Statistics for three stocks, A, B and C, are shown in the following tables: Stan

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.

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