How much of a good thing is best for you?

We spend most of our time trying to identify good investments and assemble them into an attractive portfolio. The question of how much to invest in that portfolio usually doesn’t get its fair share of our attention. Together with my friend Andy Morton (who runs Citigroup’s G10 interest rate business but may be better known for being the ‘Morton’ in the Heath-Jarrow-Morton term structure model), we wrote a short note (with a long title), ‘Optimal Trade Sizing in a Game with Favourable Odds: The Stock Market’ which explains one way to calculate ideal investment sizing by using a couple of rules of thumb based on a simple outline of individual risk aversion. We illustrate these two heuristics, which are not widely appreciated, with thought experiments involving coin flips and ketchup & French fries, which we hope will make these results easy to recall and apply well after reading the note. We conclude by posing other questions that this simple framework can be used to explore.

You can find the full note, which was accepted for publication on SSRN, here.

Below is a brief excerpt to pique your interest:

“A thought experiment: You can invest your wealth in only two assets: a risk-free one and a market portfolio of all public equities. Your investment choices however are limited to: A) put 100% in the risk-free asset, or B) 10% in the risk-free asset and 90% in equities. You cannot mix A) and B) — you must choose one or the other. What is the lowest return (above the risk-free rate) you would need to expect from equities for you to choose B?

Do you have your number in mind? Great. Now, imagine you’re still in this two asset world, and you wake up one day and find that the expected return of equities is in fact exactly equal to your answer above. But now you’re no longer limited to just options A and B; you’re completely free to invest however much you like in equities, from 0% to 100% or more. How would you invest now?

We’ve asked about a dozen friends this question, all financial professionals. If you’re like them, you’ve likely read the question twice, trying to understand exactly what we’re getting at. You may feel like you just answered that question, and isn’t 90% the answer?

Well, no, we don’t think it is.”

Read the full paper here for our explanation of why we think 45% is about the right answer, and how we can use the perspective of this problem to answer some other interesting questions.


See our pieces here, here and here on estimating the long-term expected return of the stock market and its risk.