The Relationship between Investing and Expected Utility
https://www.fool.com/investing/2019/11/17/5-investment-strategies-that-can-help-you-become-a.aspx
This article gives five pieces of investment advice. The first is to choose low-cost investments, for example, index funds. The second is to use the right accounts, which involves choosing a retirement account based on whether you will be making more or less money than now when you retire. The third is to stay well diversified, which the Motley Fool says not doing could “come back to bite you if the stock plummets.” The fourth is to practice dollar-cost averaging, which is like diversifying in time rather than in the number of stocks you invest in. The fifth is to consider help from a financial advisor, specifically one certified by the NAPFA, or a robo-adviser.
Staying well diversified was mentioned in class as an advisable strategy. To explain this, suppose it is possible to invest in 10 separate possible future events. Each event has a 50% chance of happening, gives a utility of 2n if it happens, where n is the amount of money invested, and which gives a utility of 0 if they do not. If you put all your money in Event 1, you have a 50% chance of losing all the money you invested, but if you put 1/10 of your money in each event, you have only about a 0.1% chance of losing all the money you invested. Losing all the money you invested is worse because not only do you have less money, you have less money to invest with. If you stay well diversified, then if some stocks crash, you will still have money left over to invest with. As described in the course textbook; Networks, Crowds and Markets; this decreasing value of money over time can be modeled with the equation U(w) = ln(w). Your expected utility of a bet or investment in a future event can be modeled by the function aln(OArw) + bln(OB(1-r)w), where a is your believed probability that an event will happen, b is your believed probability that it will not happen, OA is the odds on A (which is the ratio of money earned to money invested if A happens), OB is the odds on B (which is the ratio of money earned to money invested if A does not happen), r is the fraction of your wealth you decide to bet that A will happen, and (1-r) is the fraction of your wealth you decide to bet that A will not happen. The goal is to determine the value of r that maximizes the expected utility. As stated in lecture, “this is a function that investment advisors use all the time behind the scenes to give you advice.” Going to a financial advisor is logical in that they would probably have better believed probabilities a and b to make better investments. A financial advisor would most likely use this equation, but a robo-adviser as suggested in the article would be almost certain to as there is nothing it can use but equations. However, because advisors cost money, going to an advisor is itself an investment which may or may not pay off depending on how much worse you would have done without the advisor.