# Friedman-Savage Double Inflection

what Friedman-Savage Double Inflection want to tell about?

basically that your level of risk adverseness changes as you go through time.

It’s not about time. The horizontal axis (the abscissa) is _ income _, not time.

Your level of risk aversion changes as your level of _ income _ changes.

Utility vs. Risk

At low income levels and at very high income levels - The function / graph is concave (Risk averse) while in between graph is convex (Risk seeking).

try to explain with this - as to why people buy low payoff risky items - lottery tickets - while also insuring against low risks with low payoffs (flight insurance e.g.).

Bumping this.

To clarify for the double-inflection curve: it is about potential income? I’m struggling with whether the curve applies to a particular person at a particular income/wealth level, or if it applies to different people, at different income levels (ie - this is where you are on the curve now, since you’re at this income level, but if you lost your job, you’d be at a lower part of the curve). Right now i’m thinking it applies to a particular person at a particular income/wealth level, because if the curve applies to different people at different wealth/income levels, then no one should both buy flight insurance and buy a lottery ticket, because those behaviors occur at different levels of wealth. But am prepared to be wrong on that

Always think better in examples, so - For example, Bob makes \$50k per year. He purchases flight insurance with payoff of the price of a plane ticket (say \$250), with probability of say 1% paying out. He also purchases a lottery ticket, with payoff of say \$1M with probability of paying off of 1/100000 of a percent. Since Bob is risk-averse at low levels of POTENTIAL income (receiving insurance payout), he is willing to pay to insure that it’s not lost (concave portion of the curve). Since Bob is risk-seeking at high levels of POTENTIAL income (winning the lottery) he is willing to risk the cost of the ticket.

Is the above correct understanding? If so, how is the highest portion of the curve, where the individual becomes risk-averse again, described in the above Bob example? I get that at Warren Buffet levels of wealth, utility of wealth is lower. But for Bob, utility of that much wealth would still be fairly high.

Thanks for the correction S2000.

Yes, I do believe we are talking about it from the perspective of a particular person (or general people) I would say. And yes, the graph is relative to income, not time. I’m not sure why you’re talking about POTENTIAL income because it just states income in the text.

So basically if I have little \$ then I am risk-adverse. Because I want to save as much as possible and don’t want lose. However once I have earned a little bit more I am comfortable taking risks because hedging all that risk can be seen as too costly.

And then when I have significant wealth, I become risk-adverse again because the magnitude of potential loss (say airplane insurance) becomes too great, so I am risk-adverse again therefore prefer to purchase insurance. I hope that helps.

It has nothing to do with time, although it makes a little more sense if you think about it that way, I just wouldn’t put it in writing.

I agree sticking to the verbiage CFAI uses but I can understand how potential income/wealth is relevant. For example, I just passed level III, and expect to have the potential for a higher salary in the future. Seeing as I expect a higher salary, I will take more risk now. So I dont actually have that income yet, but my curve has shifted based on the potential for a higher income in the future.