= -46% The expected rate of return for the third investment is (.8 * .5) + (.2 * -1) = 20% These calculations show that in our scenario the third investment is expected to be the most profitable of the three. The second one even has a negative ROR. This means that if that investment was done an infinite number of times one could expect to lose 46% of the money invested on the average occasion. The formula of expected value is very straightforward, but its value depends on the inputs. The more alternative outcome scenarios that could occur, the more terms are in the equation. As Ilmanen stated, "The foremost need for multi-dimensional thinking is on inputs. When investors make judgments on the various returns on investments, they should guard against being blinded by past performance and must ensure that they take all or most of the following considerations into account". Historical average returns Financial and behavioral theories Forward looking market indicators such as bond yields; and Discretionary views Continuous scenarios In economics and finance, it is more likely that the set of possible outcomes is continuous (any numerical value between 0 and infinity). In this case, simplifying assumptions are made about the continuous distribution of possible outcomes. See also Abnormal return Expected value Rate of return Notes External links Using Expected Return to Maximize Growth Expected Return Calculator Theory of probability distributions Financial risk