What Our Market Return Forecasts Really Mean: Convexity in Equity Returns and its Implications for Investment Sizing

Abstract

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 very well understood. Equities, on the other hand, aren't typically regarded as convex instruments. We tend to think of equities directly in terms of their price, rather than their 'yield' as we do with bonds, and often think primarily about their annual return, which moves lockstep with price. But, as we discuss below, equities do have important convexity properties, and they tie in to two themes we think deserve more attention: how investors think about long-term returns, and how to properly size portfolios and investments. 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.

Keywords: Decision Making under Uncertainty, Risk, Utility, Risk Aversion, Kelly, Coin Flip, Heuristics, Rules of Thumb, Market Timing, Gambling, Betting, CRRA

JEL Classification: B12, B16, B20, C00, C10, C11, C50, C57, C73, D03, D81, D83, E00, G00, G02, G11, G12, G14, G17, G23