Question

Suppose Wesley​ Publishing's stock has a volatility of

65 %

while Addison​ Printing's stock has a volatility of

30 %

If the correlation between these stocks is

15 %

what is the volatility of the following portfolios of Addison and​ Wesley:

a.

100 %

Addison

b.

75 %

Addison and

25 %

Wesley

c.

50 %

Addison and

50 %

Wesley

Answer 1

We know that,

Standard Deviation of portfolio = ( (Wa*std dev of A)^2 + (Wb*std dev of B)^2 + 2*std dev of A * std dev of B * Wa*Wb * correlation )^0.5

a. Standard Deviation of portfolio = ( (Wa*std dev of A)^2 + (Wb*std dev of B)^2 + 2*std dev of A * std dev of B * Wa*Wb * correlation )^0.5

Standard Deviation of portfolio = ( (1*0.3)^2 + 0 + 0 )^0.5 = 30% Answer

b. Standard Deviation of portfolio = ( (Wa*std dev of A)^2 + (Wb*std dev of B)^2 + 2*std dev of A * std dev of B * Wa*Wb * correlation )^0.5

Standard Deviation of portfolio = ( (0.3*0.75)^2 + (0.25*0.65)^2 + 2*0.65*0.25*0.3*0.75*0.15)^0.5 = 29.66% Answer

c. Standard Deviation of portfolio = ( (Wa*std dev of A)^2 + (Wb*std dev of B)^2 + 2*std dev of A * std dev of B * Wa*Wb * correlation )^0.5

Standard Deviation of portfolio = ( (0.3*0.5)^2 + (0.5*0.65)^2 + 2*0.65*0.5*0.3*0.5*0.15)^0.5 = 37.78% Answer

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