Question

States	Probability	Asset M Return	Asset N Return	Asset O Return
Boom	34%	12%	21%	4%
Normal	51%	10%	14%	10%
Recession	15%	4%	1%	12%

Benefits of diversification. Sally Rogers has decided to invest her wealth equally across the following three​ assets:

a.  What are her expected returns and the risk from her investment in the three​ assets? How do they compare with investing in asset M​ alone?  

Hint​: Find the standard deviations of asset M and of the portfolio equally invested in 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 split between the asset​ pairs, and find the standard deviation of each asset pair.

Answer 1

FORMULAS USED :-

	E(Ri)	=SUMPRODUCT($B$2:$B$4,C2:C4)	=SUMPRODUCT($B$2:$B$4,D2:D4)	=SUMPRODUCT($B$2:$B$4,E2:E4)
Sd = Proxy for Risk	Standard Deviation	=SQRT(SUMPRODUCT((C2:C4-C5)^2,$B$2:$B$4))	=SQRT(SUMPRODUCT((D2:D4-D5)^2,$B$2:$B$4))	=SQRT(SUMPRODUCT((E2:E4-E5)^2,$B$2:$B$4))
	COVARIANCE	M & N	N &O	O & M
		=SUMPRODUCT($B$2:$B$4,(C2:C4-C5),(D2:D4-D5))	=SUMPRODUCT($B$2:$B$4,(D2:D4-D5),(E2:E4-E5))	=SUMPRODUCT($B$2:$B$4,(E2:E4-E5),(C2:C4-C5))
PORTFOLIO RISK
		M & N	N &O	O & M
STANDARD DEVIATION		=((C6^2*0.5^2)+(D6^2*0.5^2)+(2*C10*0.5*0.5))^(1/2)	=((D6^2*0.5^2)+(E6^2*0.5^2)+(2*D10*0.5*0.5))^(1/2)	=((E6^2*0.5^2)+(C6^2*0.5^2)+(2*E10*0.5*0.5))^(1/2)