# Over Bought and Over Sold, What does it mean?

When considering certain technical indicators, the terms **over-bought** and **over-sold** are sometimes used. In a nutshell,

what these mean are that the stock has moved too much in one direction and it is due to move in the other direction.

The example that I have used is to compare the flipping of a coin. While the odds of flipping heads or tails (assuming a fair coin and a fair flip) is 50%.

The odds of flipping heads twice in a row are lower than 50%.

Let’s look at the possibilities. If you flip a coin twice you will have one of the following possible combinations:

Heads, Tails

Tails, Heads

Heads, Heads

Tails, Tails

You can see here that the out of the 4 possibilities, only once do you get heads twice. That is 25%. The mathematical formula for determining the outcome

is:

(Probability of a heads) ^{[Number of Flips]}

For two flips that is:

(0.5)^{2} = 0.25 = 25% or 1 in 4

If someone were to flip heads 13 times in a row, what would you think is the 14^{th} flip would be: heads or tails? If you believed in lucky

streaks, you might pick heads. Or if you are a conspiracy theorist, you might consider that the coin is unbalanced or the flipper is cheating. If it is a

fair game, the likelihood of 14^{th} flip being heads – after flipping 13 heads – is very low.

Probability of flipping 13 heads in a row is:

(0.5)^{13} = 0.01221% or 1 in 8,192

The odds of 14 head in a row is:

(0.5)^{14} = 0.25 = 0.006104% or 1 in 16,384

It doubles, every sequential flip.

So, if you are looking at the 14^{th} flip, the odds of that flip being heads after 13 heads in a row is 16,384 – 8,192 = 8,192. It’s not

impossible, but it is very unlikely.

How does this apply to stocks? One of the greatest discoveries and the foundation of much economic theory is that stocks pricing has no memory and each

movement is random. This concept was introduced by Luis Belchelier in 1900. It was further used by Fisher Black, Myron Scholes, and Robert Merton. It is

the basis for Black-Scholes Model for option pricing and won the Nobel Prize in Economics in 1997. What these gentlemen discovered is that stock pricing

changes fit log-normal distribution. (The “log” essentially means that the movement is in percentage changes, not absolute changes.)

This can be a “Whoa, dude! You’re blowing my mind” sort of statement. It implies that stocks are random.

One can look at the day-to-day price history of stocks and find that this is true. If you look at a large enough sample of data, historical stock pricing

movements will fall into a model that is essentially a log-normal distribution.

Does this really mean that all stocks are random? Maybe it is not the stock movement that is random, but the things that cause a stock to move that are

random. Without getting into philosophical discussion, we can move forward and recognize that, like flipping a coin – a well-established random model,

stocks also follow a random model.

Using the coin analogy, we would not expect to see long streaks of either up days or down days. This tends to be is true. Even the most bullish of stocks,

will have an occasional down day. It is rare to see long streaks. As of the time of this writing (April 5, 2013), the stock the holds the record for

consecutive up days is Six Flags Entertainment Corp (SIX) with 13 up days in a row. Considering this discussion, the odds of having 13 days up in a row is

very small. There is a strong likelihood that the next day is going to be down.

We would expect that stocks would oscillate between up and down days. This is sometimes called “The Law of Averages.”

If my memory serves me correctly the all-time record for consecutive up-day is 23 by Microsoft (MSFT.)

In stock technical analysis there are a number of indicators that fall into category of “oscillators.” These include: Accumulation/Distribution Line,

Average Directional Index, Aroon Indicator, Moving Average Convergence Divergence, Relative Strength Index, On-Balance Volume, Slow and Fast Stochastic

Oscillators, etc.. All of these are based on the theory of random movement. When these indicators move too far in the bullish direction, they are

considered to be “over-bought” and a move in the bearish direction can be anticipated. When they move too far in the bearish direction they are considered

“over-sold” and move in the bullish direction can be anticipated.

I must add a word of caution here. While stocks that reach these extremes and one can rationally expect them move in the other direction, I will remind

readers of the famous quote by John Maynard Keynes: “Markets can remain irrational longer than you can remain solvent.”

While SIX has been up for 13 days in row, and it is unlikely that we will see a 14^{th} up day, it can happen. Don’t bet the farm on that one

indicator. Technical Analysis has its limitations. Traders must do their due diligence and also perform their Fundamental Analysis and Sentimental Analysis

before placing any trade. And when they do place the trade, they must define their primary exit (when are you going to take profits) and secondary exits

(what are you going to do if the trade goes against you.) That is what makes successful traders.

Eric Hale

OptionsANIMAL Instructor

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