Question

You are given the following information of two assets:

Asset	Return	Weighting	Risk
X	10%	75%	3%
Y	20%	25%	9%

The expected return of the portfolio is _____________.

The standard deviation of the portfolio with a (rho) p of +1.0 is _______________

The standard deviation of the portfolio with a (rho) p of 0 is ________________

The standard deviation of the portfolio with a (rho) p of -1.0 is ______________

Answer 1

Expected Ret is the weighted avg ret of securities in the portfolio.

Part A:

Stock	Weight	Ret	WTd Ret
Asset X	0.7500	10.00%	7.50%
Asset Y	0.2500	20.00%	5.00%
Expected Return			12.50%

Portfolio SD:

It is nothing but the volatility of the Portfolio. It is calculated based on three factors. They are
a. weights of Individual assets in portfolio
b. The volatility of individual assets in portfolio
c. Correlation between individual assets in the portfolio.
If correlation = +1, portfolio SD is the weighted avg of individual Asset's SD in the portfolio. We can't reduce the SD through diversification.
If Correlation = -1, we can reduce the SD to Sero, by investing at proper weights.
If correlation > -1 but <1, We can reduce the SD, n=but it will not become Zero.

Wa = Weight of A
Wb = Weigh of B
SDa = SD of A
SDb = SD of B

A = Asset X

B = Asset Y

Part B:

Particulars	Amount
Weight in A	0.7500
Weight in B	0.2500
SD of A	3.00%
SD of B	9.00%
r(A,B)	1

Portfolio SD = SQRT[((Wa*SDa)^2)+((Wb*SDb)^2)+2*(wa*SDa)*(Wb*SDb)*r(A,B)]
=SQRT[((0.75*0.03)^2)+((0.25*0.09)^2)+2*(0.75*0.03)*(0.25*0.09)*1]
=SQRT[((0.0225)^2)+((0.0225)^2)+2*(0.0225)*(0.0225)*1]
=SQRT[0.002]
= 0.045
= I.e 4.5 %

Part C:

Particulars	Amount
Weight in A	0.7500
Weight in B	0.2500
SD of A	3.00%
SD of B	9.00%
r(A,B)	0

Portfolio SD = SQRT[((Wa*SDa)^2)+((Wb*SDb)^2)+2*(wa*SDa)*(Wb*SDb)*r(A,B)]
=SQRT[((0.75*0.03)^2)+((0.25*0.09)^2)+2*(0.75*0.03)*(0.25*0.09)*0]
=SQRT[((0.0225)^2)+((0.0225)^2)+2*(0.0225)*(0.0225)*0]
=SQRT[0.001]
= 0.0318
= I.e 3.18 %

Part D:

Particulars	Amount
Weight in A	0.7500
Weight in B	0.2500
SD of A	3.00%
SD of B	9.00%
r(A,B)	-1

Portfolio SD = SQRT[((Wa*SDa)^2)+((Wb*SDb)^2)+2*(wa*SDa)*(Wb*SDb)*r(A,B)]
=SQRT[((0.75*0.03)^2)+((0.25*0.09)^2)+2*(0.75*0.03)*(0.25*0.09)*-1]
=SQRT[((0.0225)^2)+((0.0225)^2)+2*(0.0225)*(0.0225)*-1]
=SQRT[0]
= 0
= I.e 0 %