The anatomy of a long vol trade

Leonardo Valencia: leov@anixcorp.com Aug 19, 2016

Introduction

I don’t usually do long volatility trades, in fact I do just a handful of them during the year. The reasons are explained in detail in my article about the persistent Variance Risk Premium in index options (You can find it in the Short and Strong section). The gist of the article is that option prices contain a premium that most of the time can be collected in a profitable and systematic way. However, there are a few times when options are mispriced and it becomes profitable to play the long side of volatility.

This paper will focus on the design of a long realized volatility play. I’m highlighting the realized side of the trade as most of the profit and losses of this trade come from that component alone. In other words we are ignoring any price fluctuations due to implied volatility changes. When most of the profit and losses come the realized side of the equation we can truly say that we are doing an almost pure long gamma play.

A different way of looking at Gamma

A lot of people like  to play long gamma using ATM straddles (buying a put and a call of the same strike) however that is a terrible way of doing it as the ATM strike contains very expensive gamma which makes the position not only expensive in terms of dollars but also makes it decay really fast (as time decay is proportional to gamma). Also, as soon as we get our expected move in any direction gamma will drop drastically (see the graph in the VRP paper) so our trade won’t accelerate in price with the move.

The best way to play a long gamma move is by using an strangle (buying a put and call of different strikes). The idea is to buy cheap gamma in terms of dollars which also would make the time decay in dollars more bearable. We also get a second benefit: As soon as the underlying moves in any direction, gamma starts increasing dramatically and, because we are long gamma, that means our position starts going up in price dramatically too.

So an strangle is the way to go, however, and that is just me, I prefer to use binary options when playing long gamma moves. The reason is that the delta of a binary option is actually the gamma of a normal option. In other words, when you buy a binary option you are buying gamma right away as a first order quantity, which allows you to profit from gamma changes in a very straightforward manner (no path dependency compared with a normal option).

I know that CBOE de-listed binary options in SPX some time ago, and also that there are not decently priced, exchange traded, binary options in the USA. However there is no need to despair as binary options can be roughly replicated by a mundane vertical spread of minimum width (in the case of SPX options a width of 5 points). So here you have it, this trade will be implemented with a binary strangle that in the world of vanilla options can be replicated with the well known Iron Condor (in this case we are buying it).

The implied distribution

Of course the hardest problem of designing  this trade is picking the correct strikes and expiration to execute it. The expiration part is easy: when playing long gamma we are in the shortest possible trading game. That is, we better be right soon or the losses will pile in really quickly. For that reason we are choosing ultra short term expirations for this trade, in this case SPX options expiring on Aug 24 2016 (which is exactly 5 calendar days from now). We could go crazy shorter like using the new Aug 22 options (Monday expiration) but that is pushing it too far. For the purpose of this trade 5 days are fine (by the end of this document you will realize that they are actually priced for 3 days only).

Choosing the strikes is harder, we want to pick binary options that are priced decently. So for that we need compute the implied cumulative probability density  from option prices (man, that sounds awfully complex but it is not that hard and has been explained in many of my articles before). So without further ado here is the density for Aug 24 2016 computed in real time as I write these lines:

From the graph we are going to pick the downside strike with the best distance between the blue bar and the red line, that distance is the edge that the strike has versus a normal distribution. So for the downside puts I like the 2175 strike. For the upside move we want the opposite, we want the blue bar higher than the red one. In this case 2195 looks good but I will pick 2190 as it sits right around the limit of the 1 sigma move (which is 2192.35). In other words I like the binary puts to be closer to the mean (2181.56) and the binary calls to be closer to the 1 sigma limit.

Because we don’t have binary puts or calls in SPX, we are going to replicate those with the following Iron Condor:

-1 SPX 2175 PUT/ +1 SPX 2180 PUT/ +1 SPX 2190 CALL/ -1 SPX 2195 CALL

Where a negative sign means we are selling that strike and a positive sign means we are buying the strike. Now, we want to know what is the Profit and loss profile for that Iron Condor, so for that we simulate it in a range that is realistic for next week.  Please notice that the simulation is in hours as this is a ultra short term position so we are covering 72 hours in total (3 calendar days) which will give us realistically until Tuesday (because of heavy accelerated decay just before the weekend). If we open this position at 4:00PM today (Friday) those 72 hours might extend until early Wednesday (as most of the decay is already applied to the options).

The simulation looks really nice and from that graph you can actually see why these kind of positions are called “Condors” as it does look like a beautiful bird. Just a couple things from the graph, the color coded time dimension is actually elapsed time in hours (from the moment we opened the position) also, the Return Y axis is the total return in dollars of the strategy, that way is easier to compute the risk reward of the position.

Parameters of the trade

Now as you can see from the PL graph, if SPX remains range bound we are going to lose money. We can also see that the longer we remain in the range the higher the loss will be.

You can think about Monday morning as the blue bands of the graph, so we are going to use them as our exit parameter here. If on Monday noon time we don’t have positive PL in our trade we will close it. Quantifying that, we expect the max loss at that time to be of $0.35, in other words our exit parameter is a loss of 0.35 in the position. If we get a nice rally towards the 2195 area we can expect a profit of 0.65 to 0.68 an almost 2:1 Risk Reward to the upside (if we get to 2200, well that is like hitting a jackpot). Conversely if SPX drops towards the 2170 area we can expect a profit of 0.7 to 1.0 depending on the timing of the move (later is better). So again we have a nice 2:1 risk reward for the trade.

Thesis and Risk

Please note that in order for us to make money in this trade we need to move a meaningful amount of points in SPX before Wednesday (about 13 points up or down). In a high volatility regime that is a piece of cake, but unfortunately we have been stuck in a tight price range for a while now. In that sense, this is a risky trade so be prepared to lose your $0.35. Now my main thesis is that early next week we should see the return of high realized volatility, and in fact the thesis calls for said return to be visible during Monday morning session. The good part of the thesis is that it can get disproved early on therefore minimizing the loss. I plan to play this in very small size (a handful of contracts), however it remains risky. As usual this is just for educational purposes please manage your own positions and set your own parameters.