Statistics for three stocks, A, B and C, are shown in the following tables: Stan
ID: 2649940 • 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
0.90
1
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 for 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
0.90
1
0.50
0.10
1.00
Explanation / Answer
Answer
Portfolio of stock A & B
Stock A
Standard deviation (SD1) = risk = 40% & weight of stock A in portfolio = w1 = 0.5
Stock B
Standard deviation (SD2) = risk = 20% & weight of stock B in portfolio = w2 = 0.5
Variance of the portfolio (Vp) is square of standard deviation of the portfolio (SDp).
Vp = (w1)2(SD1)2+(w2)2(SD2)2+2(w1)(w2)(SD1)(SD2)(r12)
Where w represents weight of stock in total portfolio and r12 represents correlation co-efficient between 2 stocks which is 0.90
= (0.5)2(0.4)2+(0.5)2(0.2)2+2(0.5)(0.5)(0.4)(0.2)(0.9)
=(0.25)(0.16)+(0.25)(0.04)+0.036
=0.04+0.01+0.036
Vp=0.086
Standard deviation of portfolio is square root of Vp
SDp = 0.29
So risk of the portfolio of equal amounts of stocks A & B is 0.29
Portfolio of stock B & C
Stock C
Standard deviation (SD1) = risk = 40% & weight of stock C in portfolio = w1 = 0.5
Stock B
Standard deviation (SD2) = risk = 20% & weight of stock B in portfolio = w2 = 0.5
Variance of the portfolio (Vp) is square of standard deviation of the portfolio (SDp).
Vp = (w1)2(SD1)2+(w2)2(SD2)2+2(w1)(w2)(SD1)(SD2)(r12)
Where w represents weight of stock in total portfolio and r12 represents correlation co-efficient between 2 stocks which is 0.10
= (0.5)2(0.4)2+(0.5)2(0.2)2+2(0.5)(0.5)(0.4)(0.2)(0.1)
=(0.25)(0.16)+(0.25)(0.04)+0.004
=0.04+0.01+0.004
Vp=0.054
Standard deviation of portfolio is square root of Vp
SDp = 0.23
So risk of the portfolio of equal amounts of stocks B & C is 0.23
Answer : Risk of portfolio between stocks B & C (0.23) is less than risk of portfolio between stocks A & B (0.29)
So portfolio between stocks B & C is recommended.