July 3rd, 2019

Mathematical Trading Strategy


Let’s say you have found the perfect stock. You’ve done your homework and know everything fundamentally about the company there is to know. It’s a rock-solid business with a few near-term and potential-long term catalysts that could drive the price much higher than it is today. Based on intrinsic value you estimate now appears to be a good time to buy, so you take the plunge and buy a few shares. Here is where it gets tricky...

Even with all the homework you’ve done, NOTHING in the stock market is certain. As such, I’d like to walk through a few common scenarios I have experienced and seen myself.


The Stock Roars Higher On Short-Term Catalyst


The next day you check your brokerage app and the stock has jumped 10%. That short-term catalyst you thought could ignite the stock has done just that! You’re so proud of yourself you sit back and enjoy the next couple of days basking in your glory. Then, you check your brokerage app again...

Unexpectedly the stock has dropped down 12% BELOW what you paid in the first place. A damaging news story about the future long-term catalyst broke and sent the stock into a free fall.


The Stock Drops Then Slowly Rises Waiting For Catalyst


You’ve been waiting for the catalyst for a few weeks now and it’s still not materialized. After 21 days the stock FINALLY gets back to what you paid for it. Tired of sitting on a loss, you quickly sell happy to break even. The next day you check your brokerage app and the catalyst has finally hit. The stock roars higher leaving you behind without a single share of ownership.


The Stock Tanks Shortly After You Purchase


It just isn’t your trade. The day after you buy your shares the stock drops 3%. The next day another decline of 5%. The following day 5% again. You hang on convinced your homework is correct. Three months later you sell your shares for pennies on the dollars as the stock is about to be delisted from common exchanges when it sits well below a dollar-per-share.


What You Should Have Done


All three of these are quite common scenarios that traders around the world experience every day. While your homework could have been spot-on, the lack of a strategy AFTER purchase ultimately led to the failure in the trade. So, what can you do differently?


Get A Plan


There are two fundamental skills any successful trader must obtain. The first is the ability to identify with a reasonable degree of accuracy stocks that will go up and stocks that will go down over a given period of time.

The second just as important skill is developing a trading strategy that you NEVER deviate from ever. This requires discipline. This requires knowing you will miss some gains, but also avoid costly losses. Honing this strategy is critical and using math you can see why.


It’s All About Probability


When you make a decision to buy a stock you generally feel that the probability of it going up is higher than the probability of it going down. If you didn’t feel this way, then you would likely short it or not buy at all.

In all cases, this probability must be tied to some event, trigger or catalyst you feel is going to cause this increase in stock price. Once this event has passed, the probability has changed. This is known as conditional probability as shown below.


$$P(A|B) = \frac{P(B|A)*P(A)}{P(B)} $$


What this equation says is given some catalyst "B", the probability of a stock rise "A" is equal to the right-hand-side of the equation (also known as Bayes' Theorem). After the catalyst has passed, the “given some” portion of this equation changes to something else or is removed completely making the probability of the stock rise completely independent of events on your stock radar. At this point you must ask yourself: How do feel about the chances of a stock price increase now?

If you don’t ask this question and evaluate its answer you are essentially gambling without any mathematical basis for holding onto the stock or dumping it. This is the type of thinking that led to the losses in the first scenario.


It's Hard Sometimes Waiting For A Catalyst To Hit


In the second scenario I presented, the homework was correct, but you didn’t wait long enough for the events to materialize. I know this can be difficult waiting for a stock that does nothing but trust your homework if the stock is simply trending sideways. Unlike options, where time held matters greatly, stocks can be held without loss due to simply the passing of time. In these sideways trending cases, trust your homework and wait for events to play out in the company.


You Must Sell When You Are Wrong


If a stock continues to fall after you have completed your homework, then you must re-evaluate your homework or assess if things have changed within the company. Often times a stock that continues to decline significantly after your purchase means that you were wrong or things changed significantly that you just couldn’t predict. This is significantly different than a stock that is simply trending sideways.

Taking a loss in one of the hardest things a trader must do, but it is absolutely necessary. I’ve seen many people wipe out retirement accounts by simply refusing to take a loss on a losing trade that had deteriorating company fundamentals.


Some Tips That Have Helped My Investing


Immediately after you decide to purchase a stock the price will either move up or down (assuming you’re not buying at market close). Because daily minute-by-minute price movements are extremely difficult to predict (random noise), there is a significant probability that the price will drop just after you purchase the stock.

Emotionally this can be tough. After all, if you would have only waited a few minutes you could have gotten a cheaper price. One way to protect against this emotional hit is to dollar-cost-average a purchase. For example, put 50% of the capital to work in a stock one day. If it goes up… great! However, if it drops significantly below your cost basis you can add the remaining 50% position (after you confirm your homework is accurate and nothing has fundamentally changed). In this regard you can capture some of the random noise of the stock price and use it to your advantage by lowering your entry point into the stock.

Lastly, realize that taxes are part of the game. Paying taxes, while sometimes expensive, is a sign of trading success. Instead of holding a position to avoid taxes, consider how much the position would need to drop to cover the taxes. If the drop is small, maybe paying taxes is worth the risk of protecting for more downside? Use the calculator below if you want to see for yourself.

Tax Burden Calculator

Note this calculator assumes a long-term capital gains rate of 15%. However as of 2019, this rate fluctuates between 0% and 20% depending on your total income. For most people, 15% is what will apply and thus is used in this calculator.

If you would like to adjust the calculator to compensate for a different long-term capital gains rate, simply put in your long-term rate as your income tax rate and change the calculation to short-term.