15th letter to friends of Brunei [Portfolio Management(Part 2)]

Calculating the risk (or portfolio standard deviation) is not as straight forward as return (read my immediate previous blog entry). This is because we have to consider on important factor in the equation: the expected correlation of each asset with each of the other assets.

Correlation measures the extent to which the returns on 2 assets move together. If 2 assets move up and down together, we say they are positively correlated. If they move in opposite directions, we say they are negatvely correlated. If there are no particular relationship between the 2 assets, we say they are uncorrelated. Therefore, correlation factor between 2 assets lies between -1 to +1

Let me illustrate using a 2 assets portfolio example.

Stock X

Weightage(W(x)): 20%

Standard Deviation(risk R(x)): 15%

Stock Y

Weightage(W(y)): 80%

Standard Deviation (risk R(y)): 30%

Correlation factor (Corr(x,y)) between X & Y = +0.5

The portfolio risk [P(r)] can be calculated as follows:

P(r) = √ [W(x)2 R(x)2 + W(y)2 R(y)2 + 2 W(x)W(y)R(x)R(y)(corr(x,y))]

= √ [(0.2)2 (15)2 + (0.8)2 (30)2 + 2 (0.2)(0.8)(15)(30)(+0.5)]

= √ [(0.04)(225) + (0.64)(900) + 72]

=√ [9 + 576 + 72]

=√ [657]

=25.63%

(In real life, this is done through computer spreadsheets.)