Hi Hope you are doing well. Page 19 of ch18 says that - 'if rho is equal to +1 and -1, then there exists a portfolio with V=0: 1. if rho =-1, it means positive holdings of both securities i.e. x1 and x2>0 2. if rho =+1, it means negative holding in x2 and positive holdings in x1. I looked at the graph present on the next page, but could not figure out the reason of positive and negative holding mentioned above? could u pls explain the same.
Hi, The variance of a portfolio of two securities (a and b) Vp = xa^2 * va + xb^2 * vb + 2*xa*xb*rho*sigma(a)*sigma(b). Bearing in mind that the variance of each asset is positive then the first two terms of the above will always be positive. So in order for the whole term to equal 0 then the final term must be negative. Because sigma(a) and sigma(b) are positive, and with xa+xb=1: then if rho=1, one of xa or xb need to be negative so that the final term is negative if rho=-1 then both xa and xb will need be positive so that the final term is negative Hope this helps. Let me know if you have any further questions here. Joe
