Profiting from randomness: A money management system?

[Naked shorts]

I came across this article which basically refutes the idea that randomness cannot be profited from (as suggested in the well known book "A random walk down wall street").
What I found most interesting about this article is that a money management system can actually provide an edge. I have always been under the impression that no amount of money management can turn the odds in your favor (think roulette and all the suckers who think they can win).
So can MM actually provide an edge? or is the article flawed?

http://www.isigmasystems.com/implications.html

Malkiel's model

In his classic, A Random Walk Down Wall Street, Burton Malkiel argues that markets follow a random walk. To illustrate what he means by random walk, he provides example charts generated by tossing a coin. Depending on which way the coin fell, the market would move up or down. An anecdote in the text describes a chart analyst's excited reaction to these faux price charts. Malkiel's point here regarding chartist techniques is not without merit, but we have some other concerns with Malkiel's stance.

Malkiel presents the example of a random walk as background for the following argument against technical analysis:

1. If the market moves in a random walk, then it is impossible to use available price data to predict future prices.
2. The market moves in a random walk.
3. It is impossible to use available price data to predict future prices. (from 1 and 2)
4. If it is impossible to use past prices to predict future prices, then it is impossible to trade profitably making decisions based on available price data.
5. It is impossible to trade profitably making decisions based on available price data. (from 3 and 4)

Statement 1 is undeniable and we'll go along with statement 2 for the time being. Statement 3 is certainly valid from 1 and 2. Statement 5 clearly follows from 3 and 4. Statement 4, however, is false and causes the argument to reach a false conclusion in 5. Let's take a look at why statement 4 is false.

Constructing a random walk

To construct a model of a random walk, we begin with a hypothetical instrument trading at price level 100. At the end of one period, the price will move either up or down based on a random process such as the toss of a coin. If the coin lands heads, the new price becomes the prior price multiplied by 1.01, an increase of one per cent. If the coin lands tails, the new price becomes the prior price divided by 1.01, which exactly offsets the effect of a move up. To mimimize the effects of rounding, all price values are taken to the 10,000ths place.

Possible price paths

The following table shows all of the possible price paths through a trading week.

Possible Weekly Price Paths

**EDIT BY NAKED SHORTS: PLEASE SEE ATTACHED PICTURE**

Note that certain outcomes can happen in only one way. For example a price of 104.0604 on Friday can only occur if the market moves up on each day during the week. The odds of such a week happening are 1/16. Other outcomes are far more likely. A price level on Friday of 100.0000, no net change for the week, is the most likely outcome. The odds of a week resulting in no net change are 6/16.

Profiting from randomness

We now have a random walk model for price change which makes it impossible to use available data to predict future prices. If Malkiel is correct, no set of price based rules will be effective in profitably trading this imaginary market. Is this the case? To test this theory, we have a simple set of four rules for trading based solely on price data.

1. Enter a long position (buy) on Monday.
2. Exit the position (sell) as soon as there is a profit of 1%.
3. If today is the third down day of the week, exit the position.
4. If the position is still open on Friday, exit the position.

The next table lists every possible week that could materialize under this random walk model, as well as the outcomes of following the four rules.

Outcome Table
Entry Price Market Action Rule to Exit Exit Price Profit

100.0000 UP,UP,UP,UP 2 101.0000 1.0000
100.0000 UP,UP,UP,DOWN 2 101.0000 1.0000
100.0000 UP,UP,DOWN,UP 2 101.0000 1.0000
100.0000 UP,UP,DOWN,DOWN 2 101.0000 1.0000
100.0000 UP,DOWN,UP,UP 2 101.0000 1.0000
100.0000 UP,DOWN,UP,DOWN 2 101.0000 1.0000
100.0000 UP,DOWN,DOWN,UP 2 101.0000 1.0000
100.0000 UP,DOWN,DOWN,DOWN 2 101.0000 1.0000
100.0000 DOWN,UP,UP,UP 2 101.0000 1.0000
100.0000 DOWN,UP,UP,DOWN 2 101.0000 1.0000
100.0000 DOWN,UP,DOWN,UP 4 100.0000 0.0000
100.0000 DOWN,UP,DOWN,DOWN 3 98.0296 -1.9704
100.0000 DOWN,DOWN,UP,UP 4 100.0000 0.0000
100.0000 DOWN,DOWN,UP,DOWN 3 98.0296 -1.9704
100.0000 DOWN,DOWN,DOWN,UP 3 97.0590 -2.9410
100.0000 DOWN,DOWN,DOWN,DOWN 3 97.0590 -2.9410

By taking a total of the profit column and dividing by 16, we can determine that following this trading system on such a random market would yield 0.0111 points on average, per trade. So here we have a case where prices in the future are entirely independent of prices in the past and present, making future price prediction entirely impossible. Even so, a set of price based trading rules can be (slightly) profitable.

Additional considerations

Some might point out that the profits in this model seem small. This is largely because we opted to keep our example as simple as possible. More profitable methods of trading a random walk exist, but such methods would require an inconveniently large outcome table and other modifications.

Also, there were other models we could have used to construct a random walk. We chose the one we used because there is no bias up or down, and because it satisfies the requirement that prior changes have no predictive power for future changes.

Malkiel doesn't actually present his argument in a formal structure. The structure we present is based on our understanding of the random walk argument presented by Malkiel and others against technical analysis and is not intended to distort his case.

Implications and Conclusions

As our example clearly shows, making trading decisions based on available price data can be profitable even if that price data does not facilitate prediction making. Hence, even if the random walk theory were correct, this still would not invalidate the practice of trading according to rules based on price information. We certainly do not recommend trading from a set of rules based on a questionable model of the markets, such as random walk theory. However, the example we provide here serves as evidence that given a proper model for market movement, a system based on price is a solid way of generating profit.

 

[MichaelD]

Re: Profiting from randomness - A money management system?

Plenty here profit from randomness. Most falsely attribute this to skill rather than luck. A very small number of posters here skillfully profit from randomness.

And then there's the other issue with these models, which is to assume a normal distribution of returns from a market and no bias, both of which are false assumptions and both of which are exploited by successful traders. (Long tails and the overall upwards bias of equity markets.)

 

[gooner]

Re: Profiting from randomness - A money management system?

1% compound returns upwards is a bigger win than 1% compound return downwards. So upwards bias is built in the model as it is in real equity markets

 

[Amor_Fati]

Re: Profiting from randomness - A money management system?

They have constructed a model where the average win (1/100) is bigger than the average loss (1/101) with equal probabibilty. This is assuming that the market will rise over time, which it generally does, but that is why going long is profitable.

For a simple illustration think of the average after 2 days. There are 4 possibilities UU, UD, DU, DD with payoffs of 1.0201, 1, 1 and 0.980296. Obviously if you add those up you get more than 4 and hence the average is over 1. So to profit from randomness is pretty easy in this model, you just buy, hold, sell. It's implications for trading seem limited.

 

[tech/a]

Re: Profiting from randomness - A money management system?

Plenty here profit from randomness. Most falsely attribute this to skill rather than luck. A very small number of posters here skillfully profit from randomness.

And then there's the other issue with these models, which is to assume a normal distribution of returns from a market and no bias, both of which are false assumptions and both of which are exploited by successful traders. (Long tails and the overall upwards bias of equity markets.)

Michael.

Do you see both entry and exit as random?
Do you believe placing yourself in a position prior to a forward move is no better than 50/50 proposition (over what term--week,month,year?).

 

[motorway]

Re: Profiting from randomness - A money management system?

In the sort of Random Walk
That could apply to a market ( Not these one step fits all + metronome )

You most likely end UP where you start
and The probability of a step of size s is related to the square root of step s

Seeing both of those statements do not apply to stock markets

It is a useless model

All you are left with is

1) Don't PLAY
or 2) If there is a biased drift ,PLAY but entry does not matter exit does not matter --->Just correct money management makes the difference ( gamblers ruin etc law of small and large numbers

HOWEVER
seeing it is NOT TRUE

Then Entry matters & Exit matters
IE TIMING MATTERS
Because TRENDS MATTER ssshh because they exist

But the Entry that matters is not a matter of how
But more a case of into ( and out of ) WHAT..

motorway

 

[MichaelD]

Re: Profiting from randomness - A money management system?

Do you see both entry and exit as random?

Do you believe placing yourself in a position prior to a forward move is no better than 50/50 proposition (over what term--week,month,year?).

Really big, deep questions here. Here's the beliefs that I trade:

Charts are random. Traders are not random. Many traders use charts to trade.

 

[Mr J]

Re: Profiting from randomness - A money management system?

Really big, deep questions here. Here's the beliefs that I trade:

Charts are random. Traders are not random. Many traders use charts to trade.

You say that charts are random, and that the participants are not. If you believe the participants do not act randomly, how can you believe that the charts - which are graphical representations of the participants' actions - are random? You then suggest that the participants give value to the charts when they use them. I suggest that the charts are always usable, since the price action was never random.

 

[brty]

Random is a floored concept, I do not believe in it.

This should not be taken as a belief that it is possible to make fully accurate predictions, as rarely do we have all necessary information.

brty

 

[Timmy]

Random is a floored concept,

Those who propound it should be called on the carpet.

 

[beerwm]

Re: Profiting from randomness - A money management system?

Charts are random. Traders are not random. Many traders use charts to trade.

Do you want to clarify this?

- cause I find it contradicts itself.
Charts reflect Trades, so...
non-random trades = non-random charts.

--just not sure what you're getting at.

 

[tech/a]

Charts are random. ---Have no reliable reoccurring information for trading


Traders are not random.----Psychology is reoccuring and reliable


Many traders use charts to trade.----Read the psycology not the chart.

My take on Michaels deep and meaningful.

 

[Nick Radge]

Have no reliable reoccurring information for trading

Yes they do.

Trends.

 

[Sugar Dunkaton]

Everyone knows that sentiment plays a part in market direction.

Everyone also knows that a coin flip is an independent random even with the outcome unbiased by the previous result.

Therefore trying to use randomness to explain market moves cannot work.

 

[schnootle]

Debating whether the markets follow a random walk is an open question, fine. However i am always going to be suspicious about any one telling me you can profit from a random walk. This all sounds a bit like a brownian ratchet, ie a perpetual motion machine gaining postive net kinetic energy from particle brownian motion.

en.wikipedia.org/wiki/Brownian_ratchet

 

[mazzatelli]

Debating whether the markets follow a random walk is an open question, fine. However i am always going to be suspicious about any one telling me you can profit from a random walk. This all sounds a bit like a brownian ratchet, ie a perpetual motion machine gaining postive net kinetic energy from particle brownian motion.

en.wikipedia.org/wiki/Brownian_ratchet

It looks more like a loose attempt at a binomial tree step. Regardless of step or GBM/Levy, the model is more practical for pricing than trading pruposes.

 

[beamstas]

I'm yet to see proof that entries give you an edge.

With a simple type of trend filter for the market and a simple trailing stop, you'd be suprised at how well random entries on random stocks can work.

I do believe there are people out there who can get an edge with their entry, but the vast majority of people will simply backfit an entry from what they have seen on a chart.

 

[brty]

Sugar,

Even this bit is totally wrong.....

Everyone also knows that a coin flip is an independent random even with the outcome unbiased by the previous result.

A coin flip is not a random event and is easily proven not to be, yet most people think it is.

brty

 

[beamstas]

Sugar,

Even this bit is totally wrong.....



A coin flip is not a random event and is easily proven not to be, yet most people think it is.

brty

Huh?

 

[Sugar Dunkaton]

Might be a bit off topic, but I am definitely interested in learning how a coin flips outcome is dependent on the outcome of the last coin flip outcome. Every little bit of information I have ever collected tells me that coin flips outcomes are independent of each other.