If the actual utility you receive as a function of the total “payout” of your “investments” has diminishing marginal returns, then the character of the portfolio to maximize expected utility depends upon the failure correlations between the investment options.
IE, in the case that the utility function is sufficiently convex to payout and the various investments all fail independently of each other, a strategy of investing in only the highest yield and lowest risk choices is not optimal: a small investment in a middling investment decreases the risk of total failure (and corresponding hit to expected utility) enough to be worth the hit to expected payout.
I haven’t run the analysis, but my intuition is that advocacy for a barbell strategy limited to just high-risk stocks and T-bills is an empirical claim about the risks along the following lines:
1) The failure of middling risk stock is well correlated with the failure of high risk stock
2) The failure of less-risky investments than T-bills (paper currency, rice & beans under nitrogen, solar panels, etc.) are well-correlated with the failure of T-bills and have lower annual yields.
3) Utility is a moderately convex function of payout. (If it were very convex, you’d want most or all of your funds in T-bills, not just a bit; if it were linear or concave, “risk” isn’t a thing and all funds would be in the stocks.)
I’ll trust Taleb on #1, and #3 seems reasonable most of the time, but on #2, it would seem to me that while a good portfolio would be based around the high-risk stocks backed up with a small portion of cash-equivalents, the “insurance” against failure of both of those things is cheap enough that it should be included early on.
(As an aside, I’m pretty sure that Taleb suggests “mostly” high-yield/high-risk holdings, with only enough T-bill stuff to keep you off the streets if the stock fails. That’s not what I’d pick out as a strategy that is likely to cause bad outcomes because you didn’t take enough risk.)
If the actual utility you receive as a function of the total “payout” of your “investments” has diminishing marginal returns, then the character of the portfolio to maximize expected utility depends upon the failure correlations between the investment options.
IE, in the case that the utility function is sufficiently convex to payout and the various investments all fail independently of each other, a strategy of investing in only the highest yield and lowest risk choices is not optimal: a small investment in a middling investment decreases the risk of total failure (and corresponding hit to expected utility) enough to be worth the hit to expected payout.
I haven’t run the analysis, but my intuition is that advocacy for a barbell strategy limited to just high-risk stocks and T-bills is an empirical claim about the risks along the following lines:
1) The failure of middling risk stock is well correlated with the failure of high risk stock
2) The failure of less-risky investments than T-bills (paper currency, rice & beans under nitrogen, solar panels, etc.) are well-correlated with the failure of T-bills and have lower annual yields.
3) Utility is a moderately convex function of payout. (If it were very convex, you’d want most or all of your funds in T-bills, not just a bit; if it were linear or concave, “risk” isn’t a thing and all funds would be in the stocks.)
I’ll trust Taleb on #1, and #3 seems reasonable most of the time, but on #2, it would seem to me that while a good portfolio would be based around the high-risk stocks backed up with a small portion of cash-equivalents, the “insurance” against failure of both of those things is cheap enough that it should be included early on.
(As an aside, I’m pretty sure that Taleb suggests “mostly” high-yield/high-risk holdings, with only enough T-bill stuff to keep you off the streets if the stock fails. That’s not what I’d pick out as a strategy that is likely to cause bad outcomes because you didn’t take enough risk.)