No, I don't play golf.

M.O.N.E.Y.
M.A.N.A.G.E.M.E.N.T.

No, I don't play golf.


Money Management 2   No, I don't play golf.

back to Money Management 1

 
Ray Barros:

THE ROLE OF MONEY MANAGEMENT


Introduction

I have noticed that in newsgroups and trading magazines, the emphasis is on trading systems and/or
approaches. On the other hand, theoretical works tend to emphasize the primacy of money management.

For example, in a chapter entitled "The Secrets of Successful Trading" in Street Smarts, Fernando Diaz
concluded:

"Successful traders have a larger edge and better money management than unsuccessful traders. Unlike popular
belief however, this study shows that the smaller edge of successful traders is not the cause of their failure.
Traders' failures can be explained almost exclusively by their poor money management practices."

While I agree with this statement in principle, I am certain a trader's plan must give him an edge. Good money
management will not save a plan without an edge; all it will result in is slower ruin. In "Anatomy of a Trade", I
indicated the elements I believe are essential to giving a trader his edge.

In this article, I want to outline the best money management approach I have encountered.

W Gallagher's method set out in "Winner Take All".

Gallagher's Money Management

This section will be divided into three parts:

1) disagreement over % stops

2) the pillars of the approach

3) a spreadsheet formula for the approach

Fixed % Stops

Gallagher argues that "risk to trading equity cannot be reduced by reducing the amount risked on each trade".

Let's illustrate this by way of an example Gallagher uses in his book.

Traders A and B both have $20,000.00 and both want to take a trade in Soybeans that may net them
$4,000.00 per contract. Both decide to trade 1 contract.

Trader A decides to risk $5,000.00 and Trader B $400.00. Trader A thinks his trade has a risk reward ratio of
1:4; trader B, 1:10.

Gallagher argues that the risk /reward for both traders is exactly the same because "the strategy risking
$400.00 can be expected to be stopped out two and one-half times as often as the strategy risking $1,00.00".

To quote Gallagher:

"You can drive from Toronto to Miami in one day, or you can spread the drive over three days; it still takes the
same amount of gas to get there. The small amounts risked with very tight stops will be balanced by the high
frequency of occurrence of losing trades."

For me this is true only if you believe the market is random and/or your stop placement is a money stop rather
than a technical stop. On the other hand, if you believe, like I do, that the market has a structure, then stops can
be placed at levels which if hit indicate the trend has changed.

As an example, in "Anatomy of a Trade", I set a stop for the A$ at 7782 because if the market got to that level,
the trend would change from up to down in my time frame.

If my belief is right , you first determine your stop and then see if the dollar value from entry is within your risks
parameters. If not, you skip the trade. Given my trading results, I am happy to risk 2% to 5% of capital. Each
trader has to set his boundaries. These boundaries are determined by a trader's profitability profile, ie

* his historical run of outs,

* percentage of wins: percentage of losses,

* average $ win: average $ loss etc,

and his psychological tolerance to loss. Here I'll mention one factor. I have had the opportunity to observe many
traders over the years. On average I would say that at the 20% drawdown mark, most traders start to lose it - their
discipline starts to go, they start to look for new methods etc. So as a general rule, set your boundaries for a
maximum loss of 20% and you won't go too far wrong.

To conclude this section.

Unlike Gallagher, I believe a maximum % loss has a part to play in keeping a trader from blowing out.

Having said that, maximum % loss is not the only criteria. There will be times when the unusual event will occur
(and in trading, it seems to happen all too often!)

To protect against the rare occurrence, the key element is exposure. And it is here that Gallagher comes into his
own.


The Pillars of the Approach

By exposure Gallagher means the dollar amount needed to cover each open position.

Risk to equity increases with exposure and with time. To adopt Gallagher's approach a trader has to decide for
how long he wants to trade and the maximum draw down he would expect to experience in the period. Gallagher
postulated as a result of his trading experience, a 25 % probability of a 50% draw down in ten years.

The next step is to calculate objectively the largest equity drop (LEED).

"Once LEED is ..... determined, the trader can then make a logical decision on how he wishes to finance this
LEED. He can be aggressive, or he can be conservative - as long as he is aware of the risks he is running."

To work out the LEED, first work out the average daily range (rather average true range) over the period of the results under consideration;
then work out the $ value of your trading results in terms of the daily range. This gives you a result in units.
(example: let's say the average range of D-Mark is 40 points and you make 120. The win result is 3).

Once this is done, you can calculate two things:

1) a probability distribution of your method (ie your edge quantitatively determined) and

2) the LEED

Let's look at an example for the LEED

Trade Gain/loss (in units) Cumulative Equity LEED

1 -1 -1 1

2 -1 -2 2

3 0 -2 2

4 2 0 2

5 3 3 2

6 -1 2 2

7 6 8 2

8 -5 3 5

You get the idea.

Gallagher takes the view that most methods with a 10% edge need 40 units to finance one contract of anything.
Gallagher calls this the "R" factor.

He also found that LEED is a function of the square root of the trading time and therefore a function of the
square root of the number of the independent positions being taken.

Once you have worked out the "R" factor you can work out the dollar value of any contract.

As an example, at the time of Gallagher was writing, the US Bonds had an average daily range of 24 points for a
dollar value of $750.00

If we assume Gallagher's desire not to exceed 50% draw down over 10 years of trading and a 10% edge, we will
have a 40R requirement.

To finance the US Bonds:

Number of Positions Amount Required

1 $ 30,000.00

2 $ 21,000.00

3 $15,000.00

Note that as the number

The Formula




Col A: The instrument you are trading.

Col B: The probability of drawdown over your trading life . I have adopted Gallagher 's 25%.

Col C: The number of independent positions.

Col D: Col B/Col C

Col E: The dollar value of daily mean range

Col F: The "R" value. Notice that Gallagher worked out that for his method he needed 40R, I require
20R. You may require more or less "R"s.

Col G: Square Root of Col D x Col F

Col H: 1st line ; in the example above Row 8 , original capital / Col 6;

thereafter Col J in previous row / Col G; in the above example, J8/G9.

Col I: The actual number of positions taken.

Col J: 1st line: original capital minus (Col I x Col G)

thereafter previous Col J minus (Col I x Col G).

Note in the example above the amount required if the A$ is part of two other independent positions is
A$16,500.00; whereas if it is traded alone, the amount required is A$28,500.00.

Conclusion

In this article, I have suggested that risk to equity can managed by two factors:

a) technical stops that do not exceed a fixed percentage of the trader's equity and

b) the Gallagher formula for exposure.

Both depend on the trader's personality, profitability profile and the volatility of the market.

Dated 1st day of July 1996

R Barros

---------------------------------------------------------------------------------------

ANATOMY OF A TRADE

My aim here article is to give an example of the
principles I outlined previously. I shall be considering
the a$/US as at July 3rd 1996.

Trend Analysis

In any trading plan, the first requirement some means of
identifying of trend of the timeframe we are trading (I call
this, a "trader's timeframe"). For reasons outlined
previously, this implies:

a) we have some means of identifying moves of similar
magnitude, and

b) we have some means of identifying changes in the
trend of trader's timeframe.

I would also add that the trader's timeframe's trend may
be influenced by the trend of the next higher timeframe.

To determine trends, I use swing charts and a wave
theory of my own (R-Wave). The latter is based on
categorising corrective waves to define moves of similar
magnitude,

On July 3rd 1996, the quarterly trend had just given a
confirmed change in trend to the upside (no chart
shown). As long as the a$ did not accept below 7795
before breaking above 8045, I was happy that the
quarterly uptrend was intact.

Chart 1 shows that the monthly swing chart had just
given a confirmed breakout to the upside. As with the
quarterly, I wanted to see a lack of acceptance below
7705.



Chart 2 shows that wave (1) had completed and wave
(2) should terminate between 7890-7920 with the mean
at 7807 being the most probable termination point,



At the end of the trend analysis, I had come to the
following conclusions:

1) The trader's timeframe (monthly) was up. Acceptance
below 7705 would change this view.

2) A preliminary support zone for wave (2) termination
was 7694 - 7920, with the mean retracement at 7807.

Given what I said in (1) above about 7705, the range for
(2) was 7705 - 7920.

Once we have determined the trend, we have our
strategy. We now need a low risk entry.

Low Risk Entry

The next step in the trading plan is to identify a low risk
entry zone. I look at three factors.

1) Some area which is likely to mark the end of the
corrective move. The tools I use here are Dynamic Gann
Levels and Steidlmayer Distribution zones.

For DGL's, level 2 support came in at 7807, the same
number as the R- Wave mean. The Distribution buy zone
came in at 7841 - 7812 (See Chart 3).



2) Once a zone is determined, you need something (a chart pattern or principle) to tell
you that the zone has held - what I call a setup.

In this case, the bar of July 3rd was a Wyckoff "spring" - also known in Distribution
terms as a 313 outside - The market dipped below the previous low at 7812 and was
unable to go on with the down move.

These patterns were examples of the principle of "effort vs. result". The strong move
down of on the July 2nd should have led to some further losses. None were
forthcoming as at the close of trading on July 3rd 1996.

3) After a setup, I need an entry technique. For me that came on July 4th when the
90 mins chart (not shown) produced a confirmed change in trend.

Stops were below 7782 and made up as follows:

7806 - (8045 - 7806)* 10% = 7782

Once in the market, we have to manage the trade. Let's look at that now.

Trade Management

Normally I would wait for the market to enter the 8045 - 8014 zone before taking 1/3
or 1/2 my positions out, However on Friday July 5th (see chart 4), we had a range of
1048 points!

The mean daily range for the a$ at present is 45 points with a standard deviation of
15. That means that the 145 point range had less than a 1% chance of occuring.
Even allowing for statistical error, Friday's range was excessive.

Given that range, I pulled 1/2 my positions out once the 90 mins showed that the up
move had stalled. The point is, I am not sure if Friday's move is a sign of strength or if
like a rubber band stretched too far, there is a strong down move to come.

As it stands, I can now bring up the stops on the remaining position to

7788 made up as follows:

7806 - (7980 - 7806)* 10% = 7788.

This gives me a "free run" for this trade ie even if stopped out, I make a few dollars.

If the market, moves into the 8045 - 8014 zone, partial positions would be liquidated
and stops moved up.

So there we have it an anatomy of a trade.

A Final Comment

I have come across many traders who "just want the secret" to make money.

In a sense there is no "secret". Traders who make money do so because they have a
trading plan with an edge that incorporates effective money management. They then
have the discipline to execute it relatively flawlessly and the self esteem to accept the
money the market gives them.

Then again may be that is the "secret".

Happy and profitable trading!

---------------------------------------------------------------------------------------

Sigma of mean return declines over time
Sigma of total return rises over time

I realize if I had started trading in March last year I would have
been blown out, so will only increase position size when I can limit risk
to 2% per trade.

...ask is touched on a buy stop or when the bid is touched on a sell stop.

often exit positions long before I am stopped out !!!

I executed long trades at 1,785.
Target for my second third was 1,891 - 1,866
First resistance was at 1,843 - 1,832
I exited the first third at the low 1,830's. Not only did that zone
represent resistance, it was also the area that allowed me to break even on
the remaining 2/3s if stopped out.
I was wrong about this week's direction and took out the second third in the
high 1,800's. If I was wrong about the week's direction, it was probable I
was wrong about the mkt getting to the 18910 zone.
The stop on the remaining 1/3 has been raised so that if I am stopped out,
I should lose no more than 50 points (allowing for slippage) on the last 3rd.

Preservation of capital and consistent profitability is most important.
As Steidlmayer used to say "trading is 10 months of grind and 2 months
of gravy. If you can stay ahead in the 10 months of grind (or least lose
very little), the 2 months of gravy will make you a very successful trader".

With any system, you can "over filter" either it is by adding seasonal
considerations or just too many filters. The trick is when adding filters
one must be sure that the filters do not contradict each other. When this
happens you have created your own version of chaos.


ATR D-Mark its about 40 ticks

Set a stop at 3 ATRs under the entry, reversing when it hits the stop.
Then adding an additional contract to when the stop is moved up another ATR.
This assumes that you can get out reliably with simple stop orders. Thats not
always the case, especially when multiple contracts are pyramided up.
The money management step, adding on the contracts with each movement of the
stop and then adding positions with "the markets money" is what makes the
money. The real money is not made with the usual 1 to 3 strike moves in this
system. Its in the pyramiding that can take place after a position becomes
riskless. If it goes on past the 3 or 4 strikes and another similar position
is added, it then only takes a 2 strike move to become riskless again.
You have twice as many positions working. Then another pair of futures and
options are then added, using the equity from the previous positions requiring
only a 1 strike move to become riskless. It doesn't take much of a trend to
gather 64 or 128 contracts/options to become "ballistic" and still not have
any additional risk to your account using "the markets money" to pay the way.
It just takes getting over trying to be "right" all of the time and letting
the market take you where it wants to go. When the move is over, you just
start over again in the opposite direction with the 3% risk again - hopefully.


chi squared test: indicate that the improvements are unlikely to be random.

Look at the momentum of what is happening. If volatility and momentum go to
a certain level and get way out of line, I'm looking for a reaction in the
other direction and then I put on a trade.
search via e-mail?

-------------------------------------
Ray Barros:

You are right. Money Management attempts to answer these questions:

* how much to allocate as initial deposit
* how much to risk per trade
* how to allocate among competing opportunities.
* number of contracts to be traded.

> I tried to increase postition size according to the %return on
> margin (the higher it grows the higher the number of contracts), when
> %return on margin calms down, I decrease postition size, but the results
> are not very satisfactory.
> I also tried to increase/decrease postition size according to the
> dependency among the last x trading days of a trade. When there is a
> Win-Lose-Win-Lose pattern I increase-decrease-increase-decrease, when
> there is a Win-Win-Win-Win pattern I increase continuosly (e.g. every 5th
> day). Also not very satisfactory. Am I on the right track but on the wrong branch?

****************************************************************************
I am not a believer in increasing/decreasing the size of my capital a matter
of course (=selbstverständlich). My reasoning is thus:
"If a have a 65% probability of winning on a trade, the probability does
change because you have had a run of outs or wins."

I have simple rules about increasing the size of my capital. Whenever I
achieve a 30% increase, my capital base increase by 15%.

Example: I start out with $100,000.00. When I have made $30,000.00,
my capital base increases to $115,000.00. When I have made $35,000, (a
rounded 30% of $115,000.00) my capital base increases to $132,000.
You will note that I round up for the requirement of 30% increase and round
down for the capital base increase.

If I increase my bank by 15% and I suffer losses gives back all of the 15%,
I return to the original bank.
Example: I increase by %15,000 to $115,000.00 and losses of $16,000.00
accrue, my bank drops to $100,000.00 for money management purposes.

****************************************************************************

The best books I have come across on the subject in increasing order of
importance on my ideas on Money Management:

* Gallacher "Winner Take All". There is a chapter on MM which is better
than any book.

I take issue with (anderer Meinung sein) Gallacher's attitude to 2% on a technical and psychological
issue rather than mathematical. However that is because I am a discretionary
trader - his argument is directed to the mechanical trader.
If you read his book and want to take the discussion further, please write.

* Balsara'a "Money Management Strategies for Futures Traders". Poses good
questions but the answers are inadequate.

* Gehm's "Commodity Market Money Management". Good book for introducing the
probability issue. That title is probably out of print. However Gehm did have
a re-write 2/3yrs ago with a new title but I cannot recall its name.

regards

ray
---------------------------------------------------------------------------------------
RANKING OF TRENDS

In "Anatomy of a Trade", I said that identifying the trend of the timeframe you are
trading is important because it sets up the strategy for your trade. In other words, in
an uptrend, you buy dips or upside breakouts, in a downtrend, you sell rallies and
downside breakouts and in a sideways trend, sell the top end of the range and buy
the bottom end.

It is almost a cliche that "trends are where traders make their money". However, I
believe that you need to go beyond merely identifying a trending market. To maximise
my profits, I would rank the type of trending market I am in.

For the purposes of these notes, I am assuming a monthly uptrend. The
monthly is therefore the "trader's timeframe trend".

Moves in the direction of the trend (ie up moves), I shall be calling "impulse moves" or
"impulsive" and moves in a direction opposite to the trend (ie down moves), I shall be
calling "corrective moves" or "corrections".

This article will suggest four categories. They are ranked from "0" to "3", with "0" being
the most difficult to make money and "3" being the easiest provided you can identify
it.

The key to the categories is the relationship between the impulse and corrective
waves by the amount that one overlaps the other.

Ranking "0"



Characteristics

1 Corrections of the impulse move tend to be between > 67% to < 87.5%.

2 Breakouts are followed by a correction between > 67% to < 87.5% and a deep
re-entry (ie greater than 50%) into the previous correction.

eg After the breakout at "3", the market retraces between > 67% to < 87.5% of "2" to
"3" and greater than 50% of "1" to "2".

3 At either Point 5 or point 7, the trend or trend type will change. In other words, the
market will either change from an uptrend to a downtrend or at Point 5 or point 7
change to a Ranking of 1 or 2 or 3

Profit Potential

Unless you identify it, it is difficult to make money in this type of trend.

Breakout traders have to wear the pain of the retracement. Most will place their stops
below the 50% or 67% retracement areas and will continually get stopped out.

Responsive buyers

ie buyers on dips

will probably not get set.

Responsive sellers at the top end of the ranges will make some money if they take
partial stops or use some form of trade management. Otherwise, they also will be
stopped out continually.

Ranking "1"



Characteristics

1 Corrections of the impulse move tend to be between > 33% to < 67%.

2 Breakouts are followed by a correction between > 33% to < 67.% and a shallow
re-entry (ie 50% or less) into the previous correction.

eg After the breakout at "3", the market retraces between > 33% to < 67.% of "2" to
"3" and 50% or less of "1" to "2".

Profit Potential

Profit potential is reasonable.

The danger points are the correction following the breakout when re-entry occurs
below the point of breakout. Good trade management is necessary.

Ranking "2"



Characteristics

1 Corrections of the impulse move tend to be between > 33% to 50%.

2 Breakouts are followed by a correction between > 33% to 50% and no re-entry
into the previous correction.

eg After the breakout at "3", the market retraces between > 33% to 50% of "2" to "3"
and above "1".


Profit Potential

Profit potential is excellent as this is the most orderly of all the trends. When the
market retraces into the previous correction's range, you will KNOW that a CIT is
imminent.

Ranking "3"



Characteristics

1 Strong (in terms or price and time) directional move after a confirmed CIT on
breakout above "1".

2 No corrective moves.

Profit Potential

Profit potential is poor unless identified early or you have developed special rules to
deal with it. This type of trend can prove very frustrating for the responsive trader as
the market steams ahead without any corrections.

Breakout traders can make excellent money as the market quickly turns poor trade
location into fine ones.

Novice traders learn extremely dangerous habits as they "learn" that the market will
get them out of trouble as long as they trade with the trend and "isn't easy to identify
a trend that will go on forever" (??!!)

There you have a method of ranking trends. In my next article, I shall look at some
examples.

Happy trading 27/08/96

---------------------------------------------------------------------------------------

RANKING OF TRENDS

PART II

In the first part of this article, I outlined the concept of "ranking of trends".

Here I shall look at a practical application reviewing the current US/Jy picture. The trader's
timeframe is the monthly trend.



In the above chart, the monthly trend has been up with a ranking of "0". In the previous article I
said,

"3 At either Point 5 or point 7, the trend or trend type will change. In other words, the
market will either change from an uptrend to a downtrend or at Point 5 or point 7
change to a Ranking of 1 or 2 or 3."

The question now is:

"Will the US dollar accelerate its uptrend or will we see a deep correction to at least 10335 and
probably below?"



The quarterly trend shows the US/JY still in a downtrend and currently in a sell zone. Even if we are
to have a change in the quarterly trend from down to up, we can expect to have a test of the low at
8010. Generally the market will retrace to the 50% level around 9700 - 8965.

Given the quarterly picture, the probability is the monthly trend will break to the downside.

Identifying the actual setup and entry is beyond the scope of this example - the point of which was
to illustrate the use of "ranking of trends".

October 7, 1996

---------------------------------------------------------------------------------------

Wyckoff, Steidlmayer and my own observations on how markets behave.


Let me introduce myself. My name is Ramon Barros. I have been a professional trader since 1980.
I trade the forex markets, and interest rate futures, Australian Ten Year Bonds, US 30 Years, the
Gilts and Bunds.

What follows are the basis of my trading approach.

My approach to the markets is a combination of Wyckoff, Steidlmayer and my own observations
on how markets behave.

Here I would like to set out the principles that govern my trading so that you have a basis to follow
my line of thought in future articles.

Wyckoff:

He was the first that I know of that drew the distinction between mechanical TA and subjective TA.

The grandfather of the former is Schabacher. He studied charts looking for patterns that led to the
same result. In modern lexicon, the Edwards and Mcgee formations, head and shoulders etc. Here
the approach is observations of models and then finding as many carbon copies as possible.

With subjective TA, we begin with a set of principles. The observation is aimed at finding these
principles at work and responding to them in the appropriate manner.

"At this point there may be the inclination to say,

"What is the difference"?

There is a very basic difference. A formation is a constant. If the stock does not fit one of the
molds.....it is eliminated.

A principle ....... is more than a constant. It is an absolute. In the case of the market, it is a statement
of condition that is unequivocally true. Given a certain set of conditions, the result will always be the
same. These conditions may not and usually do not, produce carbon copy formations."

Introduction to the Wyckoff Method of Stock Market
Analysis

Wyckoff articulated three laws:

The Law of Supply and Demand:

Market go up when demand exceeds supply and vice versa. He also identified that "in between the
excess of supply and demand, or demand over supply, is a state in which the two are in equilibrium"

COMMENTS: All of the above should be self evident. However many trading systems/approaches
recognise only two trends:

up or down

It’s the reason you get such huge drawdowns in non trending markets.


The Law of Cause and Effect

The effect realised by a cause will be in direct proportion to that cause. To get an important move
(effect), there must be an important cause ie these moves take time to develop.


The Law of Effort and Result

What is important is not only price but also the character of the volume. When volume and price are
in harmony, the trend is likely to continue. When they are out of sync, positions are in danger and
defensive measures need to be taken.

For example, in the US Bonds. We have had a down move which began on or about February 13th
1996. From the 11th April lows onwards we see the market make new lows only to retrace back
into the previous congestion area.

On June 12th, we see a beak of the closing low of the past six weeks.

The volume was above its mean (in fact it was close to its mean plus 1 Standard Deviation); the
range was below its mean and the net change was a mere thirteen ticks.

Given the disharmony, I would tighten stops on long term shorts and liquidate any fresh positions
taken on the break of the six week closing low.

Wyckoff did develop a model for identifying how markets moved, terminated its trends and the
appropriate trading strategies. However, the model was secondary to the principles and a way of
illustrating their use.


Before we leave Wyckoff, I need to mention one other item.

Wyckoff believed that markets moved in waves as a trend progressed. The magnitude of the action
in time and price determined the nature of the underlying trend.

Given the above, it is critical to his approach we determine the trend of the timeframe we are
trading. The tool he used was a trend channel. What is important is not the tool but the manner in
which it is constructed.


"(In an uptrend)...The next step is to construct a justifiable trend channel (emphasis added)....The
important word here is justifiable.

An uptrend channel is formed from a support line and an overbought line....To define a support line
requires two points.... they are to be low points of two consecutive reactions of similar importance
(emphasis added)..."

Introduction to the Wyckoff Method of Stock Market
Analysis


The idea here is to measure moves of similar magnitude. I shall have more to say later on this
subject later on.

For now I would like to leave Wyckoff and turn to Steidlmayer.


Steidlmayer

Peter J Steidlmayer , floor trader and former director of the CBOT is known of his work on the
Market Profile and its subsequent evolution, the Steidlmayer Distribution.

Much of Wyckoff’s ideas are found in his work. As Steidlmayer has never acknowledged
Wyckoff’s influence, I would say that he made his observations independently of Wyckoff. I make
this point to stress that two traders, centuries apart, have made similar observations about market
behaviour.

Like Wyckoff, Steidlmayer believes that principles rather than models are the key to trading
success. His key message is that trading is no different to any other business endeavour and that the
common management techniques used in other business endeavours are applicable to trading and
investing.


My Own Work

Most of my own research lies in identifying what constitutes moves of similar importance. I believe
that one of the key failures of modern technical analysis is a failure to answer this question. To
determine the nature of the current trend, we first have to determine, the magnitude of that trend by
some relatively objective means. One of the problems with the Elliot Wave is subjective nature of
the various wave classes.

For me, there are two ways of measuring moves similar moves - by time or price.

In the case of time, swing charts are easy to apply. In my own trading I use the 12 week to
determine the quarterly trend, the 18 - 20 day to determine the monthly, the 5 day to determine the
weekly and an intra day swing chart to determine the daily.

In the case of price - what was important to me was the magnitude of the corrective move. For this
reason I classified all the corrective moves for each market and worked out the mean and standard
deviation for each. In this way, I know when one category ends and another begins.

Well that’s it. In the future, we’ll look at the specifics and their implementation.

 

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