What Our Market Return Forecasts Really Mean: Equity Convexity and Investment Sizing

This is the third in our series on how expected return, risk and risk-aversion come together to determine how much investment risk is ‘right’ for each of us. (The other two notes are here and here, if you’d like to review them.) In this short note we explore how investors think about long-term expected stock market returns as indicated by the results of a survey of 118 friends-of-Elm. The average forecast for the long-term return of the US stock market was 4.2% above inflation. We found something even more interesting in the survey results, which is that the natural way most of our respondents think of the long-term expected return of equities does not include an explicit addition for Convexity Return (the attractive feature of equities that they can go up a lot more than they can go down).

We review a few key insights from some of the pioneers of modern finance, including my former partner Bob Merton, and explain why, given how we typically think of the future, we need to add an estimate of Convexity Return to our base case return estimate when we use the standard tools for determining optimal investment sizing.

The full paper was just accepted on SSRN and can be downloaded here.

Below is a brief excerpt to whet your appetite:

You’re probably familiar, at least in passing, with the `convexity’ of long-term bonds – i.e. that yields dropping 1% produce a bigger price move than yields rising 1%. A significant amount of brainpower has gone into understanding all the ramifications of this convexity in the fixed income markets, and the various issues and opportunities that arise are now well understood. Equities, on the other hand, aren’t typically regarded as convex instruments, but equities do have important convexity properties. Our story of how equity convexity, return forecasts, and investment sizing all tie together starts in the late 1960s with a remarkable result from Robert C. Merton.

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Disclaimer: “All I say is by way of discourse, and nothing by way of advice. I should not speak so boldly if it were my due to be believed.” – Montaigne