You have $17,200 to invest and would like to create a portfolio with an expected return...

You have $17,200 to invest and would like to create a portfolio with an expected return of 11 percent. You can invest in Stock K with an expected return of 9.9 percent and Stock L with an expected return of 13.5 percent. How much will you invest in Stock K?

$10,949.07

$4,598.61

$7,007.41

$5,255.56

$11,944.44

Based on the following information, what is the standard deviation of returns?

State of Economy	Probability of State of Economy	Rate of Return if State Occurs
Recession	.23	?	.111
Normal	.26		.126
Boom	.51		.236

27.76%

19.63%

19.09%

13.82%

25.45%

Expert Solution

1)	$11,944.44

Working:

	Step-1:Calculation of Weight of each investment

	Expected return of Portfolio			=	Sum of (Weight of stock*Expeced Return of Stock)

	Suppose Weight of Stock K is "x" and so weight of Stock L is "(1-x)"

	Expected return of Portfolio			=	Sum of (Weight of stock*Expeced Return of Stock)
	or,	0.11		=	(x0.099)+((1-x)0.135)
	or,	0.11		=	0.099x+0.135-0.135x
	or,	0.11		=	0.099x+0.135-0.135x
	or,	0.11		=	-0.036x+0.135
	or,	0.036x		=	0.025
	or,	x		=	0.69

		Thus,
		Weight of Stock K is 0.69 and of Stock L is 0.31

	Step-2:Calculation of Investment in Stock K

	Investment in Stock K			=	Total Investment x Weight of Stock K
				=	$ 17,200	x	0.69
				=	$ 11,944.44
2)	13.82%

Working:

	Step-1:Calculation of Expected Return

	State of Economy		Probability of State of Economy	Rate of Return if State Occurs	Expectetd Return
			a	b	c=a*b
	Recession		0.23	-0.111	-0.02553
	Normal		0.26	0.126	0.03276
	Boom		0.51	0.236	0.12036

	Total				0.12759

	Step-2:Calculation of Variance

	State of Economy		Probability of State of Economy	Rate of Return if State Occurs	Expectetd Return		Variance
			a	b	c		d=((b-c)^2)*a
	Recession		0.23	-0.111	0.12759		0.013093
	Normal		0.26	0.126	0.12759		0.000001
	Boom		0.51	0.236	0.12759		0.005994

		Total					0.019087

	Step-3:Calculation of standard deviation

		Standard Deviation		=	Variance ^(1/2)
				=	0.01908734	^ (1/2)
				=	0.1382

	Thus,
	Standard Deviation of Return is 13.82%

jeff jeffy answered 2 years ago

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