Question

Stock Xillow has an expected return of 16% and a standard deviation of 4%. Stock Yash has an expected return of 12% and a standard deviation of 3%. Assume you have constructed a portfolio consisting of 75% weight in Stock Xillow and 25% in Stock Yash. Furthermore assume that the stocks have a correlation coefficient of -0.3. What is the standard deviation of the portfolio? A. Less than 2% B. Greater than or equal to 2% and less than 2.5% C. Greater than or equal to 2.5% and less than 3% D. Greater than or equal to 3% and less than 3.5% E. Greater than or equal to 3.5%

Answer 1

A = Xillow

B = Yash

Portfolio SD:

It is nothing but volataility of Portfolio. It is calculated based on three factors. They are
a. weights of Individual assets in portfolio
b. Volatality of individual assets in portfolio
c. Correlation betwen individual assets in portfolio.
If correlation = +1, portfolio SD is weighted avg of individual Asset's SD in portfolio. We can't reduce the SD through diversification.
If Correlation = -1, we casn reduce the SD to Sero, by investing at propoer 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

Particulars	Amount
Weight in A	0.7500
Weight in B	0.2500
SD of A	4.00%
SD of B	3.00%
r(A,B)	-0.3

Portfolio SD = SQRT[((Wa*SDa)^2)+((Wb*SDb)^2)+2*(wa*SDa)*(Wb*SDb)*r(A,B)]
=SQRT[((0.75*0.04)^2)+((0.25*0.03)^2)+2*(0.75*0.04)*(0.25*0.03)*-0.3]
=SQRT[((0.03)^2)+((0.0075)^2)+2*(0.03)*(0.0075)*-0.3]
=SQRT[0.0008]
= 0.0287
= I.e 2.87 %

C. Greater than or equal to 2.5% and less than 3% - Is correct