If the broker believes some investment has a positive expectation this year (and is not very likely to crash terribly), he could advise John Smith to invest in it for a year minus a day, take the proceeds and go to Vegas. If he arrives with $550,000 instead of $500,000, there’s a betting strategy more likely to wind up with $1,000,000 than the original plan.
The balance of risk and reward between the investment part and the Vegas part should have an optimal solution; but since anything over $1,000,000 doesn’t factor nearly as much in John’s utility function, I’d expect he’s not going to bother with investment schemes that have small chances of paying off much more than $1,000,000, and he’d rather look for ones that have significant chances of paying off something in between.
Doug S:
If the broker believes some investment has a positive expectation this year (and is not very likely to crash terribly), he could advise John Smith to invest in it for a year minus a day, take the proceeds and go to Vegas. If he arrives with $550,000 instead of $500,000, there’s a betting strategy more likely to wind up with $1,000,000 than the original plan.
The balance of risk and reward between the investment part and the Vegas part should have an optimal solution; but since anything over $1,000,000 doesn’t factor nearly as much in John’s utility function, I’d expect he’s not going to bother with investment schemes that have small chances of paying off much more than $1,000,000, and he’d rather look for ones that have significant chances of paying off something in between.