A portfolio consists of 60% of Security A (expected return of 0.10 and standard deviation of...

A portfolio consists of 60% of Security A (expected return of 0.10 and standard deviation of 0.03) and 40% of Security B (expected return of 0.20 and standard deviation of 0.05) and the correlation coefficient between A and B is -0.0012.

a) Calculate the expected return and standard deviation of the portfolio.

b) Calculate the standard deviation of the portfolio if there was no diversification benefit.

Expert Solution

Part A:

Expected Ret :

Portfolio Return is the weighted avg return of securities in that portfolio.

Stock	Weight	Ret	WTd Ret
Security A	0.6000	10.00%	6.00%
Security B	0.4000	20.00%	8.00%
Portfolio Ret Return			14.00%

Portfolio SD:

Particulars	Amount
Weight in A	0.6000
Weight in B	0.4000
SD of A	3.00%
SD of B	5.00%
r(A,B)	-0.0012

Portfolio SD = SQRT[((Wa*SDa)^2)+((Wb*SDb)^2)+2*(wa*SDa)*(Wb*SDb)*r(A,B)]
=SQRT[((0.6*0.03)^2)+((0.4*0.05)^2)+2*(0.6*0.03)*(0.4*0.05)*-0.0012]
=SQRT[((0.018)^2)+((0.02)^2)+2*(0.018)*(0.02)*-0.0012]
=SQRT[0.0007]
= 0.0269
= I.e 2.69 %

Part B:

Particulars	Amount
Weight in A	0.6000
Weight in B	0.4000
SD of A	3.00%
SD of B	5.00%
r(A,B)	1

Portfolio SD = SQRT[((Wa*SDa)^2)+((Wb*SDb)^2)+2*(wa*SDa)*(Wb*SDb)*r(A,B)]
=SQRT[((0.6*0.03)^2)+((0.4*0.05)^2)+2*(0.6*0.03)*(0.4*0.05)*1]
=SQRT[((0.018)^2)+((0.02)^2)+2*(0.018)*(0.02)*1]
=SQRT[0.0014]
= 0.038
= I.e 3.8 %

jeff jeffy answered 2 years ago

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