Statistics for three stocks, A, B and C, are shown in the following tables: Stan
ID: 2649937 • Letter: S
Question
Statistics for three stocks, A, B and C, are shown in the following tables:
Standard Deviation of Returns
Stock
A
B
C
Standard Deviation (%)
40
20
40
Correlations of Returns
Stock
A
B
C
A
B
C
1
0
0
0.90
1
0
0.50
0.10
1.00
Only on the basis of the information provided in the tables, and given a choice between a portfolio made up of equal amounts of stocks A and B or a portfolio made up of equal amounts of stocks B and C, which portfolio would you recommend? Show calculations and Justify your choice.
Standard Deviation of Returns
Stock
A
B
C
Standard Deviation (%)
40
20
40
Correlations of Returns
Stock
A
B
C
A
B
C
1
0
0
0.90
1
0
0.50
0.10
1.00
Explanation / Answer
Portfolio Standard Deviation of portfolio mix of stock A and stock B
=[ (Wa2x?a2) + (Wb2x?b2) + 2 Wa x Wb x ?a x ?b x Corr ab ]1/2
Where
Wa = Weight of A, Wb = Weight of B
?a = 0.4
?b = 0.2
Corr ab= 0.9
Standard deviation of portfolio A and B
= [(0.52 x 0.4 2) + (0.52 x 0.2 2) + 2 x 0.5 x 0.5 x 0.4 x 0.2 x 0.9]
= 0.29
Portfolio Standard Deviation of portfolio mix of stock B and stock C
=[ (Wb2x?b2) + (Wc2x?c2) + 2 Wb x Wc x ?b x ?c x Corr bc ]1/2
Where
?c = 0.4
?b = 0.2
Corr bc= 0.10
Standard deviation of portfolio B and C
= [(0.52 x 0.4 2) + (0.52 x 0.2 2) + 2 x 0.5 x 0.5 x 0.4 x 0.2 x 0.1]
= 0.23
We know that standard deviation of a portfolio shows the variability in the expected return of portfolio. To mitigate the risk we should use diversification approach because diversification reduces the risk.
The lesser correlation between B and C with respect to A and B will reduce the standard deviation from 0.29 to 0.23. Which indicate a reduction of risk in portfolio of stock B and stock C.
Conclusion- As Portfolio of stock B and stock C is less risky hence it is recommended.