Hi Everybody,The starting point for the dispersion is : Var(X+Y) = Var(X) + Var(Y) + 2 * covariance… (1) Index_Price = w1 * S1_Price + w2 * S2_Price (2) Thus(????) (Vol_Index)^2 = w1^2 * (Vol_Stock1)^2 + w2^2 * (Vol_Stock2)^2 + 2*w1*w2*covariance… (3) But to get a relation btw the vol of the index and the vol of the stocks (and the correl), we need to express the return of the index as a function of the return of the stocks (as vols are std deviation of the returns and not of the prices). But we don’t have a nice relation in terms of return… Am I missing something cause (3) would work with: Return_Index = w1 * Return_Stock1 + w2 Return_Stock2 (4) But seems no to be valid...Any idea why this is ? Thank you,Daoud

Hi again,Ive computed the difference between (Vol_Index)^2 and \Sum_{i=1}^N w_i^2 Vol_i^2 + 2 \Sum_{i=1}^N \sum_{j<i} w_i w_j Vol_i Vol_j \rho_{ij}.For the stock prices it matches perfectly and not for the returns as I mentionned before.But the error seems to be very acceptable (I run this with 1 year historical correlation ans vols over 3 years), do you know why the error is small and can someone quantify the error ???Im really stuck with taht thing....Thank you everyone.Daoud

I think you are making a classical mistake that many people make - confusing number of shares with weights. I am guessing w1, w2 etc are the weights of the stocks S1, s2 etc in you basket or index right ? if your index is initially set to I(0) then the number of shares of stock 1 in the index is:n1*S1(0) = w1 * I(0)n1 = w1*I(0)/S1(0) where S1(0) is the stock price at time 0.at any time you calculate the current valueof the index as follows:I(t) = n1*S1(t) + n2*S2(t) + .. = w1*I(0)/S1(0) * S1(t) + w2 * I(0)/S2(0) * S2(t) + ...the retrn at time t is given byI(t)/I(0) - 1 = w1*S1(t)/S1(0) + w2* S2(t)/S2(0) + ... - 1 = w1 * ( S1(t)/S1(0) - 1) + w2 * (S2(t)/S2(0) - 1) + ... = w1 * r1(t) + w2*r2(t) + .... since w1 + w2 + ... = 1 by definition.hth otherwise if i have the wrong end of ths stick I apologise.

Oh yeah, thank you !Now I really understand the meaning of this.Your help was precious.Godd afternoon,Daoud

Oh yeah, thank you !Now I really understand the meaning of this.Your help was precious.Godd afternoon,Daoud

glad to be of service.