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Losses Are A Function of Expected Gain

September 08, 2014

Life insurance companies run their operations in accordance with mortality tables that are based on population samples, showing the percentage of people who are likely to die by a certain age. From these tables, insurance companies can predict with a high degree of accuracy the number of people at any particular age who probably will be alive a certain number of years in the future.


Although they cannot tell a particular person how long he or she will live (just as we don’t know if the next trade will be successful), the average can be estimated with enough accuracy to set premium levels accurately. By setting premiums correctly, insurance companies can assure themselves of having enough money in any year to cover the payments to beneficiaries and the cost of doing business and secure a decent profit.


Just as an insurance company utilizes mortality tables, you can use a similar method for your trading as I have done for for mine for many years. You have no control over how much a stock goes up, but you can, however, control the amount you lose on each trade. You should base that amount of loss on the average mortality of your gains.


This is similar to the insurance company having control over how much it charges in premiums, which are a direct function of the mortality tables. Similarly, your losses are a direct function of the mortality tables of your gains and where they tend to expire on average.


To make money consistently, you need a positive mathematical expectation for return; you need an edge. That is, your reward/risk ratio must be greater than one to one (net of costs). To achieve this, your losses obviously need to be contained on average to a level lower than that of your gains.


During my 30 years trading tens of thousands of stocks, I have been correct on winning trades only about 50 percent of the time. I’m wrong just as often as I’m right as far as wins and losses go; however, though the losses may be the same or at times even greater in number, the dollar amounts the profitable trades have been much larger than the losses on average.


Imagine: being wrong just as often as being right allowed me to amass a fortune. This is because I follow a very important rule: always keep your risk at a level that is less than that of your average gain.



At What Point Should You Cut a Loss?


As I’ve just discussed, the level at which a trader should cut his losses is not arbitrary. Loss cutting is a function of expected gain. The more accurately you can predict the level of gain and the frequency at which you can expect it to occur, the easier it is to arrive at where you should be cutting your losses. Your maximum stop loss depends both on your batting average (percentage of profitable trades) and on your average profit per trade (expected gain).


Let’s assume that a trader is profitable on 50 percent of his trades. Therefore, he must on average make at least as much as he loses to break even over time. Although going forward these numbers can only be based on assumption, it’s the average gain from your actual trades that’s the key number.


After you have calculated these numbers, you will be able to get a much clearer picture of where you should be cutting your losses. A rule of thumb could be to cut your losses at a level of one-half of your average gain. In the words of Warren Buffett, “Take the probability of loss times the amount of possible loss from the probability of gain times the amount of possible gain. . . . It’s imperfect, but that’s what it’s all about.”



Avoid the Trader’s Cardinal Sin


Allowing your loss on a trade to exceed your average gain is what I call the trader’s cardinal sin. You must make more on your winners than you lose on your losers, remember? How can you possibly make money over time unless your winners return more dollars than your losers lose?


The fact is that most traders don’t even know what their average gain is. When setting a stop loss, I have a rule of thumb that the amount of loss should be no more than one-half the amount of expected gain based on one’s real-life trading results. For example, if your winning trades produce a gain of 15 percent on average, you should sell any declining stock at no more than 7.5 percent off the purchase price. If you buy a stock at $30 a share, you would set your initial stop loss at $27.75.


I also suggest that most investors, no matter how large their average gains, not allow any stock to fall more than 10 percent before selling. If you can’t time a purchase well enough that you need more than 10 percent fluctuation from your point of purchase, something is wrong with your timing and selection criteria.


Let’s say that you sell your winners for an average gain of 30 percent. I would not recommend allowing losses of 15 percent even though that would be half of your expected gain. In my experience, a 10 percent decline signals that something is wrong with the trade, assuming that you purchased it correctly in the first place.


Over time your average gain will improve as you learn how to trade more effectively. You should monitor your average gain on a regular basis and make adjustments to your stop loss accordingly. However, keep in mind that there’s also an absolute level at which you need to cut your loss: the “uncle point.” When you were a kid, someone would twist your arm until you couldn’t take it anymore and said “uncle,” meaning, “Okay, I’ve had enough; I surrender.” Next time you allow a loss to grow larger than your average gain, ask yourself how you can you be profitable if your losses are bigger than your gains.


The best thing you can do is to keep your losses small in relation to your gains. With more experience, you will become a more effective trader. You’ll realize larger gains on average and have more money to reinvest. Improved trading skills will compound your trading account, but only if you keep your losses small and avoid the trader’s cardinal sin. Never let a loss grow larger than your average gain.



Except from Trade Like A Stock Market Wizard; How to Achieve Superperformance in Stocks in Any Market (McGraw Hill 2012)

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