Question

Arbor Systems and Gencore stocks both have a volatility of 45%. 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

Given, the standard deviation of the individual stocks in the portfolio= 45%

Weight of each stock= 50%

We know portfolio standard deviation= sqrt(w²_A*?²(R_A) + w²_B*?²(R_B) + 2*(w_A)*(w_B)*?(R_A)*?(R_B)Corr(R_A, R_B))

a. For Corr(R_A, R_B)= 1, standard deviation of portfolio= 45%

b For Corr(R_A, R_B)= 0.5, standard deviation of portfolio= 38.97%

c. For Corr(R_A, R_B)= 0, standard deviation of portfolio= 31.82%

d. For Corr(R_A, R_B)= -0.5, standard deviation of portfolio= 22.5%

e For Corr(R_A, R_B)= -1, standard deviation of portfolio= 0%

Hence, the volatility is the lower of the original stocks in all the cases except first, or in cases where the correlation is less than 1.