Use of mathematics in trading can range from very basic to extremely complex.
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Peter Lynch, one of the most successful professional fund managers of all time said, ‘Everyone has the brainpower to follow the stock market. If you made it through fifth-grade math, you can do it.’ Trading and investing boils down to dealing with numbers. One thing common among all businesses, be it banks or selling milk, is all generate numerical data. An investors or a fund manager’s job is to read through these numbers. Numbers, as they say, do not lie. With the advent of artificial intelligence an analyst’s job is soon getting redundant.
The teachings of investors like Warren Buffett and Charlie Munger can be broken down numerically and fed to computers which can generate signals when there is enough ‘room for safety’ to buy these companies. In his bestseller ‘The little book that beats the market’ author Joel Greenblatt has run some very simple mathematical queries to generate output based on stocks that offer the best investing yields.
Investing blindly in the top stocks has given yields two and a half time the market indices and twice as much as the average of top funds. If investing can be based on simple numerical queries as taught by the ‘Magic Formula’ in Joel’s book, there is little need to look for other sources for investing. It is in trading that one finds active use of math rather than the relatively passive mode in investing.
Use of mathematics in trading can range from very basic to extremely complex. There are quant funds that employ PhDs who try to find predict future movement based on complex series between two markets or two stocks. Quants try to see patterns which are not visible to naked eyes or are not depicted in chart patterns. Algorithmic trading now accounts for 70 percent of trading volume in most exchanges.
For an individual trader this knowledge is of little use as they do not have the wherewithal or the capital to deploy in the series of output that is thrown out by such algorithms.
However, basic knowledge of mathematics can give an edge to a trader as compared to the novice. Many charting patterns and trading strategies are built on simple mathematical concepts. We shall look at a few.
Before looking at these concepts, for a trader it is most important to have a good knowledge in arithmetic. One should be able to perform basic calculations orally as the market is moving. For example, if there is a signal generated on the charts, a trader should be able to calculate his distance between his entry price and stop loss and what will be his reward based on this risk, especially when he is trading in a shorter time frame.
Another important point for a trader, especially novice traders is to think in terms of percentages rather than absolutes. Thinking in absolutes, like a profit or loss of Rs 10,000 can influence the novice trader’s judgment, but he is unlikely to panic if the same number is viewed as a loss or profit of say 2 percent.
In terms of concepts, a trader needs to understand probabilities and start thinking on those lines; this is especially true for derivative traders. Trading, like betting is a game of probabilities, you don’t have to be right every time, you just have to follow the rules and trade when the edge is in your favour.
But to know when the edge is in your favour you should know how many times it has worked in the past and whether or not the probability of it working in your favour is high. As the legendary investor Jesse Livermore said referring to his trading probability - ‘A battle goes on in the stock market and the tape is your telescope. You can depend upon it seven out of ten times.’
Another concept that needs to be understood is standard deviation, or more importantly the ‘Bell Curve’. This too is important for the options traders. ‘Bell curve’ also known as normal distribution of events in a series of data depicts in a graphical manner all possible occurrences around the most probable event (probability distribution).
One of the most popular trading tools – Bollinger band is designed using standard deviations. While one does not need to know the exact definition of calculating standard deviation, at least the trader needs to know its interpretation. Thus a Bollinger band with a standard deviation of 2 will carry within it price movements that could occur in 95 percent of the time. Or a standard deviation of 3 would mean the prices have not moved outside the band in 99.7 percent of times.
Standard deviations are calculated around the ‘mean’ level. Many strategies that traders use are based on reversion to the mean. Thus a stock going through the oversold level is bought in the hope that it will revert to the mean.
Finally, one concept that is found abundantly in nature and what is called as a ‘Fibonacci ratio’ is commonly used by traders. Fibonacci retracements is created by taking highs and lows of the sharp move and dividing the vertical distance by the ratios 23.6%, 38.2%, 50%, 61.8% and 100%. Horizontal lines around these levels act as important support or resistance levels. These levels are closely followed by many traders and have worked well in the past. Traders again only need to know the levels and interpretation rather than the simple math behind it.
Ultimately trading in the long run depends on keeping risk reward ratio in your favour and average wins to average losses ratio to be as high as possible. For a trader these two ratios will decide his success or failure and is undoubtedly the most important mathematical number in his trading life.