I used to have a direct reporting relationship to a CEO-boss of a mid-size US public company where if he said something once it was generally regarded as imperative and immediately so. If he said it twice yellow lights needed to start flashing in my head. And if he said it three times: "mayday mayday we're going down." I learned to tune into patterns of repetition. So, now three times in the last year when I have read something about retirement finance I have run into something in the article or footnotes about relative-risk utility functions and certainty equivalents as it relates to retirement investing or consumption. I won't call it a maday situation here but I did feel that I needed to make sure that I understood what they were talking about. Here are three examples of links to something where this has come up:
OK, so I dove into the math and I think I finally made sense of at least part of it after a couple days -- including solving for certainty equivalents by inverting a U function used against different probabilistic outcomes. I won't bore us with the details here. While there are many utility functions that can map to reasonable real-world behavior I at least have a bead on how I might fold it into my own analysis (future posts will reveal if I actually made sense of it or if I made a totally embarrassing hash of it). In the meantime I thought that
this quote from Aswath Damodaran at the Stern School puts all of this utility stuff in a proper context before I get too far down the road and before I take the research efforts and conclusions of others too seriously:
While utility functions have been mined by
economists to derive elegant and powerful models, there are niggling details
about them that should give us pause. The first is that no single utility
function seems to fit aggregate human behavior very well. The second is that
the utility functions that are easiest to work with, such as the quadratic
utility functions, yield profoundly counter intuitive predictions about how
humans will react to risk. The third is
that there are such wide differences across individuals when it comes to risk
aversion that finding a utility function to fit the representative investor or
individual seems like an exercise in futility. Notwithstanding these
limitations, a working knowledge of the basics of utility theory is a
prerequisite for sensible risk management.
And we haven't even discussed at this point whether or how risk aversion changes over time or in response to current changing conditions. Mine probably changes every day because I am at least as irrational as everyone else.
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