Gamma Gamma Hey!

One approach to asset allocation that can better position portfolios for increasing volatility is to increase convexity, or gamma.  By instituting a barbell approach to asset allocation, portfolios will be positioned for increased payoffs from more extreme events without adjusting the delta, or first derivative effects of changes in the underlying.  For example, what’s the difference between the following two portfolios?:

Portfolio A: 80% equities with a beta of 1.25, 20% cash

Portfolio B: 100% equities with a beta of 1

Both portfolios have a beta of 1, and the first derivative effects are the same in each for small changes in underlying equity prices.  However, the second derivative effects on Portfolio A are favorable to Portfolio B in the case of increased volatility, as non-linear effects impact the portfolios differently.  The two portfolios have the same exposure to small moves in the underlying, but when more extreme moves occur, non-linear effects have historically increased, and higher convexity portfolios have outperformed.

Does adding gamma, or convexity, to portfolios provide an advantage if that ultimate increase in volatility is less predictable?  We believe it does.  By positioning to take advantage of the non-linear effects of outsized moves in the underlying, portfolios that are longer-convexity are also much better able to capture additional returns using a systematic approach to rebalancing.

Consider two portfolios of equal volatility, with Portfolio A comprised of corporate bonds, and Portfolio B comprised of equities and treasuries.  As values in the underlying change by small amounts, the two portfolios perform similarly.  However, after a significant move up (down) in credit, equities are likely to have moved up (down) by a greater amount, alongside a concurrent down (up) move in treasuries. 

Subsequent to such a move, rebalancing Portfolio B to get back in line with initial risk objectives allows the investor to add more cheap treasuries (equities) with profits from their equities (treasuries), improving the average price within Portfolio B.  Portfolio A, on the other hand, can only endure the volatility without being able to extract any benefits from it.

Portfolio B will therefore outperform Portfolio A over the long run, so long as it is rebalanced (otherwise, it will have the same performance).  A rebalanced Portfolio B will generate higher long-term returns on similar volatility, and those excess returns are alpha.  The same alpha is generated in our first example by using cash to buy additional equities after a correction – something Portfolio A can do and Portfolio B cannot.

Factors affecting the level of this alpha are the frequency and magnitude of multi-standard deviation moves in the underlying.  If you are implementing a systematic approach to rebalancing, more frequent outsized moves in underlying assets will increase the portfolio-level alpha generated, as will an increased magnitude in those moves.  While we cannot control the frequency of moves in the underlying, we can increase the magnitude of the moves within our portfolios.  This can be accomplished by using the barbell approach, which increases convexity, or gamma.


Dave Donnelly is the Founder and CEO of Strategic Alpha, a rebalancing service dedicated to helping financial advisors improve client outcomes.