Question

State of   Economy		Probability of State		Return on Asset J in State		Return on Asset K in State		Return on Asset L in State
Boom		0.26		0.050		0.230		0.290
Growth		0.37		0.050		0.150		0.210
Stagnant		0.22		0.050		0.020		0.050
Recession		0.15		0.050		−0.150		-0.180

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 12​% in asset​ J, 48​% in asset​ K, and 40​% 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.

Answer 1

Solution:
Notes:	There is no specific requirement in question about final answers decimal, I have provide all answers in 4 decimals place, but if you may required in 6 decimal or in percentage form. Then you have to just do is comment in the comment section of this solution with your specific requirement and wait . you will definitely get your solution updated with that specific form which you want. As per instruction given all intermediate calculation are within there guidelines.
a.		Expected Return
	Asset J	0.0500
	Asset K	0.0972
	Asset L	0.1371
Working Notes:
	Asset J
	Expected return of Asset J (Er J) = Sum of ((prob of each state) x (Return of Asset J at each state))
	=(0.26 x 0.050)+ (0.37 x 0.050) + (0.22 x 0.050)+ (0.15 x 0.050)
	=0.0500
	0.0500
	Asset K
	Expected return of Asset K (Er K) = Sum of ((prob of each state) x (Return of Asset K at each state))
	=(0.26 x 0.230)+ (0.37 x 0.150) + (0.22 x 0.020)+ (0.15 x (-0.150))
	=0.0972000
	0.0972
	Asset L
	Expected return of Asset L (Er L) = Sum of ((prob of each state) x (Return of Asset L at each state))
	=(0.26 x 0.290)+ (0.37 x 0.210) + (0.22 x 0.050)+ (0.15 x (-0.180))
	=0.13710000
	0.1371
b.		Variance	Standard deviation
	Asset J	0.0000	0.0000
	Asset K	0.0161	0.1269
	Asset L	0.0248	0.1575
Working Notes:
Asset J	The variance of this Asset J = Sum of [(Prob. Of each state) x ( Return of the Asset J at each state - Expected return of the Asset J)^2 ]
	=0.26 x(0.050 - 0.050)^2 + 0.37 x(0.050 - 0.050)^2 + 0.22 x(0.050 - 0.050)^2 + 0.15 x(0.050 - 0.050)^2
	=0.000000
	0.00000
	The standard deviation of Asset J = Square root of the variance of Asset J
		=(0.000000)^(1/2)
		=0.000000
		0.0000
Asset K	The variance of this Asset K = Sum of [(Prob. Of each state) x ( Return of the Asset J at each state - Expected return of the Asset K)^2 ]
	=0.26 x(0.230 - 0.0972000)^2 + 0.37 x(0.150 - 0.0972000)^2 + 0.22 x(0.020 - 0.0972000)^2 + 0.15 x(-0.150 - 0.0972000)^2
	=0.0160941600
	=0.016094
	0.0161
	The standard deviation of Asset K = Square root of the variance of Asset K
		=(0.0160941600)^(1/2)
		=0.12686276
		0.1269
Asset L	The variance of this Asset L = Sum of [(Prob. Of each state) x ( Return of the Asset L at each state - Expected return of the Asset L)^2 ]
	=0.26 x(0.290 - 0.13710000)^2 + 0.37 x(0.210 - 0.13710000)^2 + 0.22 x(0.050 - 0.13710000)^2 + 0.15 x(-0.180 - 0.13710000)^2
	=0.0247965900
	0.0248
	The standard deviation of Asset L = Square root of the variance of Asset L
		=(0.0247965900)^(1/2)
		=0.15746933
		0.1575
c.	Expected return of the portfolio	0.1075
Working Notes:		A	B	C = A x B
		Weight	Expected return	W x Er
	Asset J	12%	0.0500000	0.0060000
	Asset K	48%	0.0972000	0.0466560
	Asset L	40%	0.1371000	0.0548400
		Expected return of the portfolio		0.1074960
	Expected return of portfolio = Weighted average expected return of Individual assets
d.
	Portfolio's variance	0.0153
	Portfolio's Standard deviation	0.1238
Working Notes:
	First of all we calculate Return of portfolio at each state of Economy.
Return at Boom (rb)	Return of portfolio at Boom (rb)= Weighted average return of individual asset
	=Sum of ( return x weight of % invested)
	= 12% x 0.050 + 48% x 0.230   + 40% x 0.290
	=0.23240000
	0.2324
Return at Growth   (r Growth)	Return at Growth   (r Growth) = Weighted average return of individual asset
	=Sum of ( return x weight of % invested)
	=12% x 0.050 + 48% x 0.150   + 40% x 0.210
	=0.16200000
	0.1620
Return at Stagnant   (r Stagnant)	Return at Stagnant   (r Stagnant) = Weighted average return of individual asset
	=Sum of ( return x weight of % invested)
	=12% x 0.050 + 48% x 0.020   + 40% x 0.050
	=0.0356000
	0.0356
Return at Recession   (r Recession)	Return at Recession   (r Recession)= Weighted average return of individual asset
	=Sum of ( return x weight of % invested)
	= 12% x 0.050 + 48% x( -0.150)   + 40% x (-0.180)
	= -0.1380000
	-0.1380
Expected return of portfolio(Er) = Sum of ((prob of each state) x (Return of portfolio at each state))
	=0.26 x 0.2324000 + 0.37 x 0.1620000 + 0.22 x 0.0356000 + 0.15 x (-0.1380000)
	=0.1074960
	0.10749600
The variance of this portfolio = Sum of [(Prob. Of each state) x ( (Return of the portfolio at each state - Expected return of the portfolio))^2 ]
=0.26 x (0.2324 -0.1074960)^2 + 0.37 x (0.1620 - 0.1074960)^2 + 0.22 x (0.0356 - 0.1074960)^2 + 0.15 x (-0.1380 - 0.1074960)^2
	=0.015332846784
	=0.0153328
	0.0153
	The standard deviation of Portfolio = Square root of the variance of portfolio
	The standard deviation of Portfolio = (0.015332846784)^(1/2)
	The standard deviation of Portfolio = 0.1238258728
	The standard deviation of Portfolio = 0.123826
	The standard deviation of Portfolio = 0.1238
	The standard deviation of Portfolio	0.1238
Please feel free to ask if anything about above solution in comment section of the question.