This article discusses option strategies that are particularly adapted to directional bets. I provide an in-depth study of these strategies revealing their pitfalls, advantages and how they ought to be managed in order to maximize asymmetry and our gains.

I will assume that the reader is familiar with the basics of options, first order Greeks and perhaps some strategies, although it's not necessary.

All models were made using the author's own option pricer made in VBA/Excel.

### How are options priced?

I will first explain why and how options are priced the way they are. We will then delve into what this price tells us about the underlying.

### The Market Maker (MM)

The option MMs who dominate option sales are all meant to be as direction neutral as possible by mandate. The way to accomplish that is by hedging his delta: Delta *δ* in % is the % by which your option increases or decreases for a 1% increase/decrease in spot price, i.e. how does the option contract follow the moves of the underlying pre-expiration.

Below, the formula of Delta, where *P* is the price of your option and *S* is the spot price at any given time:

The simplest way to accomplish this is by going long or short δ# of shares. Thus, if you are going to do it this way, your only issue is finding the delta before slapping on your edge (spread) and giving the client what he wants.

To compute this adequate hedge, we require an assumption on the path of the underlying by the time of the expiration: we consider an underlying trading at S_{0} facing a binary outcome the next trading session. Either it goes up 10% to 1.1*S_{0} or falls by 5% to 0.95*S_{0.} Thus, if the market maker's position is going to be short a call expiring by the next trading session with a strike at S_{0} while he is long δ amount of shares, then he wants both outcomes to be equivalent, algebraically:

Inverse of the payoff of the call if the underlying moves up and the δ shares = Inverse of the payoff of the call if the underlying moves down and the δ shares

-(1.1*S_{0}-S_{0})+P+δ*1.1*S_{0} = P + δ*0.95*S_{0}

Solving the above equation for δ we find that: = Thus, we can see that indeed it is not the direction that matters but the range of outcomes and payoffs. A notion that is already close to what most option traders would intuitively call volatility. If you generalize the proof above to a high enough number of successive binary outcomes and if you make the following assumptions on the log returns of the underlying:

- They are independent (no serial correlation aka momentum)
- They follow the same distribution

You end up with the Black Scholes Merton formula which requires the following inputs:

Spot, strike, days to expiration, volatility, risk free rate of return, distribution of log returns *(mostly assumed to be a normal distribution of mean the risk-free rate of return and standard deviation being the volatility)*.

Anyone who has experience with the markets knows these assumptions to not always be true and so does the option seller. That is why around certain meaningful events such as earnings releases, weekends or political events, the seller will naturally adjust the inputs of the model to reflect the non-normal distribution of the return following a certain time point. Hence, the famed volatility crush or weekend theta crush, as examples, where the option sellers and MMs will arbitrarily deviate from the usual assumptions/model to adjust the model to reality. My point being that this model is not perfect but it is very simple to use and astute traders know how to adjust it to get what they want, hence its popularity.

Still, most of the time, option pricing reflects these assumptions and some participants, among the delta neutral ones for example, are just fine with that.

### Delta neutral participants

Delta neutral participants, ranging from hedge funds to retailers, accept the odds as laid out by the markets and do not want, or are not able, to predict the direction of the market. They will engage in delta neutral or very low delta positions and are most often sellers than buyers. They will opt for strategies such as iron condors. The common themes are high probability but low (very low) maximum gain to loss potential. That is not the subject of this article so I won't dwell on this any longer, but for these strategies to be worth one's time, a LOT of capital is needed in my opinion. Predicting volatility is easier than predicting direction because the former is mean reverting, the later isn't.

### Directional speculators

The pricing as explained above implies a certain distribution of returns that is represented in the graph below:

You often hear people talking about the implied move around earnings days, what they are actually talking about is the 1SD range, meaning that the underlying has a 68.2% chance of being in this range, assuming a small enough move (a mathematical detail, not that important) and a normal distribution.

The opportunity for the directional speculator only exists when you **VERY STRONGLY** disagree with the distribution the market is pricing in*.* Yes, very strongly: If you only think that the odds are slightly or moderately higher or lower for any particular outcome, then you are still in the realm of probabilities. As a reminder, these only matter over a high number of occurrences. So, unless you plan on running some sort of trade that will repeat, at good odds, enough times for the law of large numbers to actually kick in, then it's useless. If you want to win as a directional speculator, you need to actually be better enough than the market at guessing its direction to benefit from an expectancy that is considerably and consistently in your favor.

The only way to achieve this is through trades that are:

- Independent, that's a lot harder than it sounds: if you go long QQQ on Monday and add another long of SPY the next day, your trades are highly correlated and you can easily succumb to the trap of ...
- Gambler's ruin: the number of consecutive losses you can afford is negatively proportional to the % of assets you risk on each trade,
*assuming (1)* - Skewed to enhance your expectancy meaningfully: Option Strategies/Positioning/Timing and Catalysts/Valuations are all helpful in achieving this

### What are the components of a good directional bet?

A good directional bet isn't just about guessing the direction. Direction alone is useless and can lead to losses even if you get it right. Instead, you need to predict a range and assign discrete or continuous probabilities to each interval within your range. The late market wizard, John Bender, provides a great example:

The best example I can think of involves the gold market rather than stocks. Back in 1993.[...] My perception was that if the market went back down to about the $390 level, their stops would start to get triggered, beginning a chain reaction. I didn't want to sell the market at $405, which is where it was at the time, because there was still support at $400. I did, however, feel reasonably sure that there was almost no chance the market would trade down to $385 without setting off a huge calamity. Why? Because if the market traded to $385, you could be sure that the stops would have started to be triggered. And once the process was underway, it wasn't going to stop at $385. Therefore, you could afford to put on an option position that lost money if gold slowly traded down to $385-$390 and just sat there because it wasn't going to happen. Based on these expectations, I implemented a strategy

that would lose if gold declined moderately and stayed there, but would make a lot of money if gold went down huge, and a little bit of money if gold prices held steady or went higher. As it turned out, Russia announced they were going to sell gold, and the market traded down gradually to $390 and then went almost immediately to $350 as each stop order kicked off the next stop order.The Black-Scholes model doesn't make these types of distinctions. If gold is trading at $405, it assumes that the probability that it will be trading at $360 a month from now is tremendously smaller than the probability that it will be trading at $385. What I'm saying is that under the right circumstances, it might actually be more likely that gold will be trading at $360 than at $385. If my expectations, which assume nonrandom price behavior, are correct, it will imply profit opportunities because the market is pricing options on the assumption that price movements will be random.

John Bender, Questioning the Obvious - Stock Market Wizards, Jack D. Schwager

Let us sum up what a good directional bet is made of:

- A range of price intervals with different probabilities assigned to them
- A timeline and catalysts, be it simply a time zone (have you ever heard of the infamous Eurozone close rally?), a data release, or some other form of event

### Implementation - Getting more bang for your buck

Your "buck", what you're inputting into the market, is your prediction and the bang is your P&L.

Consider an investor with 100K to invest who thinks $ABC, currently trading at 99.5, will in the next 7 days:

- Most likely reach 101
- Is extremely unlikely to go below 99
- Is extremely unlikely to go beyond 102

Outside of options, he can invest his 100k in $ABC with a stop loss at 99 (around 500$ loss), take profit at 101 (1.5% move from 99.5, thus a 1500$ gain). His payoff ratio is 1500/500=3x

**What we will be showing is how he can get a higher payoff ratio than 3x using options and gain more than 1500$ for the exact same move in the underlying, using 500$ of risk.**

We will refer to the first strategy as the linear equivalent as of now (linear because the payoff looks like a straight line, option payoffs are convex).

We will consider a few *option* strategies for common situations and compare their payoffs to that of the linear equivalent.

First, you have to realize that your predictions are (and must be) akin to a new distribution that is obviously different from that of the market. Assigning some arbitrary %s to the words "likely" and "unlikely", it would look something like this:

The option market's distribution [Y=Probability of the spot at expiry being at any given point in the X-axis], because of what I explained about MMs in the first half, will look like a normal distribution while yours, in orange, is obviously different. If it wasn't different enough, there wouldn't be much to do as a directional speculator.

There are many strategies that could be useful here, so let's highlight some of them:

- Buy a call at a strike K when the spot is at 99.5.

Our payoff will hugely vary based on three variables:

**How fast we get to 101**- Volatility
- Strike

Consider the following strategy: *Long Call(K,7days)* and exit as soon as the underlying touches target of 101.

The values indicate the P&L when using exactly 500$ of maximum possible risk. A value > 1500 means the option strategy did better than the linear equivalent.

Using ATM strike (99.5) reveals that this option will under-perform the linear equivalent *even at very low implied volatility* and is thus far from ideal when we have clear targets. The trade-off is that by sacrificing the payoff ratio, you get a higher probability trade than under the linear equivalent: the option is inherently higher probability than the linear equivalent because the stop loss of the latter would take you out of the trade, even though a reversal can still occur while the option lets you stay in the trade. Although, as we saw in the table, the longer it takes for your target to be reached, the worse your payoff ratio is.

### A short primer on implied volatility

Sigma in the table above is the implied volatility for the option you are buying at the strike you are buying it at. It reflects the standard deviation input *[again this is also a mathematical approximation but it's not important as long as the implied volatility is not a huge number >100%]* into the normal distribution

The bigger the implied volatility, the more expensive the price of the option is, independently of the strike's distance to the current trading level. Hence, why it is a measure of the "price" of the option.

For each expiration, each strike has its implied volatility:

This is what it looked like for QQQ last week. In green for puts and blue for calls. [Y=Sigma in %, X=Strikes]. That's all we need to know for the rest of the article.

Going back to our initial problem.

We show that the call with ATM strike of 99.5 doesn't do much for us, so how can we make it work?

First comes something that is entirely in our control: choosing a better strike!

The way to maximize the bang for your buck (i.e. beating the linear equivalent), is to take the 101 strike, because that is the option for which the extrinsic value will be the highest when you exit at your target which is 101. Graphically, the strike is the point at which the distance between the payoff at expiration and theoretical value is the highest:

Let's see how we would have done with the Call (101,7)

Here, we can actually beat the linear equivalent. For example, if our move occurs in 2 days using an underlying with a 9% volatility (close to what you can see in SPY), then our trade will beat the linear equivalent by 40% which is great!

But it still isn't worth it as soon as volatility is above 10% and even then, you would still be hoping for a quick swing as theta** is working against you.

**Time decay of the option's extrinsic value - this happens because as we near towards expiration you have less time for your trade to work and thus no one will be willing to buy the option from you at the price you paid for it two days ago all else constant

*A quick but important reminder: all of this assumes the usual assumptions for Black Scholes Merton are valid AND that there are no special events that would prompt a modified theta crush, for example, before an earnings release where the option would sustain virtually no theta decay before the event, that will actually move the price, happens*

In the first two option strategies that we've talked about, we actually only used one of the three predictions. Remember that we did not just predict a direction or a target but a range of outcomes and probabilities:

The underlying will:

- Most likely reach 101
- Is extremely unlikely to go below 99
- Is extremely unlikely to go beyond 102

We will show that, by using the second and third information, we can implement strategies that have a better ratio than the ones we've introduced so far.

One way of translating the second information into an option trade is by selling the 99 strike put in addition to buying the 101 call that we've studied before.

Below is a representation of the strategy's payoff which shows how the payoff evolves when you vary both time remaining to expiration and the spot price

Source: Author's model, DTE means days to expiration

This one is less straightforward. First, we have to remember that, by both selling and buying an option, our exposure to volatility is greatly reduced. It is ideal for when you have no idea which way volatility is heading or if you think it will drop (which is likely to be the case after any sharp draw-downs that recover with a quick swing in a V fashion). Second, we have to notice that in this strategy, theta decay is your enemy when the underlying is going your way, but is your friend if your prediction turns sour. Indeed, the maximum loss here is reached if the underlying drops even further, from 99.5 to 99, quickly after the trade is initiated. At first sight, the combination only does marginally better than the linear equivalent

But that's not all there is to it. If you are really sure that in a few days the underlying is unlikely to be below 99 as was stated in our prediction initially and you have the guts/conviction to stick to it, then this combination will very handsomely reward you. At expiration, as long as we are above 99, your P&L will be equal to around 1x your risk, hence a 100% gain depending on volatility when you initiated the trade - Remember theta works for you here when you are losing.

If you are highly certain that the price will not wander below 99 in 2 days for example, you could greatly enhance the payoff by buying more contracts (albeit your true maximum risk in case we do breach 99 in less than 2 days, will be higher). As you can see, by conceding an additional risk of 140$ at a 10% volatility level, you can increase your best payoff by close to 400$. **This asymmetric leverage is what I want you to take note of here.**

Having a view on the timeline is crucial and can be leveraged into much higher payoffs, *even at high volatility levels which is the really important advantage here*.

If you are totally averse to naked puts, here's the risk defined version of the strategy that uses a bullish put spread to finance the call instead of a naked put:

This one takes on the same characteristics with regards to time decay as the previous one albeit to a lesser extent. Otherwise, this strategy is pretty tricky because the maximum risk is not always achieved at the same time depending on volatility, the lower it is, the more speed is a factor. If you are losing, waiting until expiration will always be best for you, otherwise, getting out as soon as 101 is hit will give you the best result.

Finally, we did not tell the market that we thought the underlying would probably never hit 102, the way to do this is by using a double vertical spread:

This one only works well if you plan to keep it till expiration and the payoff is less than what you would get using the previous combination, because the 4th additional leg decreases your P&L if the underlying moves from 99.5 to 101.

### Conclusion

Making a good directional bet isn't just about getting the direction right and you can get a lot more bang for your buck if you work on predicting ranges and trading them in the option's market for better payouts. All of this needs to be in your mind already so that when the opportunity arises and a given underlying trades around a favorable entry price you are ready to lay down your strategy. You want to exit your trade at a point that maximizes the value of your strategy, so as soon as we hit the target for all strategies that have theoretical unlimited payoff. You must also be aware of the volatility levels that make options more favorable than the linear equivalent.

**Disclosure:** I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.