Convexity as a Factor

Finally, a Free Lunch?

November 2024. Reading Time: 10 Minutes. Author: Abhik Roy, CFA.

SUMMARY

  • Convex stocks provided tail risk protection over the last 20 years
  • However, a long-short convexity index would have underperformed the stock market
  • The hedging characteristic is limited to the short side of the portfolio

INTRODUCTION

Higher returns in finance are generally associated with higher risk and vice versa. As a straightforward example, we have previously researched leverage as a tool to increase performance but it comes with a higher risk and a deteriorating Sharpe (read Outperformance via Leverage). Similarly, buffered ETFs offer lower risk but underperform markets over a long period and can simply be replicated using a diluted equity exposure.

How about convexity? Convexity is often discussed in the context of bond markets, where a bond with higher convexity provides a higher upside and lower downside than a lower convexity bond. But generally, this is priced into the yields and consequently, a higher convexity bond offers a lower yield. Since equity pricing is very subjective, we might just find an uncompensated advantage in stocks.

In this research article, we compare the performance of stocks with different convexities and evaluate if there is any edge in these stocks.

WHAT IS CONVEXITY?

Convexity is a measure of the curvature of the relationship between an asset’s price and an underlying factor. In bonds, convexity is measured with respect to changes in interest rates. For equities, we investigate the relationship between stock prices and market returns.

We take the example of Pfizer Inc. (PFE), where we plot the weekly returns against the market and fit a linear and quadratic curve to the distribution. The red dot line shows the linear fit while the green curve indicates a quadratic fit in the chart below. We observe a convex quadratic curve i.e. the coefficient of the quadratic term is positive for the stock so; Pfizer Inc. can be considered as a stock with positive convexity, i.e. it outperformed the market in extreme upward or downward moves.