Question

Ebenezer Scrooge has invested 60% of his money in share A and the remainder in share B. He assesses their prospects as follows:

	A		B
Expected return (%)	15		20
Standard deviation (%)	20		22
Correlation between returns		.5

a. What are the expected return and standard deviation of returns on his portfolio? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.)

Expected return	17.00 %
Standard deviation	18.08 %

b. How would your answer change if the correlation coefficient were 0 or –.5?

Answer 1

Wa= Weight of investment in stock A 60% OR 0.60

Wb= Weight of investment in stock A 40% OR 0.40

Ra = Return of Stock A

Rb = Return of Stock B

SDa = Standard Deviation of Stock A

SDb is the Standard Deviation of Stock B

R is the correlation between Stock A and B

Expected Return = Ra*Wa + Rb*Wb

= 15% * 0.60 + 20 * 0.40

= 17%

SD of Portfolio =

( SDa)2 * Wa2 +SDb}2 x Ꮃb2 +2 Ꭱ * SᎠa : Wa * SᎠb * Wb

=  $\bg_white \large \sqrt{(.20)^2*0.60^2+(0.22)^2*0.40^2 + 2*0.5*.20*0.60*0.22*0.40}$

= 0.1808 OR 18.08%

SD of Portfolio When R = 0

SD of Portfolio =

( SDa)2 * Wa2 +SDb}2 x Ꮃb2 +2 Ꭱ * SᎠa : Wa * SᎠb * Wb

=$\bg_white \large \sqrt{(SDa)^2*Wa^2+(SDb)^2*Wb^2 + 2*0*SDa*Wa*SDb*Wb}$

= $\bg_white \large \sqrt{(SDa)^2*Wa^2+(SDb)^2*Wb^2 + 0$

=  $\bg_white \large \sqrt{(.20)^2*0.60^2+(0.22)^2*0.40^2$

= 0.02214 OR 2.214%

SD when R= -5

SD of Portfolio =

( SDa)2 * Wa2 +SDb}2 x Ꮃb2 +2 Ꭱ * SᎠa : Wa * SᎠb * Wb

=  $\bg_white \large \sqrt{(.20)^2*0.60^2+(0.22)^2*0.40^2 + 2*(-0.5)*.20*0.60*0.22*0.40}$

= $\bg_white \large \sqrt{0.0144+ 0.007744- 0.01056}$

= $\bg_white \large \sqrt{0.011594}$

= 0.1076 OR 10.76%

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