Gamma Concepts- The Rates of Change

by Adam Millers, University of Iowa

Related to the Iowa Economics Forum discussion, dated Monday December 8th, 2014

On October 15, Treasury markets experienced an unprecedented spike in the price volatility of 7-10 year securities.  Despite the brevity of this anomaly, and the ease with which it could be identified (or at least written off) as nothing more than a statistical outlier of normal market movements, the October 15 spike provides deep insight into the changing dynamics of both financial markets and the economy as a whole.

As reported by the New York Times on October 19th, the precipitous decrease in Treasury yields (from 2.2 to 1.9 percent) was the sort of erratic behavior characteristic of flash crashes or, even worse, events like the collapse of Lehman Brothers in the heart of the 2008 financial crisis; it wasn’t the kind of instability that investors like to see in the market for quintessentially vanilla bonds.

The Oct 15 spike was the result of a confluence of seemingly unrelated events, borrowed here for the purpose of setting up a contextual framework from Matt Levine of Bloomberg View ( and an article in Risk Magazine (  They are as follows:

  • The collapse of M&A negotiations between Abbvie and Shire.
  • An extremely disappointing report from the retail sector.
  • Huge, unexpected declines in energy prices.
  • Losing bets on the Federal Reserve increasing rates.

To briefly summarize the chronology, as it makes sense to me:

1) The perception of positive trends in certain underlying economic indicators had convinced a number of funds to take prominent short positions in 7-10 Treasuries, founded on the assumption that the Fed would respond to the specter of inflation embedded in credit-engendered growth by increasing rates.  (In this case, increased available returns on the market would increase Treasury yields to a proportional level by lowering their price).

2) When retail and energy stocks tanked along with the massive long positions that funds had taken in Shire (betting on the return to be earned from the share premium that would likely be paid in the potential acquisition), there was a net movement of capital into the safety of Treasuries.

3) Treasury prices therefore increased.  (The dynamic here is worth further discussion, as a number of other factors are implicated in the recent downward trend of yields, including the effects of an appreciating dollar and the relative appeal of US government-backed, dollar-denominated debt in a climate of global economic instability).  Now the short positions were in trouble…

Which brings us to the concept of gamma.

In the valuation of options, the explanation of the relationship between the contract itself and the underlying security naturally relies on derivatives.  Delta is the rate of change of the option value relative to the value of the underlying security.  In economic terms, you can think of it as the price elasticity of, for instance, an option contract on one share of Apple stock to that share itself (i.e. if one share of Apple stock increases by $1, the relative increase in the value of the option tied to that share of Apple stock is the option’s delta).

Gamma is essentially the second derivative of the relationship of the option to the underlying security, or the first derivative of delta, or – more specifically – the magnitude of acceleration of the rate at which an option increases/decreases in response to an increase/decrease in the value of the underlying security.  More comprehensibly, as the price of that one share of Apple stock gets higher and higher, the rate at which the value of the option changes in proportion to those increases (delta), also increases.  This secondary rate is gamma.

Back to the Oct 15 spike…

Funds now needed to cover their short positions, and so entered into a desperate scramble to buy Treasuries, even as the price at which they were buying them increased (due to the interplay of constant supply with rising demand).  There is a bitter irony here in that the coverage of the short positions was actually making it exponentially more costly to cover the short positions.  This, then, is the theoretical reason for the Oct 15 spike- the unraveling gamma of the short position that forced funds to buy increasingly high and sell increasingly low.

But this gamma concept is not confined to the world of esoteric financial products.  The ability to comprehend the inherent properties of change itself adds color to a world in which infinite variables evolve endlessly according to transforming rate convexities of the second, third, fourth, fifth degree (etc).  Tulip bubbles in 17th century Holland or housing bubbles in 21st century America– the underlying dynamics of change are, paradoxically, the only constant.

The ability to distinguish these dynamics from the framework in which they operate is the ability to consider life on the margin.



*article still pending editing