Question

P9-21 (similar to) Question Help Expected return and standard deviation. Use the following information to answer the questions: a. What is the expected return 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 8% in asset J, 46% in asset K, and 46% 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. a. What is the expected return of asset J? Data Table (Click on the following icon in order to copy its contents into a spreadsheet.) State of Economy Boom Growth Stagnant Recession Probability of State 0.25 0.38 0.23 0.14 Return on Asset J in State 0.050 0.050 0.050 0.050 Return on Asset K in State 0.220 0.120 0.040 -0.070 Return on Asset L in State 0.250 0.230 0.060 -0.190 Print Done Enter your answer in the answer box and then click Check Answer.

Answer 1

a)

Expected Return on Asset J in State = Probability * Return on Asset J

= 0.25 * 0.05 + 0.38 * 0.05 + 0.23 * 0.05 + 0.14 * 0.05

= 0.0125 + 0.019 +0.0115 + 0.007 = 0.05 or 5%

Expected Return on Asset K in State = Probability * Return on Asset K

= 0.25 * 0.22 + 0.38 * 0.12 + 0.23 * 0.04 + 0.14 *(- 0.07)

= 0.055 + 0.0456+ 0.0092 -0.0098 = 0.100 or 10%

Expected Return on Asset L in State = Probability * Return on Asset L

= 0.25 * 0.25 + 0.38 * 0.23 + 0.23 * 0.06 + 0.14 *(- 0.19)

= 0.0625 + 0.0874 + 0.0138 -0.0266 = 0.1371 or 13.71%

b)Variance and SD of each asset

Asset J

Calculation of variance

State of Economy	P= probability	Return on J in State (a)	Mean (b)	c = (a-b)	d =(a-b)2	e = P* d
Boom	0.25	0.05	0.05	0	0	0
Growth	0.38	0.05	0.05	0	0	0
Stagnant	0.23	0.05	0.05	0	0	0
Recession	0.14	0.05	0.05	0	0	0
						0

Variance = 0

Standard Deviation = Square root of variance = 0

Asset K

Calculation of variance

State of Economy	P= probability	Return on K in State (a)	Mean (b)	c = (a-b)	d =(a-b)2	e = P* d
Boom	0.25	0.22	0.1	0.12	0.0144	0.0036
Growth	0.38	0.12	0.1	0.02	0.0004	0.000152
Stagnant	0.23	0.04	0.1	-0.06	0.0036	0.000828
Recession	0.14	-0.07	0.1	-0.17	0.0289	0.004046
						0.008626

Variance = 0.008626 or 0.86%

Standard Deviation = Square root of variance = 0.09288 or 9.29 %

Asset L

Calculation of variance

State of Economy	P= probability	Return on L in State (a)	Mean (b)	c = (a-b)	d =(a-b)2	e = P* d
Boom	0.25	0.25	0.1371	0.1129	0.012746	0.003187
Growth	0.38	0.23	0.1371	0.0929	0.00863	0.00328
Stagnant	0.23	0.06	0.1371	-0.0771	0.005944	0.001367
Recession	0.14	-0.19	0.1371	-0.3271	0.106994	0.014979
						0.022813

Variance = 0.022813 or 2.28%

Standard Deviation =Square root of variance = 0.1510 or 15.10%

c)Expected return of a portfolio is

= Asset J 8% Asset K 46% and Asset L 46%

= 5% * 8% + 10% * 46% + 13.71% * 46% = 0.004 + 0.046 + 0.063066 = 0.113066 or 11.31 %

d) Portfolio Variance and Standard Deviation

The portfolio’s return in each state of the economy with the allocation of assets at 8% in J, 46% in K, and 46% in L.

Expected Return Portfolio in Boom= 0.08 * 0.05 + 0.46 * 0.22 + 0.46 * 0.25

= 0.004 +0.1012 +0.115 =0.2202 or 22.02%

Expected Return Portfolio in Growth = 0.08 * 0.05 +0.46* 0.12 + 0.46 * 0.23

= 0.004 +0.0552+0.1058 = 0.165 or 16.5 %

Expected Return Portfolio in Stagnant = 0.08 * 0.05 + 0.46 *0.04 + 0.46 * 0.06

= 0.004 + 0.0184 + 0.0276 =0.0500 or 5%

Expected Return Portfolio in Recession = 0.08* 0.05 + 0.46 * (-0.07) + 0.46 *(-0.19)

= 0.004 - 0.0322 -0.0874 = -0.1156 or - 11.56%

Calculation of Variance of portfolio

State of Economy	P= probability	Return of Portfolio (a)	Mean (b)	c = (a-b)	d =(a-b)2	e = P* d
Boom	0.25	0.2202	0.1131	0.1071	0.01147	0.002868
Growth	0.38	0.165	0.1131	0.0519	0.002694	0.001024
Stagnant	0.23	0.05	0.1131	-0.0631	0.003982	0.000916
Recession	0.14	-0.1156	0.1131	-0.2287	0.052304	0.007323
						0.012129

Variance = 0.012129 or 1.213%

Standard Deviation =Square root of variance = 0.11013 or 11.01 %