Walking on the Long Side of the Force

After the two previous sections, we are ready to start designing some basic trading strategies. The first kind of trade that we are going to design is called a long gamma trade. We call it long gamma because our positions will have a net positive total gamma. Buying one put option, or buying one call option, are examples of a long gamma trade for instance.

In general. we want to enter into a long gamma trade because we want to exploit convexity, and also because our thesis is calling for a move in the underlying that can overcome the effects of time decay and vega risk. Remember, it is very important that we enter any trade with positive expectations of profit, so if the forecast calls for a quiet market, don't even bother looking into long gamma trades. As a rule of thumb, long gamma trades are favored under the following circumstances (this is, of course, a partial list):

When we are in a very volatile market (so we know that big swings up or down in the underlying are very frequent).
When the market is very quiet but we are sure that a big move will happen sooner than later.
When we think that implied volatility is very cheap compared to realized volatility (there is a whole section of the book dedicated to that).

Once we have established that a long gamma trade fits our thesis, we need to decide if we are going to take on directional risk or not. In other words, is our thesis strong enough to predict direction? If yes, then taking the extra delta risk is worth it, and we will earn a nice additional profit if the move is in the direction that we expect. If the only thing that we know is that the underlying will move big, but we don't know in what direction, then we need to make sure we don't take any delta risk, and we need to figure out a way to get rid of it. However, by removing directional (delta) risk, we are also decreasing our potential profit. So again, choosing directional versus no-directional trades comes down to the strength and depth of our thesis.

Directional Adventure

To enter a directional trade, we need to have a very strong thesis that not only supports the direction we want to trade, but that also gives us an idea of how big the move will be - and in what time frame it will happen. If the only thing we have is something vague like "the market will go up at some point", then we shouldn't bother trading it with options at all. In order to successfully trade gamma, we need at least three pieces of basic information:

Direction of the move
Magnitude of the move: How many points will the underlying move?
Time frame: Are we expecting this in the next 24 hours? Days? Weeks?

Let's start with the last of these: the time frame. The time frame of the move is fundamental. Since options decay with time, we need to make sure that we are picking the expiration that delivers the best return within that time frame. The magnitude of the move is required because options are already pricing expectations of moves in the underlying. We need to make sure that the predicted move overcomes at least what is priced in the option - otherwise there is no point in even entering the trade. And finally, a knowledge of the direction is required, since we need to know what type of option should we use: calls or puts. Knowing those things will give us an edge that can be amplified using a non-linear instrument like options.

Now, please don't ask me how can we come up with that thesis; that is not really the goal of this book. You, my reader, need to have a methodology in place that will provide you with such information. The world is full of different directional methodologies, so you need to evaluate each of them and pick one that suits your trading style.

Magnitude of the move

Once the direction of the move has been established, we need to focus right away on the magnitude of the predicted move. This is very important because not only do options decay every day, they are also priced in such a way that they reflect expectations of how much the underlying will move until expiration. If our predicted move can't at least overcome the daily implied move, then it means we won't get optimal returns from our trade. Because of this, we need to find a way to compute such an implied move. Conceptually doing that could be really simple if we had the implied volatility from the option prices. However, because we have already seen that options have different implied volatility values per strike and expiration, then we could have many different implied moves depending on the strike and expiration we are using. This problem is compounded since we also know that implied volatility is dependent on the mathematical model that we choose to price our options.

To solve the added complexity of model dependency and strike dependency, I suggest using a model free methodology to arrive at a good estimate of implied volatility per expiration. Luckily, CBOE already has done the work of designing and implementing such methodology, and they call it the VIX index. A very detailed explanation of how VIX is computed can be found here. So, now that we have a good methodology, we can just compute the model free implied volatility (IV) per expiration, and then with that value, we can compute the implied move per expiration. The equation for the implied move is the following:

Move = ATM*(exp(IV/sqrt(365))-1)

Where Move is the expected move per day

ATM is the value of the underlying when IV was computed

IV is the model free implied volatility computed using the VIX methodology

Note: There is an alternative formulation using a negative sign for IV which gives very similar results. I prefer to use the one with a positive sign.

To illustrate this point, I'm providing expected daily moves for different points in time. For instance, here is a graph for January 4 2016:

Remember that this was a time a high volatility in the markets, which can be seen in the expected moves. For the nearest options to Jan 4 (expiring on Jan 8), the implied daily move is 25.79 points. However, notice that as we move farther away in expirations, the implied move becomes smaller - though by not that much. The graph is telling us something interesting: most of the SPX options were priced at that date with expectations of moves of more than 20 points daily. So, if our thesis called for a move of 10 points in the next 24 hours, we would not get an optimal return using options. As we can expect, the higher the implied volatility of the options, the higher the implied move will be. Please consider a similar graph, this time computed on January 8, which was the last day of a very turbulent week in the market:

The implied move has now gone to almost 29 points for the nearest expiration (which is 7 days away), and in general, the implied move needs to be higher than 26 points for all of the other expirations. So again, if our thesis was calling for a move of 10 points, we would not be getting optimal returns by using expensive options. I want to go even further here and show how bad a trade would be if options were used. Please take a detailed look at this graph:

This is a very interesting graph. It is showing us the percentage return for each possible strike between 1820 and 2100 of SPX call options, with different expirations all the way from 7 to 52 days away. Several things can be seen right away:

In the money options return a very small profit, which is expected as they are very expensive and the move was very small.
The highest return seems to peak around 23%, and it is obtained if we use OTM options with 28+ days before expiration.
The nearest expiration seems to outperform the returns of all the other expirations up to the 1950 strike, and then it becomes a very bad investment to the point that we can lose money, even though the underlying moved in the right direction. This is consistent with time decay being higher for it, and also for OTM strikes.

So in this case, it seems that short term options didn't work well, and also that the max return of the strategy was not that compelling, considering our expectations of optionality. All of this, of course, was expected, since implied volatility was very high, making all options very expensive. Also, our expected move was too small in comparison to the implied move.

Let's do the same exercise again, but this time with a move that is higher than the implied. Let's imagine that our thesis now calls for a 35 point move up in SPX and repeat the same simulation:

The results are very different this time. We can clearly see that the nearest expiration (7 days) is now outperforming everything else. Also, here we can see the effects of optionality in full display, with returns of more than 250% for that move when using the 2040 Call expiring 7 days away. The results are noisy because some options have noisy end of day quotes, but in general, we can see a few things here:

The strike that produces the best return varies per expiration, and it seems to move farther OTM the farther we go in expirations.
Clearly, out of the money options are the ones that deliver the best return.
We can see that the return percentage peaks, so we need to make sure we don't go beyond it when picking our strikes.
Near term expirations are favored this time. However, take into account that the move is expected within 24 hours of our trade.

Even though it looks very good, the trade was still very lousy because of the high price of SPX options to begin with. Just compare exactly the same kind of move but this time using cheaper options, as was the case on Feb 19 2016.

Here we can see a complete different picture with SPX options: the implied move is less than 18 points for the nearest expiration, and it rises steadily the farther we move away from it (the only exception is the end of month expiration, which for some reason always looks undervalued). It is clear then that at this date, options are priced in a more reasonable range. And here are the returns if we got a similar 35 point move:

Because SPX options at that date had a much better cost, the returns are way higher, with peak returns of more than 600% using the near expiration options. I hope that at this point it is clear how important it is to identify a favorable time to play a directional move. As a rule of thumb, don't go long gamma when options are very expensive.

A more complete design

In the first part of this section, I wanted to illustrate the importance of entering long gamma positions during times of low implied volatility, and for that purpose, I picked some contrasting days of early 2016 - one in January with very high IV, and another in February with more reasonable IV. However, we have so far only focused on the implied move and on the total return of the trade for the comparison. Although we were able to see why a low IV regime is more advantageous, we are still missing more elements to properly design a directional long gamma trade. In particular, we are missing a discussion of what is called the Risk Reward factor of a trade.

Risk Reward

No matter how strong the thesis that we have is in terms of direction, magnitude, and time frame, things could go wrong at any time. Therefore, we need to have an exit strategy in place before even entering the trade. We should never allow the trade to go catastrophically wrong (total loss), so we need to define a point when we will bail out, take the loss, and then look again for other trading opportunities. For instance, our thesis calls for a 30 point move up in SPX within 24 hours, but we can decide that if instead we get 10 points against us (down), we will close the trade. We could have an even tighter stop, like 5 points against, but we need to consider the volatility of the underlying, as we don't want to close the trade prematurely. So for now, let's go with a 30 point up move and a 10 point stop for our directional trade. If we implement this trade with a linear instrument like futures or CFD's, our expected Risk Reward for this trade is exactly 3.0 (30/10). That is, our profits are expected to be 3 times bigger than our max loss. That kind of Risk Reward is actually attractive, and if our thesis is strong, we could make decent money with the linear instrument alone. Now the question is: Is it worth playing the same thesis with options? And if it is, what kind of strike and expiration will work best for us?

The answer, as usual, is: it depends.

First, we need to make sure that our predicted move is higher than the implied move. In this case, we can model this trade on Feb 19 2016. We know that the near expiration implied move is 17.62 and that our predicted move is 30, so we are more than good in that regard. The second thing we need to do is compute the expected return per strike and expiration for a 30 point move up with SPX calls:

From the point of view of total return alone, we can see that we can get more than 400% profit when using the nearest options with 7 days to expiration and a strike just above 2000. However, we also need to check the Risk Reward profile to see if using options is actually justifiable. For that purpose, please look carefully at he following graph:

The Risk Reward profile is very interesting, as it reveals a number of important features of options:

Notice how in the money options have a RR that is very similar to the 3.0 value for linear instruments. This is expected as ITM options have almost no optionality.
We can see that just by using the right OTM options, we can enhance the Risk Reward of the trade from 3.0 to a little more of 5.5! That is the power of optionality and also why options are not leveraged plays in the usual sense of word.
The strike on the near expiration line with the best RR is actually just before the 2000 strike this time, so it doesn't coincide with the strike with the best total return.
The best play here in terms of risk reward is actually a Call option with 10 days to expiration and strike around 2025.
After the RR peak, the decay is more dramatic than in the total return graph. One more reason to not go crazy with OTM options that are farther than the optimal one.
Please remember that this an ultra short-term trade, meant to be closed after 24 hours of entering. Any longer period of time will alter all the values dramatically.

Now using Risk Reward as the final decision parameter, let's try the same trade again, but this time in a very high volatility environment, like the one we were in back on Jan 8 2016. The implied move of the nearest expiration was 28.89, so our predicted move is barely higher than it. Let's look at the total return:

Because of the expensive options (very high implied volatility), the total return is now lower at 175% when using the nearest options with 7 days to expiration. However, that is just a siren song. Don't think for a minute that this is a good trade. I mentioned before that long gamma in a high volatility environment is a lousy trade, and here is the real reason why. Please take a look at the Risk Reward profile for that day:

The Risk Reward profile reveals the whole truth: with implied volatility so high, the trade is terrible across expirations. In fact, even with optionality, we don't seem to get more than 3.4 in terms of Risk Reward, which is almost no improvement whatsoever when compared with a linear strategy. Also, notice how in particular the nearest expiration at 7 days is actually worse than a linear instrument. The Risk Reward factor is below 3.0 for all the strikes considered. That is why the whole 175% return was just a siren song; this is a bad trade no matter how one looks at it. In cases like this, when the RR factor is similar to or lower than the same factor for a linear trade, it is much better to just play the linear instrument. There is no point in taking the extra risks when optionality is not going to help at all.

The inevitable passing of time

I think so far we have established very emphatically that a long gamma trade should only be considered if the implied volatility of the options is in a favorable environment. And for that we developed the implied move indicator, which helped us decide if it was even worth considering the use of options for our directional trade. I also introduced the concept of the Risk Reward profile, which is fundamental when choosing the right strike and the expiration that best suits the trade. It also can reveal if the trade will deliver a better RR than the one obtained by using conventional linear instruments. However, so far we have limited our analysis to trades that are 24 hours long. This was very deliberate because I wanted to provide a feeling for the design of directional day trades, and also because I wanted to minimize the effects of time decay and vega risk on our trades.

To see the massive effects of time decay, let's try out a scenario that calls for a 40 move up within the next 3 days. As usual, we will use a 10 point stop. Also, we are going to compute a very pessimistic Risk Reward profile that assumes that we either take profit or stop at the very possible minute of our trade window. Of course, doing either of the two at an earlier time will have better returns, but it is better to start pessimistic. With those parameters, the basic RR for our trade is 4.0 (40/10), so let's start with our checklist.

First, let's check the implied move for the next 3 days:

We can see that the implied move is bit more than 30 points for the near expiration, and then it starts to rise steadily, so in that sense our expected move of 40 points seems right there within the limits. Now we want to check the strike and the expiration that deliver the best return for that kind of move and timeframe:

The returns don't look that bad - around 400% for the 7 and 10 day option lines. Considering that this is a worst case scenario, it looks decent. So finally, let's look at the Risk Reward of this trade:

The Risk Reward profile is actually not that good. However, remember that we are using a worst case scenario here, where the loss or the profit is taken at the very last second of the three day window. But in general, you can see that things start to deteriorate rather quickly. For instance, the RR factor is below 4.0 for almost all the strikes. In particular, notice how the in the money options are consistently below it for all expirations. The trade is still attractive when using the 2000 strike call option with 10 days to expiration, as the RR reaches more than 5 for it. Another thing to observe from our RR profile is that long dated options are starting to become attractive. It is not a coincidence that options with more than 30 days on it are actually performing well for strikes around 2100.

This latest RR profile hints to us that playing long gamma for long term is not that advantageous, and also shows us that we need to move a bit further in expirations to obtain the best return. To better illustrate the issues with long term, long gamma plays, let's simulate a directional bet that requires 20 days to pan out. Of course, with that time frame, we are betting on a sizable move of 100 points in the underlying. Also, to make it more realistic, we will stop out of the trade if, after 5 days, it is not moving the way we want or if it moves 20 points against us (notice that the stop is a bit higher and that we also introduced a time frame for it).

Here is the total return for that trade:

Notice how in this time frame, options with farther away expirations are finally beating near term options. Also notice that there are some strikes that will make you lose money, even with that nice move, which is why strike selection is so important. Just look at strikes above 2040 for options expiring 21 days from the date of the simulation - they will lose money no matter what.

Now, let's check how the Risk Reward profit looks like:

Again, in the Risk Reward profile, options that expire far away seem to perform really well compared with the near ones. However, we again need to be very careful here, as we need to remember that vega risk increases with time to expiration. What that means is that the same options that are giving us such a nice total return and RR factors are also very sensitive to changes in implied volatility. Because of the way that equity options work, implied volatility tends to drop when the underlying moves up, which affects negatively all call options - and in particular call options that expire far away.

Let's now include a realistic drop in implied volatility that is consistent with historical 100 points moves over several days and see how it affects our RR profile:

Now the truth is finally exposed. Because of vega sensitivity, those far away options are not performing that well any more; those call options are more negatively affected by the drop in implied volatility. So from the point of view of the Risk Reward profile, it is better to stick with an expiration that is just enough to cover the time frame that our thesis requires. Also, please don't forget: this trade is working because the 100 point move up is higher than the implied move of 90.69. I can't emphasize that strongly enough. Please make sure that the expected move overcomes the implied one.

There is one more important note here: the vega risk only negatively affects call options. That is, if you are playing a downside move with puts, the situation is the opposite. We can actually gain even more when using far away options because they will increase in value due to the higher implied volatility due to the drop. So when using puts, you can stick with the original expiration suggested by the Risk Reward profile.

What is in a number?

So far, we have laid down a bunch of scenarios and a hint of a methodology on how to pick the right strike and expiration for the kind of move we are expecting in terms of total return, as well as in terms of Risk Reward. In all the exercises thus far, we have seen that the optimal strike seems to be really far away from the at the money value, and in fact, it keeps moving farther away the farther we move in expirations.

It would be nice if we could get a sense of how far that optimal strike should be without being dependent on the at the money value. After all, the ATM value will be very different from the moment we design the trade to the moment when the trade is actually executed. Luckily for us, there is another way to visualize the total return and the Risk Reward profile without involving strikes at all. It turns out that there is a number that connects that distance from strike to the ATM value, and that number - for the keen readers here - is actually the delta of the option.

So without further ado, let's explore our classical 30 point move up in SPX within 1 day (a day trade), but this time expressed in deltas instead of strikes:

The x axis represents the delta value in percentage terms (so it goes from 0 to 100). Please remember that a delta of 50 represents the ATM value, and values higher than that are ITM options. Conversely, values lower than 50 are OTM options. As you can see from the graph, the total return of the trade increases dramatically the farther OTM we move. Also, when expressed in deltas, we don't seem to get such a big shift of the optimal option as the expiration date moves.

Let's zoom in a bit on the area of interest here, which is between 0 and 15 deltas, to see what we get:

In this graph, we get a much better sense of the optimal delta we need to use to play this move. The optimal options are actually really deep OTM, and you can see how the returns start to accelerate once we start picking options with delta lower than 10 (0.1 in standard terms). The optimal delta really depends on how big the move is compared to the implied move per expiration, but you can see that short term options with very low delta, around 2.5% (0.025 in standard terms), seem to be the way to go when playing a big move in a short period of time.

Note also how the return decreases dramatically once delta becomes very small, so do be careful when selecting the correct option. As a safety margin, you could pick a 3 or 4 delta option for this kind of move. I know this looks very surprising, and that people are used to picking options with bigger deltas (25 or 20), but this modeling is very accurate, in particular for very short term type of trades. Of course, you could play this as safe as you want and pick deep ITM options if you'd like, but remember that the great benefits of optionality only start to manifest themselves once you start going deep OTM, as the previous graph clearly shows.

Where are the Puts?

Until this point in the discussion, I have only been using upside moves and call options to play them. My mention of puts has thus far been limited to perhaps a single sentence or two. As you can imagine, there is good reason for that, and it is related to the tremendous negative skew that is present in index options, in particular in SPX puts. The whole point of this section has been to illustrate the role of optionality in long gamma trades, and for that, I needed setups that could actually show said optionality. With SPX options, the only ones that work well are trades using calls.

There is no nice way to say this, but using puts to day trade downside moves in SPX is a terrible idea. In fact, most of the time (if not always), using puts to play downside - no matter the time-frame - is just plain inefficient. It sounds a bit too extreme, but it is true. SPX puts are so incredibly overpriced that designing long gamma trades with them is basically a fool's errand. The problem is compounded because the overpricing becomes even more extreme as we move towards OTM strikes, which is in complete opposition to SPX calls (they get cheaper and cheaper).

To advance my point, let's repeat our standard trade, but this time to the downside. Same date as always, same magnitude 30 points down, a stop of 10 points up, and we'll make this a day trade. Our first simulation will have limited volatility surface dynamics, and then we will run another one with full volatility effects.

Here is a look at the total return from that trade:

As you can see, even though the move down is significantly higher than the implied move, the expected returns are not that impressive, with peak return lower than 150%. This underperformance is expected, as the puts are very overpriced. Now, let's check how do they look in terms of Risk Reward profile:

The Risk Reward profile is terrible. In fact, the whole trade is barely better than the same trade executed with futures, for instance. At this point, observant readers might object to this simulation, arguing that during downside moves, implied volatility goes up, which should provide a boost to puts and provide another source of profit. To that, I answer that of course that is correct, and in that regard, the trade now stops being an actual long gamma trade (which was very bad, as we could see before). It is now shifting to an actual vega play, so playing downside with puts is more about being long vega than being long gamma in the sense that most of the profits will come from an increase in implied volatility - only a fraction of the profits will come from optionality itself. I just want to make sure that you understand the risks. In particular, during high implied volatility regimes, you can have downside action with very little to no increase in implied volatility.

Here are the results of the simulation:

The total return seems to be a bit better. However, it is still very inefficient when compared with an equivalent move up. Also, remember that we are now dependent on a nice pickup on implied volatility in order to see this kind of return, which could be a bad idea if implied volatility is already very high. Finally, let's take a look at the Risk Reward profile:

It has improved dramatically, although not at the levels of the same play on the upside - and again, we are dependent on an unknown increase in implied volatility. A few interesting features are revealed with these graphs for puts:

Because puts are so overpriced, the optimal returns are with strikes that are closer to the ATM value when compared with calls.
Far away expirations don't really do much across strikes. This is expected, as far away options are very expensive both OTM and ITM.
Even though we improved the RR factor from 3.0 to 4.0, it is done at the expense of introducing vega risk. If implied volatility increases very little, we are in for the profiles on the first two sets of graphs.

The relationship between implied move and expected move is more critical with index puts. Really, there is no point in playing a 10 point move with puts if the implied move is 17. This doesn't mean that puts should not be used for trading. I only want to drive home the point that a long gamma trade with puts in index options is very inefficient, and I advance the notion that downside should be played with a whole different strategy, which of course we will explore later on in this book. Finally, if we are expecting a catastrophic move (end of the world kind of scenario), then puts will behave very nicely, as the overpricing will only get worse once the move down starts. That said, how many times has the world ended in recent memory?

The end of the directional trade

I hope that so far this discussion about directional long gamma trades has been interesting, and that the material presented will help you prepare and analyze future trades. Remember that once you have a directional thesis, you need to check a few things:

Is the expected move higher than the implied move?
What strike and expiration deliver the best total return?
What strike and expiration deliver the best Risk Reward?

Some traders want to score a great payday, and they will be swayed by the total return numbers, but I always recommend checking the Risk Reward profile and seeing if it actually makes sense to play the expected move with options. Please remember that if the RR from options comes below the RR from a linear trade, it could be better to just execute the trade with a linear instrument like shares, futures, or CFD's.

Now, my readers, I hope you are still enjoying this book so far. We still have plenty of material to cover, in particular in the next part of this section, which deals with non-directional long gamma trades.