you would end up in the same spot regardless of whether you’re maximizing utility or maximizing wealth.
But under conditions of uncertainty, expected utility is not a monotonic function of expected wealth.
Well, the first thing that the decision depends on is the risk aversion and there is no single right one-size-fits-all risk aversion parameter (or a function).
I’ll defer to the SSC link on why I think it would be better to make one up—or rather, make up a utility function that incorporates it.
Note that the market prices risks on the bet-is-a-tiny-percentage-of-total-wealth basis.
Indeed. The case in question wasn’t a market-priced risk, though, as the reward was a potential tax advantage.
Under uncertainty, you must have a risk aversion parameter—even if you try to avoid specifying one, your choice will point to an implicit one.
A made-up risk aversion parameter might also be a reasonable way to go about things, though making up a utility function and using the implicit risk aversion from that seems easier. The personal financial planning advice I’ve seen doesn’t use any quantitative approach whatsoever to price risk, which leads to people just going with their gut, which is what I’m calling dumb.
making up a utility function and using the implicit risk aversion from that seems easier.
Um, I feel there is some confusion here. First, let’s make distinct what I’ll call a broad utility function and a narrow utility function. The argument to the broad utility function is the whole state of the universe and it outputs how much do you like this particular state of the entire world. The argument to the narrow utility function is a specific, certain amount of something, usually money, and it outputs how much you like this something regardless of the state of the rest of the world.
The broad utility function does include risk aversion, but it is.. not very practical.
The narrow utility function is quite separate from risk aversion and neither of them implies the other one. And they are different conceptually—the narrow utility function determines how much you like/need something, while the risk aversion function determines your trade-offs between value and uncertainty.
The personal financial planning advice I’ve seen doesn’t use any quantitative approach whatsoever to price risk
Well, I don’t expect personal financial planning advice to be of high quality (unless you’re a what’s called “a high net worth individual” :-D), but its recommendations usually imply a certain price of risk. For example, if a financial planner recommends a 60% stocks / 40% bonds mix over a 100% stocks portfolio, that implies a specific risk aversion parameter.
But under conditions of uncertainty, expected utility is not a monotonic function of expected wealth.
I’ll defer to the SSC link on why I think it would be better to make one up—or rather, make up a utility function that incorporates it.
Indeed. The case in question wasn’t a market-priced risk, though, as the reward was a potential tax advantage.
Under uncertainty, you must have a risk aversion parameter—even if you try to avoid specifying one, your choice will point to an implicit one.
You can also use the concept of the certainty equivalent to sorta side-step the uncertainty.
A made-up risk aversion parameter might also be a reasonable way to go about things, though making up a utility function and using the implicit risk aversion from that seems easier. The personal financial planning advice I’ve seen doesn’t use any quantitative approach whatsoever to price risk, which leads to people just going with their gut, which is what I’m calling dumb.
Um, I feel there is some confusion here. First, let’s make distinct what I’ll call a broad utility function and a narrow utility function. The argument to the broad utility function is the whole state of the universe and it outputs how much do you like this particular state of the entire world. The argument to the narrow utility function is a specific, certain amount of something, usually money, and it outputs how much you like this something regardless of the state of the rest of the world.
The broad utility function does include risk aversion, but it is.. not very practical.
The narrow utility function is quite separate from risk aversion and neither of them implies the other one. And they are different conceptually—the narrow utility function determines how much you like/need something, while the risk aversion function determines your trade-offs between value and uncertainty.
Well, I don’t expect personal financial planning advice to be of high quality (unless you’re a what’s called “a high net worth individual” :-D), but its recommendations usually imply a certain price of risk. For example, if a financial planner recommends a 60% stocks / 40% bonds mix over a 100% stocks portfolio, that implies a specific risk aversion parameter.