Traditional finance literature says that individuals may choose their risk-tolerance in order to adequately model their financial preferences. A person who chooses a high-risk financial option is willing to deal with greater variability; a person who chooses a low-risk option prefers outcomes with low-variability.
Underlying these notions is the idea that risk-tolerance is a stand-alone, unique, irreplaceable concept.
I like to compress ideas to their simplest form, and I think we can model individual financial preferences without the notion of risk-tolerance:
Risk-tolerance can be wholy framed as prefering a utility function with a particular curve of marginal diminishing utility. There is no need for extra calculus beyond standard von Neumann-Morgenstern (vNM) rationality, which involves acting so as to maximize expected utility, considering one’s utility function. Financial modeling is as simple as assigning an amount of utility per dollar over the range of the real numbers, and acting so as to maximize one’s expected utility.
If one appropriately updates their utility function, they don’t have to deviate from this simple application of vNM. If my preference is to definitely make $9,000 over a 1% chance of $1 million, you could just say I give greater utility to the first $9k, less utility per dollar for higher amounts of money, and I still should just act so as to maximize expected utility as per vNM.
I am not saying the use of the term “risk-tolerance” has to go, but let’s not think it’s this special thing when it is not.