Let’s say there are 2 securities in the portfolio whose standard deviations are 10% and 15%.
Let’s say we’ve invested $1000 in our portfolio of which $750 is in security 1 and $250 is in security 2. So the weight of security 1 in portfolio is 75% (750/1000) and the weight of security 2 in portfolio is 25% (250/1000).
Its value lies between -1 and 1. -1 implies that the two securities move exactly opposite to each other and 1 implies that they move in exactly the same way in same direction. 0 implies that there is no relation as of how the securities move with respect to each other. For our example, let’s take correlation as 0. 25 which means that if one security increases by $1, the other increases by $0. 25.
For this example, variance would be calculated as (0. 75^2)(0. 1^2) + (0. 25^2)(0. 15^2) + 20. 750. 250. 10. 15*0. 25 = 0. 008438.
So, it would be equal to 0. 008438^0. 5 = 0. 09185 = 9. 185%.
If correlation equals 1, standard deviation would have been 11. 25%. If correlation equals 0, standard deviation would have been 8. 38%. If correlation equals -1, standard deviation would have been 3. 75%.
