| # Rate of return of a financial portfolio The rate of return (or, return) of a financial asset over a given period (say, a year, or a day) is the interest obtained at the end of the period by investing in it. In other words, if, at the beginning of the period, we invest a sum in the asset, we will earn at the end. For assets, we can define accordingly the vector of rates of return. Assume that at the beginning of the period, we invest a sum in all the assets, allocating a fraction (in ) in the -th asset. Here is a non-negative vector which sums to one. Then the portfolio we constituted this way will earn The rate of return of the porfolio is the relative increase in wealth: The rate of return is thus the scalar product between the vector of individual returns and of the portfolio allocation weights . Note that, in practice, rates of return are never known in advance, and they can be negative (although, by construction, they are never less than ).