Question

Expected return and standard deviation Use the following information to answer the questions: a. What is the expected retun of each asset? b. What is the variance and the standard deviation of each asset? c. What is the expected return of a portfolio with 12 % in asset J, 51 % in asset K, and 37 % in asset L? d. What is the portfolio's variance and standard deviation using the same asset weights from part (c)? Hint Make sure to round all intermediate calculations to at least seven (7) decimal places. The input instructions, phrases in parenthesis after each answer box, only apply for the answers you will type. d: re: - X Data Table (Click on the following iconin order to copy its contents into a spreadsheet) n1 ( Return on Asset J in State Return on Rolurn on Asset L in State 5 ( Probability of State State of Asset K in Economy Boom State 9ן 0.24 0.060 0.230 0.260 Growth 0.36 0.060 13ר 0.110 0.220 Stagnant Recession 0.065 0.23 0.060 0.070 0.17 0.060 -0.150 -0.220 Print Done TICCN73Wer

Answer 1

a) Expected return of each asset :

It is the sum of total of possible returns with respective probability

Asset J : 0.24*0.060 + 0.36*0.060 + 0.23* 0.060 + 0.17 * 0.060 = 0.060 i. e. 6%

Asset K :0.24*0.230 + 0.36*0.110 + 0.23* 0.065 + 0.17 * -0.150 =0.08425 i.e. 8.425%

Asset L = 0.24*0.260 + 0.36*0.220 + 0.23* 0.070 + 0.17 * -0.220 = 0.1203 i.e. 12.03%

b) Variance and Standard Deviation of Each Asset

Asset J

State of Economy	Probability of state ( p)	Return	Deviation( d) ( Return - Average Return )	d2	Product( d2*p)
Boom	0.24	0.06	0	0	0
Growth	0.36	0.06	0	0	0
Stagnant	0.23	0.06	0	0	0
Recession	0.17	0.06	0	0	0
			Variance( sum of pd2)		0

Standard deviation = Variance^^1/2 = 0.^1/2 = 0

Asset K

State of Economy	Probability of state ( p)	Return	Deviation( d) ( Return - Average Return )	d2	Product( d2*p)
Boom	0.24	0.23	-0.14575	0.021243063	0.0050983
Growth	0.36	0.11	-0.02575	0.000663063	0.0002387
Stagnant	0.23	0.065	0.01925	0.000370563	0.0000852
Recession	0.17	-0.15	0.23425	0.054873063	0.0093284
				Variance	0.0147507

Standard Deviation = Variance^^1/2 = 0.01457507^{^1/2} = 0.121452408

Asset L

State of Economy	Probability of state ( p)	Return	Deviation( d) ( Return - Average Return )	d2	Product( d2*p)
Boom	0.24	0.26	-0.13970	0.01951609	0.0046839
Growth	0.36	0.22	-0.0997	0.00994009	0.0035784
Stagnant	0.23	0.07	0.0503	0.00253009	0.0005819
Recession	0.17	-0.22	0.3403	0.11580409	0.0196867
				Variance	0.0285309

Standard deviation = Variance^^1/2 = 0.0285309^{^1/2} = 0.1689109

c) Expected return of portfolio with 12% of Asset J, 51 % of Asset K, 37 % of Asset L

= 0.12*0.060 + .51* 0.08425 + .37* 0.1203 = 0.09468 i.e. 9.468 %

D) Variance and Standard Deviation Calculation of Portfolio

Return under different Economy

State of Economy	Probability of state ( P)	J	K	L	Weightage ( W)			Return = sum(P*W*Product)
Boom	0.24	0.06	0.23	0.26	0.12	0.51	0.37	0.052968
Growth	0.36	0.06	0.11	0.22	0.12	0.51	0.37	0.052092
Stagnant	0.23	0.06	0.065	0.07	0.12	0.51	0.37	0.0152375
Recession	0.17	0.06	-0.15	-0.22	0.12	0.51	0.37	-0.025619

State of Economy	Probability of state ( p)	Return	Deviation( d) ( Return - Average Return )	d2	Product( d2*p)
Boom	0.24	0.052968	-0.04171	0.001739766	0.0004175
Growth	0.36	0.052092	-0.04259	0.00181361	0.0006529
Stagnant	0.23	0.0152375	-0.07944	0.006310872	0.0014515
Recession	0.17	-0.025619	-0.12030	0.014471489	0.0024602
		0.0946785		Variance	0.0049821

Standard deviation = Variance^^1/2 = 0.0049821^{^1/2} = 0.0705839