0.50%

Expected return of a portfolio with 50% N and 50% O = 8.90%; standard deviation for the (N,O) portfolio = 2.00%

Option A is correct.