When we have sigma = 0 for a portfolio should the retuns not be equal to zero in that portfolio? i mean for any market condition any positive return in the portfolio is offset by assets returning same negative return. so when we say expected return from portfolio is equal to the individual expefcted returns what is the basis for that, in a portfolio where sigma is zero it should be zero.
Std dev of returns on the risk free asset is zero, but returns are positive.
yeah but … to simply consider a portfolio of only two stocks and both have a correlation of -1 and equal std. dev. every single time stock A goes up stock B goes down by the same amount