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Game Theory
The Smart Profits Report: Issue #171
Friday, December 31, 2004
Game Theory: Making Profits With Mathematical Precision
By Dean Albrecht
Advisory Panelist, Mt. Vernon Research
Last night there was a terrific documentary on PBS about mathematician John Nash. So what does that have to do with options? Well, quite a bit, as it turns out.
This particular mathematician - along with going completely mad at one point in his life - won the Nobel Prize in 1994 for his work on “game theory.”
Game theory is one of the most powerful mathematical models used by modern economists to explain and predict the behavior of the markets (and many other hard-to-grasp phenomena).
Predicting the behavior of the markets has obvious advantages if you’re trading options. In fact, by using a mathematical technique I’m about to show you - one Nash might appreciate for its simplicity - you can determine both stop losses and expectations of gains on any trade you enter.
You can also time your put and call trades with greater precision. In fact, the predictability built into this approach lets you know how large a gain to expect - or how far to let the price of a stock or option drop before bailing out of the position - with mathematical precision.
Let me explain…
Finding Meaning In Repeated Patterns
The strategy of game theory uses a mathematical system where we look at historical numbers that constantly repeat themselves. (People, as Nash’s theory proved, also behave in predictable patterns.)
We test for price patterns in stocks, options and ETFs. We look at percentage moves rather than penny or dollar moves, which makes it easier for us. We then look to identify repetitive instances of price action.
For example, in our research we found that stocks on the NYSE move just a little differently than stocks traded on the Nasdaq. We also found that AMEX stocks move differently than their NYSE and Nasdaq cousins. (By moves we mean distance and by distance we mean percentages.)
Game Theory & The QQQQ
Let’s take a look at the Nasdaq index (Nasdaq: QQQQ - formerly QQQ). The “Qs”, as they’re often called, move an average of 3.5% when they change direction, up or down.
This piece of information is valuable because it allows us to set profit targets and stop losses whenever we enter a position, by giving us the precise numbers of what to expect.
The interesting thing is that the percentage didn’t change when QQQQ was trading at $50, $60 or $30.
That gives us an expectation of gain. Let’s say you buy an ETF at $40, and you know from observation that the upside potential of a move is 3.5%. From that, you also know to expect a move of about $1.50 to the upside. So once that move is completed, you can take your profits - rather than buying and holding while the trend reverses against you.
Speaking of the downside… We do studies to get statistical averages of downside expectation of price, given certain market conditions. For instance, QQQQ is currently in an uptrend (see chart below), and pullbacks are smaller than when the QQQQ is in a downtrend.
That means the downside expectation is less than the upside, so we know how far to let a stock’s price go against us in all market conditions.
How To Take Advantage of Game Theory
So how to take advantage of game theory for yourself? If you have a favorite stock that you trade, such as QQQQ, then simply do the following:
Overlay a 50-day moving average line on a daily chart going back about one year. You can easily do this online at www.bigcharts.com (see chart below):
Then plot the move of the price in percentage terms when the price goes above and below the 50-day moving average.
You’ll find that the price drifts about 8% or so above or below the 50-day moving average.
Which means your expectation of profit on this simple crossover system is about 8%.
You can also count the number of times the price moves above and below the 50-day MA line, going back several years. Now you will have a gauge on how many positions (or potential option trades) to expect per year.
This is a simple example, but it should give you an idea of how easy it is to start incorporating quantitative research, like game theory, into your own trading.
Good Trading,
Dean Albrecht
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Today’s Smart Profits Cribsheet
- At Quantitative Equity Research, where I work, instead of doing our research by hand we use automated computers screening the data based on our inputs throughout the day. But again, you can do your own “quant” research using simple techniques like the one I showed you today.
- Check out the Smart Profits Glossary, chock full of over 150 option terms like “QQQQ,” “game theory” or “technical indicators.”
Related Articles:
- Quantitative Research: An Interview with Dean Albrecht
- Fundamental Analysis: Three Screens For Technical Traders
- Portfolio Diversification: Falling In Love With Investments Can Cost You Millions
