Question

Arbor Systems and Gencore stocks both have a volatility of 36%. Compute the volatility of a portfolio with 50% invested in each stock if the correlation between the stocks is (a) +1.00, (b) 0.50, (C) 0.00, (d) - 0.50, and (e) - 1.00. In which of the cases is the volatility lower than that of the original stocks?

Answer 1

1.
=sqrt((50%*36%)^2+(50%*36%)^2+2*50%*36%*50%*36%*1)
=36.0000%

2.
=sqrt((50%*36%)^2+(50%*36%)^2+2*50%*36%*50%*36%*0.5)
=31.1769%

3.
=sqrt((50%*36%)^2+(50%*36%)^2+2*50%*36%*50%*36%*0)
=25.4558%

4.
=sqrt((50%*36%)^2+(50%*36%)^2+2*50%*36%*50%*36%*(-0.5))
=18.0000%

5.
=sqrt((50%*36%)^2+(50%*36%)^2+2*50%*36%*50%*36%*(-1))
=0.0000%

6.

In all the cases except case a)