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Homework answers / question archive / An investor invests 35 per cent of her funds in Company A's shares and the remainder in Company B's shares

An investor invests 35 per cent of her funds in Company A's shares and the remainder in Company B's shares

Finance

An investor invests 35 per cent of her funds in Company A's shares and the remainder in Company B's shares. The standard deviation of the returns on A is 15 per cent and on B is 10 per cent.

Calculate the standard deviation of return on the portfolio assuming the correlation between the returns on the two securities is:

1) +1.0

2) +0.8

3) 0

4) -0.8

What do your answers show?

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1) Computation of the standard deviation of return on the portfolio:-

Standard deviation = (((WA*Stdev.A)^2)+((WB*Stdev.B)^2)+(2*WA*WB*Stdev.A*Stdev.B*Correlation))^(1/2)

= (((35%*15%)^2)+((65%*10%)^2)+(2*35%*65%*15%*10%*1.0))^(1/2)

= (0.276%+0.423%+0.683%)^(1/2)

= 1.381%^(1/2)

= 11.75%

 

2) Computation of the standard deviation of return on the portfolio:-

Standard deviation = (((WA*Stdev.A)^2)+((WB*Stdev.B)^2)+(2*WA*WB*Stdev.A*Stdev.B*Correlation))^(1/2)

= (((35%*15%)^2)+((65%*10%)^2)+(2*35%*65%*15%*10%*0.8))^(1/2)

= (0.276%+0.423%+0.546%)^(1/2)

= 1.244%^(1/2)

= 11.15%

 

3) Computation of the standard deviation of return on the portfolio:-

Standard deviation = (((WA*Stdev.A)^2)+((WB*Stdev.B)^2)+(2*WA*WB*Stdev.A*Stdev.B*Correlation))^(1/2)

= (((35%*15%)^2)+((65%*10%)^2)+(2*35%*65%*15%*10%*0))^(1/2)

= (0.276%+0.423%+0)^(1/2)

= 0.698%^(1/2)

= 8.36%

 

4) Computation of the standard deviation of return on the portfolio:-

Standard deviation = (((WA*Stdev.A)^2)+((WB*Stdev.B)^2)+(2*WA*WB*Stdev.A*Stdev.B*Correlation))^(1/2)

= (((35%*15%)^2)+((65%*10%)^2)+(2*35%*65%*15%*10%*-0.8))^(1/2)

= (0.276%+0.423%-0.546%)^(1/2)

= 0.152%^(1/2)

= 3.90%

The answers shows that as correlation decrease, standard deviation decreases.

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