where 
the portfolio variance is equivalent to the portfolio standard deviation squared as the number of assets in the portfolio grows the terms in the formula for variance increase exponentially for example a three asset portfolio has six terms in the variance calculation while a five asset portfolio has 15 using software like excel can make the calculation of these numbers easier portfolio variance and modern portfolio theorymodern portfolio theory mpt is a framework for constructing an investment portfolio mpt takes as its central premise the idea that rational investors want to maximize returns while also minimizing risk sometimes measured using volatility investors seek what is called an efficient frontier or the lowest level of risk and volatility at which a target return can be achieved risk is lowered in mpt portfolios by investing in non correlated assets assets that might be risky on their own can actually lower the overall risk of a portfolio by introducing an investment that will rise when other investments fall this reduced correlation can reduce the variance of a theoretical portfolio in this sense an individual investment s return is less important than its overall contribution to the portfolio in terms of risk return and diversification the level of risk in a portfolio is often measured using standard deviation which is calculated as the square root of the variance if data points are far away from the mean then the variance is high and the overall level of risk in the portfolio is high as well standard deviation is a key measure of risk used by portfolio managers financial advisors and institutional investors asset managers routinely include standard deviation in their performance reports example of portfolio variancefor example assume there is a portfolio that consists of two stocks stock a is worth 50 000 and has a standard deviation of 20 stock b is worth 100 000 and has a standard deviation of 10 the correlation between the two stocks is 0 85 given this the portfolio weight of stock a is 33 3 and 66 7 for stock b plugging in this information to the formula the variance is calculated to be variance is not a particularly easy statistic to interpret on its own so most analysts calculate the standard deviation which is simply the square root of variance in this example the square root of 1 64 is 12 81 