Question

t udio Hop P8-24 (similar to) Benefits of diversification Sally Rogers has decided to invest her w ith equally across the following trees What we her expected retums and the risk from her investment in the vee assets? How do they compare with investing in asset Malone? Hint Find the standard deviations of asset Mand of the portfolio equally invested in assets M, N and O. b. Could Bally reduce her total risk even more by using assets M and Norly, assets M and only or assets and only? Use a 50/50 split between the asset pairs, and find the standard deviation of each asset pair .. What is the expected return of investing equally in all three ass M, N, and 07 7.92 % (Round to two decimal places) Data Table What is the expected return of investing in Malone? Round to two decimal places. (Click on the following icon in order to copy its content to a spreadsheet.) Pruty ASM AS Enter your answer in the answer box and then click che 10 Pering Hier

Answer 1

Solution :-

		Asset M
Probability (P)	Returns (M)	ER	Retrun - ER	(R - ER)^2	P * (R-ER)^2
			(R - 6.280%)
33%	10%	3.300%	3.72%	0.138%	0.0457%
48%	7%	3.360%	0.72%	0.005%	0.0025%
19%	-2%	-0.380%	-8.28%	0.686%	0.1303%
	ER    =	6.280%		Variance =	0.1784%
Now SD =	=	Sqrt(Var)	SQRT(0.1784%)		4.22%
		Asset N
Probability (P)	Returns (M)	ER	Retrun - ER	(R - ER)^2	P * (R-ER)^2
			(R - 12.88%)
33%	21%	6.930%	8.12%	0.659%	0.2176%
48%	12%	5.760%	-0.88%	0.008%	0.0037%
19%	1%	0.190%	-11.88%	1.411%	0.2682%
	ER    =	12.880%		Variance =	0.4895%
Now SD =	=	Sqrt(Var)	SQRT(0.4895%)		7.00%
		Asset O
Probability (P)	Returns (M)	ER	Retrun - ER	(R - ER)^2	P * (R-ER)^2
			(R - 4.6%)
33%	-2%	-0.660%	-6.60%	0.436%	0.1437%
48%	7%	3.360%	2.40%	0.058%	0.0276%
19%	10%	1.900%	5.40%	0.292%	0.0554%
	ER    =	4.600%		Variance =	0.2268%
Now SD =	=	Sqrt(Var)	SQRT(0.2268%)		4.76%
Assets	Return	Weights	ER
M	6.28%	0.333333	2.093%
N	12.88%	0.333333	4.293%
O	4.60%	0.333333	1.533%
	Return of Portfolio		7.920%

Variance of Protfolio =

(W_M)² * Var(M) +  (W_N)² * Var(M) + (W_O)² * Var(M) + 2 (Wm*Wn*SDm*SDn) +2(WnWoSDnSDo) +2(Wm*Wo*SDm*SDo)

= (1/3)² * (0.1784%) +  (1/3)² * (0.4895%) + (1/3)² * (0.2268%) + 2 (1/3*1/3*4.22%*7%) +2(1/3 * 1/3 * 7%*4.26%) + 2(1/3*1/3*4.22% *4.76%)

= 0.0002 + 0.00025 + 0.00054 + 0.00033 + 0.00037 + 0.00022

= 0.00192 = 0.192%

Standard Deviation of Portfoilo = (Var)^1/2 = (0.192%)^1/2 = 4.377%

	Portfolio	Asset M	Diff
Std dev.	4.38%	4.22%	0.16%
Return	7.92%	6.28%	1.64%

Here we see if we invest in Asset M as compared to portfolio then Risk (SD) increase by 0.16% but retrun increase by 1.64% so better to invest in Asset M

Dear it takes too much time to solve first first and there is not sufficient time to solve next so please ask it as seperate one