I was thinking about whether it's worthwhile for younger investors to take more risk for a higher reward. I posed the question, what if you could invest 100% of your portfolio in one of two investments each year. Investment One is the "high risk" investment, 45% of the time it was worth zero at the end of the year, but 55% of time it would double at the end of the year.
Your other option is the "no risk" investment. 100% of the time it's worth 10% more at the end of the year. You are 25 years old and saving 50k per year, and want to retire wealthy, which you believe will require $5M.
On the surface, the EV of both should be the same, +10% per year. But the high risk option offers much more upside, at the risk of having to start over every so often. Let's also assume you are 25 years old when you start.
If you only choose the no risk option, I estimate you'll have $5M about age 50. The high risk option can get you there in a little over 6 years (age 31). But only does this once in thirty six times. Presuming you switch to the conservative approach after busting, 97% of the time you'll have to work an extra one to six years until retirement.
I looked at taking shorter periods of risk, then switching to the no risk investment. For example, if you only tried the high risk option for three years, one sixth of the time you'd make $550k by the third year and retire by age 46.5. But the rest of the time you'll be working an extra two or three years. Two years of high risk only allows you to retire at age 48 a little less than one third of the time, while adding two more years of work the majority of the time.
These are all assuming I did the math right. And I don't pretend to say my super simplified scenario closely approximates the index funds vs. putting it all into one investment risks/rewards.
But I just couldn't find a scenario where I felt that taking the risk was clearly the better option. And I think it's because of one important factor, the relative utility of having more money. Having $2M doesn't normally make you twice as happy as having $1M. The relative utility of every increasing dollar you accumulate is less than the previous.
In fact, just having a significant amount of cash in the bank has tremendous value. It provides you with more opportunities. More investment opportunities (i.e. buying a business for example). It gives you more freedom, the ability to work at jobs you like over jobs you need, for example. Going back to zero has significant opportunities costs. You'd hate for it to happen just before finding the one great investment opportunity of your life. Having money provides so many options it would be miserable to go back to ground zero after you've accumulated a reasonable amount.
Or maybe I'm just getting cranky and conservative in my old age
