The following video provides a general overview of Monte Carlo and in particular of expected lifetime utility beginning at the 9:10 minute mark in the video.

Modern financial economics tell us that we want to choose our spending and investment strategies to maximize our expected utility over our remaining lifetimes. The word "expected" means average and the word "utility" means happiness. The mathematical utility function we are using to form this table is the constant relative risk aversion function, which is standard in economics. Utility from your living standard in year t is assumed to equal Ct^(1-g)/(1-g), where Ct is your living standard (also called consumption) in year t and g is your coefficient of risk aversion. Your remaining lifetime utility is the weighted sum of each year's future annual utility value with weights determined by what you enter for the Standard of Living Index under Settings and Assumptions. Thus, if you tell the program that you want your living standard to decline starting, say, at age 80, the weights on your utility after year 80 will be smaller than before age 80. When your risk aversion coefficient, g, is larger, you get less additional happiness in year t from a given increase in Ct. You also lose more happiness from a given decrease in Ct. In other words, the higher your risk aversion, the more concern you have with downside than with upside risk.

In running MaxiFi's risk analysis, you are telling it you are investing at risk. Consequently, the particular living standard trajectory you'll experience is uncertain. A generally high trajectory that has few years of low living standards will produce a high value for your realized (experienced) lifetime utility. A generally low trajectory with large declines in your living standard in particular years will produce a low value of your realized lifetime utility. Since neither you nor MaxiFi knows what trajectory you'll experience, it averages across the possible realized lifetime utilities (one for each living standard trajectory) that you'll experience. This is your expected remaining lifetime utility.

When you consider our table of living standard reward-risk value for different degrees of risk tolerance and your three different spending/investment strategies, you'll have to decide your degree of risk aversion. We show you the question 'How much risk are you willing to accept?' to which the responses can be 'Almost None,' 'Very Little,' 'Moderate,' 'Some,' and 'A Lot' corresponding to risk aversion levels of 9, 7, 5, 3, and 1. As you can see by considering investment strategies that are safer or riskier, holding fixed your spending strategy (as set by your specified safe rate of return), the more risk averse you are, the better safe investment strategies will look in terms of our reward-risk index compared with risky investment strategies.

How do we measure utility (happiness)? We don't. There is no absolute measure of utility (happiness). Instead, we calculate for a given alternative spending/investment strategy the percentage increase (decrease) in your Base Strategy living standard under all possible trajectories that's needed to provide you the same expected remaining lifetime utility as you'd receive from that alternative strategy. If this so called consumption equivalent percentage difference for an alternative strategy is, say, 17 percent, we report that your Base Strategy expected remaining lifetime utility, which we call your living standard reward-risk index, is 100 and your alternative's reward-risk index is 117. If the alternative strategy produced lower average remaining lifetime utility and you'd need to consume 17 percent less in every circumstance under your Base Strategy to do as poorly, on average, as the alternative strategy, we'd set the index to 83 for that alternative.