Quantifying a GLD Trade

People often ask me how do I know when to make a trade? Most of the stockguy22 people know I a Mr Roboto type trader.  Yes I have a computer telling what trades to make and how to structure them. The reality is that while the computer tells me things, it only does so because I worked through the mathematics. For example recently Ashraf Laidi (@alaidi) said the following:

“if Ireland gets help from EU & NOT via debt restruct., its’ GOOD for stocks/euro/ezone bonds & BAD for Merkel/Sarkozy #forex #franc $$”

Really Ashraf? And you know this how? Merkel gave you late night tweets? She called you up and whispered the sweet nothing, “Hey Ashraf I think if Ireland gets help from the EU it will be bad for me and I want you to tweet about it.” Now before we all get our undies in a jam, yes yours truly makes statements like this as well. I am not trying to pick on Ashraf, because what I want to know how he quantifies that statement. Is it based on quantifiable numbers? Or is it a feeling? Feelings are a bad thing in the market because they cloud your judgement. Yes we need to make judgement calls but such a comment is a major buy or sell and hence it better be well rationalized because otherwise the trade is a lotto ticket.

Thus what I want to do is take a trade apart and quantify it for a potential risk to reward. Many people think risk to reward means that if my trade has a target of 10, and stop of 1 I either win 10 or loose 1. That sounds good in theory, but the big question is how often do you win, and how often do you loose? Its a small detail but it is a huge detail and will determine your profitability.

Lets take a trade apart, and in specific the following GLD calendar spread. Please read the article first to get a full understanding of the trade.

The trade is the following:

  • Buy a deep in the money GLD call option strike 120, expiry Jan 2012.
  • Sell weekly ATM money GLD call options to finance the long GLD call option.

This trade sounds good in theory, but I wonder what the real probability of profitability will be. I am not questioning the fundamentals, I am questioning the odds of the trade.

Right now the cost of the long term dated option is 22.20 USD. Thus the profitability of the trade is the following:


The maximum risk of the trade is 2,220 dollars, and the profitability depends where Gold will end up in a bit more than a year from now. Thus the first question to ask is what is the potential for the trade to exceed the value of 142.20 USD.

The way I calculate this is that I go through the historical data and create what I call a seesaw. An example see saw is drawn up as follows:


What I want to know is what happened in the past and what will happen in the future from a current time. That way I can establish a relationship where the future is tied to the past. Now you might say, but the future cannot be predicted. And I would completely agree with you because all that I want to know is a rough ballpark figure. I am not interested in specifics. I just want to know if this trade has any merits.

So for those situations where Gold was up 25% in a year you get the following cumulative percentile diagram.


This concerns me because the 50’th percentile is hovering around 2.5%, and if you take the current price of the GLD 133.69 then the 50th percentile price one year later is  137.03. Right now the option will expire with a loss as the break even point was 142.20. But assuming you are convinced of gold, what about the upside? How much upside is there? Lets change the cumulative percentile diagram to a price diagram, and the following picture is generated.


Notice that the break even point of the option is at the 66th percentile. For those who know their option pricing this is a striking correlation. The correlation is that the market price is a bit more than a standard deviation than what the market model is pricing. Simply put the market is pricing a fairly priced option. Of course this should not surprise you since the market has plenty of funds that run mathematical models. This means the probability of you making money is not good. Thus you need to offset the cost of the gold option, which can easily be done by selling weekly GLD options, which is part of this trade.

To reduce the cost of the long term option the idea is to sell weekly premium, and from the article it appears the idea is to sell atm the options. I can understand that since those are the options with the most premium and hence they give you the most breathing room if GLD goes up. But there is a problem. Imagine for the moment you are selling the 130 strike for 1 USD, and the market moves from 130 to 140. It means you just incurred a loss of 9 USD. So the next week you again sell a 1 USD option, but instead of moving up GLD moves down. You pocket the dollar, but you are still missing 8 dollars. My point is that you don’t know whether or not you have more winners than losers.

The most important question to answer is whether or not this weekly premium selling will work. After all right now the odds of you making money on the long dated option are pretty remote and hence you need to reduce your cost basis. My approach is Monte Carlo based, and encompasses the following steps:

  1. I go back in history and calculate all of the option premiums for a weekly option based on the historical volatility and then look at how that trade did a week later.
  2. These values are put into a pot
  3. I randomly choose a week.
  4. I look at the profit for that week and make a note of it.
  5. I put that week back  and then go back to Step 3.
  6. Once I have completed a large number of loops I create a frequency distribution chart.

What the frequency distribution chart tells me is how profitable the underlyer has been for its historical past. While many will say, “why not just add it up and see what the net total is?” I respond that it does not give me a frequency distribution chart. It just tells what my net total is. For example imagine having 10 loosers of 1 USD, but 1 winner of 11, the net total is 1 USD and profitable. But the frequency distribution is bad and will indicate that the system got lucky.

The is generated frequency distribution chart is as follows (I already included the profitability aspects).


This chart is interesting because what it indicates is that most of the weeks are profitable. Again not a big surprise as selling premium for the most part is profitable. The problem with selling premium is that sometimes you can be completely blown away. Notice how there were some big losers.  Taking a quick eyeball the middle of the chart is around the 6 USD (Gold premium) and that would translate to about 0.60 USD for the GLD.

Knowing that on average 0.60 USD is generated per week we can multiply this by 58 which represents the number of weeks before the long dated option expires. A total of 34.80 USD is generated in premium. Going back to the long dated option this means the trade will at the minimum generate a grand total 12.60 USD (1260 USD). That in itself is not bad since you are writing a form of covered call.

However, I am not happy about this trade because you will need about 39 weeks to make the trade completely risk free. That’s a long time and I would add one extra trick to the trade. Let’s go back to the cumulative price diagram. The extreme price is 169 from a historical basis. Though a question is if that includes gold spikes or not?

And that is interesting because you now have to ask the question do you want a profitable trade or do you want a lotto ticket? If you include the super spikes of the past you are saying I want to trade a lotto ticket. I myself don’t like lotto tickets. I like to make money because lotto tickets on the whole are loosing propositions.  Thus I tend to ignore super spikes as they skew data, unless I am selling premium.  When selling premium super spikes can completely mess up your trade.

My idea is to convert the long GLD option into a spread, thus lowering my cost basis and the number of weeks that I need to sell premium. I would sell the 165 GLD option, which is trading for 6.25 USD. Subtracting it from 22.20, we get a debit of 15.95, or 26 weeks of premium selling. Thus half of your time you are going to be selling premium. That is better and makes this trade a potential trade that could be profitable.


Would I do this trade? No, because what bothers me is the requirement to sell premium to make this trade work. If I created a 120-165 spread this trade works, since 50th percentile is 137, and the cost basis is 135.95. Though your win would be 1.06 USD for having to put up 15.95 USD. A 6.7% return, on invested capital, but a potential 49% loss. I get the 49% loss based on the standard deviation historical calculation which puts GLD at 128 a year from now. Overall a bad win to loss ratio.

What this means is that you have to sell weekly GLD options to make any money and that is what bothers me in this trade. I don’t like that that fact since so many things can go wrong. Even though it appears I have analyzed this trade, I only analyzed whether or not I put on the trade. I have not analyzed what my exit criteria would be. That would be a second step since I would want to optimize my profit, or loss.

Note if you want your trade analyzed to this degree send me an email at christianhgross at g.mail.com.

Posted in General Trading