The Bell Curve- What is it in Lay mans

B

Bullz n Bearz

Hi, I hear the term "Bell curve" used in trading. I heard it is wise to avoid it. Well, what is the bell curve? Hopefully you can provide a clear to understand explanation that even us not so savy traders can understand.

Thank you
 
I've been trading for 20 years, and never heard that term in a trading context.

So, it probably means... "if you get yourself 'out on the curve', somebody's gonna ring your bell!"
 
The Bell curve is the form of the distribution of returns used in the random walk model.
Also known as "Normal distribution".
But traders know that this distribution is a great approximation of the market returns distribution, this one having usally (depending on markets) fater tails.
Perhaps this is why people recommend to avoid it :-)

JC
 
The bell curve comes out of the mathematics of probability developed by Karl Friedrich Gauss. It takes a population set (just a set of seemingly random numbers), and determines the mean (simple average) and a standard deviation (the spread of the population sets values). A smaller std dev. means a more accurate data set about the mean. The shape of the distribution of numbers around the mean is what is referred to as a bell curve.

For trading, just look at a yearly chart and many times it looks like prices move in an unpredictable random fashion. You can take the population set of daily closing prices for example and calculate the mean and standard deviation. Standard deviation in this context is akin to volatility.

Trading can be looked upon as probabalistic in nature because of the apparent random movement of prices in the market.
 
The Market Profile graphic uses the bell-shaped curve to identify value, i.e. the prices where most of the volume traded. The MP graphic basically looks like a bell curve on its side. The first standard deviation of the distribution, approximately 68%, is considered the Value Area (usually near the middle of the distribution, but can also be skewed). Value is considered to be more important than price by MP traders, because value changes slowly compared to price. Price is used to advertise trade opportunities (i.e., price away from value). The areas outside of the value area is considered to be unfair prices. A typical trade is to fade the extremes of the distribution (i.e., where price is considered too high or too low) with the expectation that price would revert back to the mean. The bell curve is a concept that can be applied to just about anything in life, such as to graphically depict the annual income or weight of people living in the US. My trading strategy is MP-based which embraces this concept. IMO, it's an excellent way to provide structure to the markets.
 
Before understanding the bell curve, you first need to understand what a distribution is. If you would take a bet on the direction of the market each day for a few months and write down your P/L at the end of each day, you could lump these P/L numbers into bins:
bin A: number of times P/L falls between -2% and -1%
bin B: number of times P/L falls between -1% and 0%
bin C: number of times P/L falls between 0% and 1%
etc.

the numbers you get for each bin are called frequencies and together they form a distribution (of your daily P/L).

If you would plot these numbers as bars (P/L on vertical axis, the bin on the horizontal axis), you would get a "histogram" with usually the tallest bars in the middle and the smallest at both ends.

If you would make the bin size very small and record your P/L for many days, a line drawn through the tops of the bars would start to look like a smooth curve.

You can get similar curves for other data, e.g.
- roll 10 dice each day and record their sum
- take the average IQ of ET members posting between 9-10am each day
etc.

If the curve meets certain statistical properties, e.g. when the underlying data come from a process similar to rolling the dice, the curve is called a bell curve, and the distribution is called "normal" or "Gaussian".

The nice thing is that as soon as you can call your distribution (the one you derived by recording your daily P/L) a bell curve, a lot of statistical properties can be easily computed from your data, e.g. you can predict the probability that one of the daily losses will exceed -5%.

But if it's not a real bell curve (as is often the case in the stock market), this prediction is much harder, and using the easier to obtain prediction from the bell curve can be very misleading if you aim to predict rare events ("black swans").
 
All of these explanations are correct, particularly the preceding one. I think the expression you are thinking of, is to stay away from the tail ends of the bell curve.

The bell curve (like taco bell) is just a visual metaphor for a mathematical probability function, because when you graph it it looks like a bell. The events that are more likely to occur (like say a daily change of +/-1%) occur in the middle or fattest area of the curve. The outliers or tails are the smaller areas of the curve.


These are the unusual large changes that do not occur often; like an 87 style market drop. Although, in reality, markets do not exactly follow a bell curve, which is why IMO it's even worse than a bell curve would predict (that's why LTCM blew up).

<img src="http://elitetrader.com/vb/attachment.php?s=&postid=1520040" border="0" alt=""><br />

BTW. You often will hear arguments about whether the markets follow a "random" walk or not. If the markets were truly random, they would have a probability distribution like the bell curve we are discussing. But, unfortunately, a simple graphing of daily changes show that tail end events
can be much worse than a bell curve would predict.. ie. markets are not random, but worse. If they were truly random in the bell curve (gaussian) sense, we would not have days like the 87 crash. Nor would they occur so many times.
 

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