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How Negative Gamma Works and Why It’s Impacting the Market

Have you been wondering what has been causing violent gyrations in the stock market over the past week? Why does it have a record down day followed by a massive up day only to be reversed the very next day?  Look no further than the pervasive Negative Gamma held by many investors in the stock market. Caused primarily due to Massive Put Option Selling by market participants, this is the fundamental cause behind the whiplashes as the market yo-yo’s between one extreme and another.

Before explaining what Negative Gamma is, one must understand how and why it is present in the market. Over the past 7 years, the stock market has been on an incredible run, increasing at the rate of 10-20% each year.  This has accelerated over the past 2 years with very few drawdowns, setting records for the longest such streak without a 3% drawdown in 2017.  This historic enigma, combined with the largest corporate tax cuts in US history, has led investors to believe that stock prices will keep gradually rising without experiencing sell-offs.  Therefore, in addition to buying their favorite stocks like Amazon (AMZN), Facebook (FB) and Netflix (NFLX), investors have been Selling Put Options to receive additional premium (income) during this rising market.  In investing parlance, this is where the “Greed” in the old mantra of “Greed & Fear” takes over.  Let’s define this:

Put Option = An Option to sell a stock at an agreed-upon price (Strike Price) on or before a particular date.  A Put Option Seller will receive a small premium, say $3/share, while a Put Option Buyer will pay this premium upfront.  Put Buyers receive protection while Put Sellers may have to buy that stock price at a much higher level than market levels in the event of a crash.


Payoff Profile for a Put Option Buyer


For example,  Netflix trades at $200 a Put Option seller, believing the stock price will keep going higher, will sell a $190-Strike Price Put Option for $5, which expires in 3-months.  As long as the stock price keeps going higher, the Put Option Seller gets to keep his $5 and the option expires worthless.  However, if Netflix trades down to, say $150 in 3 months, the Put Option Seller will face a predicament of having to buy the Stock at $200, even though the price is much lower in the market.  The Put Option Buyer, on the other hand, will now own a Put Option worth $50 – 10x times the amount he originally bought it for!  But how do you know that Put Option’s worth during the life of the option, say after 1-month?  That depends on the underlying price of Netflix and something called the Option’s Delta:

Delta = Ratio of the change in price of an Option (in this case, Put Option) to the change in price of the underlying stock, also called the hedge ratio.  For a Put Option on a stock, a delta of 0.50 means that for every $1 change that the stock goes down, the Put Option’s price rises by $0.50.  


Payoff Profile for a Put Option Seller

Going back to our original example, if the Delta of the Put Option at inception is 0.30 and the stock goes down to $199 from $200, that Put Option’s price will increase from $5 to $5.30.  This is not a one-for-one change in value because the option still has a long time before maturity and while the probability of expiring ‘in-the-money’ below $190 is now higher, there’s still a decent probability that the Stock finishes higher and the Option would be worthless in 3-month’s time. However, an Option’s Delta is NOT a static variable but rather changes in price depending on 3 primary factors: 1) Time until Option expiration  2) Volatility of the Stock and 3) Underlying Stock Price.  The Rate of Change of an Option’s Delta – how much the delta fluctuates relative to time and underlying stock price - is called Gamma, which changes over the life of an option:


Gamma = Measure the Rate of Change of Delta, which is how much an option price changes given a one-point movement in stock price. As delta increases or decreases with 1) time to maturity 2) volatility of the stock and 3) underlying stock price, the Gamma represents this rate of change. That is, the gamma of an option is the second derivative of the option value with respect to the underlying stock price.  Put Option Sellers have Negative Gamma, meaning their Delta-exposure increases as the Stock Price goes lower and they’ll need to sell more underlying stock as the market sells off (sell low / buy high).  Put Option Buyers have Positive Gamma, meaning they can buy more underlying stock as prices go lower (buy low / sell high).


Gamma is affected by Time to Maturity, Underlying Stock Price & Implied Volatility


Gamma does not always stay constant.  It fluctuates over the life of the option & underlying stock price.  Another way to think about Gamma is thinking about the probability of a stock price finishing above or below the Strike Price.   If that probability is close to 0% or 100% (the extremes), then the Gamma is LOW as the value of that Put Option will not change too much given the certainty.  For example, if Netflix were at $275 in 2.5 months with just a couple weeks left, that value of the option is worthless as the probability of it finishing below $190 is virtually non-existent and the gamma is close to 0.  Likewise, if Netflix were a $125 in 2.5 months with half a month left, that value of the option is extremely valuable but the delta is very close to 1.0 because the option’s value will probably rise or fall around $1 for every $1 move in the underlying stock price.  

However, in the event that Netflix were at $192 with only 2 weeks left to expiry, it is unknown whether the stock will finish above or below $190 – it could go either way.  In this scenario, the Delta is around 0.5 while the Gamma is extremely high – that Delta could go down to 0.2 if the stock rises to $203 in a week or could go up to 0.8 if the stock falls to $177 in week.  In other words, it’s highly indeterminable if that stock will finish ‘in-the-money’ or ‘out-of-the-money’.  Here is a look at the Gamma Profiles of different investors who trade options:


Which brings us to Today. If you recall, I mentioned that in the past few years, investors have been Selling Put Options and thus, have been increasing their Negative Gamma profiles in the market.  That is, they’ve been leveraging their bets, hoping that the stock market will keep rising and selling Put Options to earn extra income from the Option Premium.  This has been a very popular strategy for many retail investors, leading to a mammoth-sized Negative Gamma position in the market.  If things go right, it’s Happy Days.  However, if the market turns on its head and volatility spikes higher, they’ll have to Sell Low & Buy High – the exact opposite thing you want to do as an Investor – as their Delta keeps changing & fluctuating and their Gamma is high.  This has culminated in the price action we’ve been seeing of the past week – many Put Option sellers have been forced to sell as the market goes lower (as Delta increases), then buy as the market rips higher back through their Strike Price (as Delta decreases) and finally Sell again as the market goes yet again lower, as it’s been doing today.   This is Financial Bipolar Disorder (F.B.D.) as the investor is put in the unenviable position of buying high and selling low, compounding his losses that he’s suffered on selling the Put Option in the first place. Imagine Wild E. Coyote falling off a cliff, rebounding back higher and then falling back down.   Time after time, it’s exasperating and causes a lot of pain.  On top of this, because volatility was relatively low when investors fell victim to Goddess Low-Volatility’s Siren Song, the premium they received for selling that option was miniscule compared to the losses they’ve suffered as the market yo-yo’s back and forth.  Painful lesson indeed.


Where to from Here?

If we take the previous examples of these Negative-Gamma induced Market Sell-offs in August 2015, February 2016, and February 2018, history suggests we can see more back and forth action for a couple weeks or months before the market returns to a lower-volatility regime.  Shocks like the one the market has experienced over the past week should be expected given the amount of Negative Gamma and Short Volatility positions that have dominated investment strategies over the past few years, luring in Hedge Funds and Retail Investors alike.  Does this mean this is a Top for the Market?  While it could be, it doesn’t necessarily confirm a Top, which is usually associated with systematic credit event (think 2008). However, it could mean that the Market goes sideways or yo-yo’s for a while as many of the Negative Gamma and Short Volatility positions are “flushed out of the system” as they expire or are exited.   While there are surely other factors contributing to the market sell-off, what is very much true is that Negative Gamma has been a major culprit contributing to the Up-and-Down price action we’ve seen over the past couple weeks.