Question

Teena is considering investing in Stock A and stock B. She plans to invest $ 25,000 in the low risk stock and $ 50,000 in the high-risk stock. You have been given the following information about these two stocks in the table below:

Stock	A	B
E(R)	15%	10
?	25%	22%
Correlation between A and B	0.20

Based on the given information above, you are required to:

i. Calculate the portfolio weights.  

ii. Calculate the portfolio return.   

iii. Calculate the portfolio risk.

iv. Compare portfolio risk with the individual stock risks and identify the benefit of the diversification of the portfolio.

Answer 1

Given facts,
Stocks	A	B
Return	15%	10%
Standard Deviation (SD)	25%	22%
Correlation of A & B	0.20
Here, Stock A is higher risk stock and Stock B is lower risk stock. Because of Standard deviation, higher standard deviation higher risk. Lower standard deviation means lower risk. So, $25000 invested in Stock B and $50000 invested in Stock A.
i) Portfolio Weights:
Assets	Invested Amount	Proportion
A	50,000.00	66.67%
B	25,000.00	33.33%
Total	75,000.00	100.00%
ii) Expected return on Portfolio:
Assets	Return	Proportion in Portfolio
A	15%	66.67%
B	10%	33.33%
Return of Portfolio
iii) Standard deviation of Portfolio:
Standard deviation of portfolio contains A,B Stocks:
=√(W(a)*SD(a))^2 + (W(b)*SD(b))^2 + 2W(a)*W(b)*SD(a)*SD(b)*Correlation(a,b)
=√(66.67%*0.25)^2+(33.33%*0.22)^2+2*66.67%*33.33%*0.25*0.22*0.2
0.1951
=(or) 19.51%
iv) Comparision of risks:
Assets	Return	Risks
A	15%	25.00%
B	10%	22.00%
Portfolio	13.33%	19.51%
Here, after diversification risk reduces to 19.51% it is less than both securities risks in the portfolio