Money Management: The Foundations of Money Management I
I've found such a system. With numerous tests it
almost never had under 90% profitable trades. The
results of one such a test are given in Table 1
in Omega Research TradeStation format. The code
for the system is in Appendix 1; you may copy it
to Omega TradeStation or SuperCharts and go along
winning (in the sense they usually mean winning,
that is, having a profit on most trades). The
system's main secret is a pseudo-random number
generator (too "pseudo" in TradeStation, but
doesn't matter much). Then it all goes as usual:
if the position is profitable, close it. If the
market goes against us, turn investors. Having
enjoyed working and socializing with customers of
two brokerages over a couple of years, I can
insist that is just what most traders do - except
the fact they formally replace the random number
generator with analytic forecasts, indicator
signals, the neighbor's opinion in the pit or
just a momentary impulse. The problem is that
winning at an exchange and earning money at an
exchange are far from being the same.
Surely, the profit seen in the Table 1 example is
casual, a result of a lucky dice roll, whereas it
would not be profitable in most cases. But if one
changes the system entry parameters to more
reasonable levels, i.e. sets mmstp=1, pftlim =4,
maxhold =10, this will make the system profitable
in most tests.
So exploiting the principal idea of speculation -
close losing trades fast and let profits grow -
combined with money management allows to earn
money even from random trades. Most people act
just opposite to this principle; they let losses
grow, hoping the market turns and proves how
right have they been, and quickly close their
profitable positions to prove how right they're
at the moment. Most beginners and many self-
styled pros, as our experience shows, are sure
that the skill of market forecasting equals the
ability to earn money at the market. Getting a
profit on a given trade for them means proving
their prognostic abilities and, consequently,
their skill in making money.
A person unfamiliar with trading as a business
could be puzzled by the fact that "successful
investing and trading have nothing in common with
forecasting"*.
There is bad news and good news. The bad news is:
markets cannot be prognosed. The good news is:
one doesn't need to do that to have profit. We
are concerned not with getting a profit on every
trade, but on making large sums when we're right.
The number of profitable trades may in this case
be less than losing, that is, it is possible to
use worse-than-random forecasting!
As a famous trader Paul Tudor Jones said: "I may
be stopped four or five times per trade until it
really start moving". That is, Paul may win only
on a measly 20-25% times! Yet he'd had three-
figure (percents) of income in five consecutive
years with very low capital corrections1. Almost
100% of Steve Cohen's very large profits are
taken off 5% of trades, and only 55% of his
trades are profitable at all. Despite that in the
last seven years he'd made 90% per year on the
average, and had only three losing months (the
worst losses were -2%)2.
The widely used by professional methods of trend
following, as a rule, bring about 30-40% of
profit. Profits or losses in any given trade do
not matter - as long as the amount of money
earned per average trade is positive. This value
is called mathematical expectancy. The
mathematical expectancy equals the sum of
products of profit probabilities minus the sum of
products of losses probabilities, multiplied by
the losses' size
Simplified, the expectancy may be estimated as
the probability of profits multiplied by the
average profit minus probability of losses
multiplied by the average loss. In terms of the
Omega Research TradeStation this looks like:
Table1.
| Total Net Profit |
$562.70 |
Open position
P/L |
($75.60) |
| Gross Profit |
$1,269.40 |
Gross Loss |
($706.70) |
| Total #of trades |
276 |
Percent
profitable |
92.75 % |
| Number winning
trades |
256 |
Number losing
trades |
20 |
| Largest winning
trade |
$54.90 |
Largest losing
trade |
($126.50) |
| Average winning
trade |
$4.96 |
Average losing trade
|
($35.33) |
| Ratio avg win/avg
loss |
.14 |
Avg trade (win &loss)
|
$2.04 |
| Max consec.Winners |
39 |
Max
consec.losers |
2 |
| Avg #bars in
winners |
1 |
Avg #bars in
losers |
17 |
| Account size
required |
$177.30 |
Return on
account |
317.37% |
In a newsgroup discussion one follower of
Elliott's theory said: "Market is no gambling -
we make no bets". Not being an Elliott adherent,
for whom everything is pre-arranged, we do make
bets. Since the result of any trade is unknown,
any trade is a bet where we win or lose a certain
sum. The principal difference between gambling
(betting) and market trades (speculations) is
first, that gambling creates its own risks and
speculations re-distribute the risks already
present on the market; second, the on a market a
trader is able to provide himself with a
statistical advantage, that is, a positive
expectancy.
Let us review betting on a color when playing
roulette. There are 18 red sectors, 18 black and
the zero. The expectancy of winning for a single
bet on a color is 18/37 - (18+1/37) = - 1/37. On
the average the house wins from a single gambler
this amount multiplied by the bet size. Despite
the fact some gamblers may win a lot, it is the
house that wins always - because of the biased
expectancy, not because the dealer knows where
the ball stops.
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Appendix 1.
A system giving over 90%
profitable trades.
{*************************************************
********
Random System №1.
Copyright (c)2001 DT
Parameter values by default: mmstp =1,pflim
=4,maxhold =10
**************************************************
********}
Inputs: Bias(.025), {Random entry
parameter}
mmstp(100), {Stop loss parameter}
pflim(.1), {Profit target limit}
maxhold(50); {maximum holding period};
Var:Trigger(0),Signal(0),ATR(0),num(1);
trigger =random(1);
if trigger < bias then signal = -1;
if trigger >1 - bias then signal =1;
ATR =XAverage(TrueRange,50);
{ Random Entry}
If signal =1 then Buy("Random_Mkt.LE")num
contracts next bar at open;
If signal =1 then Sell("Random_Mkt.SE")num
contracts next bar at open;
{ Standartized Exits}
if marketposition >0 then begin
ExitLong ("MM.LX")Next Bar at EntryPrice -
mmstp*ATR stop;
ExitLong ("Pt.LX")Next Bar at EntryPrice
+pflim*ATR limit;
if barssinceentry >=maxhold then
ExitLong ("Hold.LX")at close;
end;
if marketposition <0 then begin
ExitShort ("MM.SX")Next Bar at EntryPrice
+mmstp*ATR stop;
ExitShort ("Pt.SX")Next Bar at EntryPrice -
pflim*ATR limit;
if barssinceentry >=maxhold then
ExitShort ("Hold.SX")at close;
end;
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Appendix 2.
The simplest system number
2.
{*************************************************
************
The Simplest System №2.
Copyright (c)2001 DT
**************************************************
************}
Input:Price((H+L)*.5),PtUp(4.),PtDn(4.);
Vars:TrendLine(C),LL(99999),HH(0),num(1);
if MarketPosition <=0 then begin
if Price < LL then LL =Price;
if Price cross above LL +PtUp *.001 then begin
buy("Simpl.LE ")num contracts next bar at
market;
HH =Price;
end;
end;
if MarketPosition >=0 then begin
if Price >HH then HH =Price;
if Price cross below HH -PtDn *.001 then begin
Sell("Simpl.SE ")num contracts next bar at
market;
LL =Price;
end;
end;
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Appendix 3.
Data output to a file to compute
mathematical expectancy
{*************************************************
************
Expectancy Output
Copyright (c)2001 DT
**************************************************
************}
Var:RMult(1),R1(1),Trades(0);
Trades =TotalTrades;
R1 =PctUp *.001 *BigPointValue;
RMult =PositionProfit(1)/R1;
If barnumber =1 then
print(file("D:TS_Export M
trading.csv"),"Qty",",","Profit",",","Initial
Risk",",","R multiple");
If Trades <>Trades [1 ]then
print(file("D:TS_Export M
trading.csv"),Num:10:0,",",PositionProfit
(1):10:4,",",R1:10:4,",",RMult:10:4);
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To be just we should mention that it is possible
to create a "gambler's advantage" - so a
mathematician Edward Thorp has developed
strategies with a positive expectancy for playing
blackjack, which he'd successfully used in Las
Vegas gambling houses. When they stopped letting
him in, he published his methods1, after which
blackjack rules had to be altered to remove the
gambler advantage. In late sixties Thorp took
interest in shares market and became a manager
for a private investing partnership: " Our
significant rival then was a Harry Markowitz, a
future Nobel prize winner. After 20 months we had
+39,9% profit compared to Dow Jones' +4,2%.
Markowitz went negative in a couple of years, and
we're satisfied with our stable results… about
20% yearly (standard deviation around 6%0 and
zero correlation with the market".
The market allows to play games with a positive
expectancy. This is a necessary condition for
successful stock trading. Actually, as Ralph
Vince says, "it doesn't matter how negative or
how positive; only positive or negative matters".
A doubtful claim from our point of view; a larger
positive expectancy is superior to a smaller one.
Besides expectancy, most traders have problems
understanding risk. For instance, a historian by
education, (former) head of a regional investing
company with assets over a million dollars by
summer 1997 was sure that "risk doesn't exist so
it cannot be measured" and also sure that "one
shouldn't sell shares at a loss". What can one
say about amateurs then… Risk does exist and it
can be measured. It is considered that risk is a
volatility measured as the standard deviation of
the changes of actives traded. This holds true
for investing risk, speculative risk is more
adequately defined as standard deviation of
capital changes. By both those definitions risk
is heavily underestimated. According to Murphy's
laws, the worst is yet to come; We shall employ
the following definition: risk is the amount of
money we are ready to lose before withdrawing
from a losing trade.
Before opening a position it is necessary to
define the point where we close the position wit
a loss to save capital - the so-called stop
loss1, or where we open an opposite position,
having made sure of our mistake concerning the
market direction - the so-called stop-and-
reverse. The difference between the entry point
and the stop loss point multiplied by the number
of lots is the starting risk or 1 R2, independent
of how and in which units we measure the stop
level, be it dollars, percents, volatility units
or six-packs. This definition of risk is not
equal to the first definition - the risk may be
many times the 1 R if the stops are not executed
due to lack of discipline3, gaps against the
position or unexpectedly high slippage. The
profit, then, can be defined in units of risk per
share or in multiples of R. In terms of multiples
the basis rule of speculation will be formulated
as: keep losses at the level of 1 R as long as
possible and let profits reach many times R.
The expectancy in multiples of R will mean how
much can we win or lose per unit of risk in an
average trade. To calculate expectancy in terms
of multiples of R we must place the results of
our trades in a table with the following
columns:
| Number of lots |
Profit or Loss |
Starting risk |
Multiple of
R |
The Profit or Loss must take into account broker
commissions and slippage. Multiple of R is
calculated by dividing the second column by the
third. Then to calculate expectance it is enough
to add up the values of the fourth column and
divide by the number of trades. This method is
also works with "intuitive" trading.
So, we do have a winning strategy - what next?
We can open a brokerage account and bet all our
capital with the maximal leverage.
Here the most important thing - the money
management begins. To clear the situation here is
a pair of facts. Ralph Vince invented a game,
where bet size was the only moveable parameter.
He chose forty doctors of sciences (i.e. not the
dumbest people at least) as players, none of
which were professional traders or studied
statistics. The doctors played a game where 100
random trades were generated, one by one. Every
one began at $1000, and before every trade one
had to make a single decision - how much (up to
50% of the capital) to bet. 60% of the time the
players won their bet, and 40% of the time they
lost their bet. This game has an expectancy of 20
cents per dollar risked, i.e. in the long run the
player can receive 1 dollar 20 cents per dollar.
The academicals made their 100 bets, enough to
resolve the expectancy. Making the same trades,
they finished the game with different results.
Guess how much of them increased their
starting capital? Two of forty. 95% of doctors
lost money playing a game with a positive
expectation!1
Van Tharp made an even more striking example. In
an Asian Tour for Dow Jones Telerate TAG
(Technical Analysis Group) he gave lectures in 8
cities before 50-100 listeners each time, most of
them professional traders for large companies or
banks that traded shares, bonds or exchange rates
on Forex. In an analogous game over a half of
highly professional traders lost!2
Another personal example - a trader offered a
similar game to a friend employed by Charles
Schwab as a leading analyst. At the first level
the distribution of multiples of R with an
expectancy of 0,45 and 60% profitable trades. To
get to the second level one had to make 50%
profit in 100 trades. The result was "I cannot
get to level 2 in a day!"3.
In 1991 Brinson, Singer and Beebower published a
research of the efficiency of 82 portfolio
managers in a 10-year period, which showed that
91,5% of all profit was generated by asset
distribution3. The asset distribution meant the
division of capital between cash, shares and
bonds. Only 8,5% of profit was due to buying and
selling the right stocks and bonds at the right
time.
Let us play the game described by Vince. If there
was no risk, i.e. we knew the result of each
trade beforehand, it would make sense to bet all
the capital each time. So every player would have
gained $1000 ..(1.2 ^100)=$82,817,974,522.01 .
In reality, if we bet all $1000
on the first trade, we have a 40% risk to lose
all at the first attempt. Even if we win and have
$2000, betting all on the next trade would be
exactly as insane.
Now suppose we bet $200 at a
time. So if five first trades are losing, we
again lose all. The probability of such an event
is small, just over 1%. But are we ready for such
a "small" risk, if we can lose all the money?
Suppose we lose in the first two trades (16%
probability), so we'd lose 40% of the capital.
Beginning from the next trade we must gather 67%
of profit just ot restore the starting capital.
This effect is called "asymmetric leverage"5.
Table 2 shows that loses of over
50% need improbably large profits just to
recover; so if we risk relatively large sums and
lose our chances to end up wit a profit are
negligible.
The result in the doctors' case
is explained not only by oversized bets. A widely
spread pitfall is so-called "gambler's error":
People tend to suppose that after a series of
losses the probability of a profit increases, so
we raise our bets. But in this game the
probability is not affected by previous results
and always remains at 60%.
Suppose that we bet a certain
percent of our capital and record the current
capital after each trade. Repeat the 100-trades
sequence again and again, and after a lot (1000
or so) series we'll be able to estimate the
distribution of results. Evidently, we'll have
different end profits, since the game is random-
based. This is called Monte Carlo modeling.
Let us arrange the 1000 profit
performances from 1000 series from smaller to
larger. Then let us divide this range into 100
parts with equal number of variants in each - so
every such a percentile will have 10 variants of
performance. The first percentile will contain 10
worst results, and its top limit (number 10) will
correspond to what they usually formulate
as: "In 1% of cases the results will be inferior
to… value". Statistically this percentile is
called k-1. The border of the 50 percentile (k-
50) would correspond to: "In 505 of the cases the
result will be inferior to…"
Table 3 displays the outcomes of the 1000 series
with different bet sizes in percents of the
capital.
With 10% bet for each trade the
minimal capital after 100 trades was 181,1$. In
1% of all trades our capital was under $405
(Profit k1). In 50% the trading yielded $4501 and
less (Profit k-50). In 95% of cases the end
capital was below $22411 (Profit k-95), and,
corerespondingly, in 5% of cases the end capital
was above $22411.
Let us review drawdowns (DD in
the table). The drawdown is the difference
between the maximal capital and its subsequent
minimum before the new maximum is reached. With
10% bets in 50% of the cases the DD was over 48%,
in 1% over 78% and the maximal DD was almost 90%
of the capital. With bets over 30% of the capital
we ape practically doomed to ruin. Once again we
remind that this game has a positive expectancy -
at win/loss probability 60% to 40% the win size
relates to loss size as 1 to 1.
Steve Cohen says that: "the
traders' general mistake is taking too large
positions in relation to their portfolios. The,
when the shares move against them, they are hurt
too much to remain in control, they finally
either panic or freeze in shock"1.
These examples described the
importance of bet size in games with an
undetermined outcome. So what is money
management? An Internet search with those
keywords yielded links to services for personal
financial control, advices on handling others'
money, how to control risk, on Turtle Trading,
etc. According to Van Tharp, money management is
NOT:
· a part of system that dictates how much you
will lose in a given trade
· a way to exit a profitable trade
· is not diversification
· is not risk control
· is not avoiding risks
· is not a part of a system that maximizes
performance
· is not a part of the system that tells where to
invest
Money management is a part of a trading system
that tells "how much". How many units of
investitions should be held at a time? How much
risk may be taken?
So, money management is controlling the bet size.
Te most radical definition known to us is given
by Ryan Jones3: money management is limited to
defining what sum from your account should be
risked on the next trade. Pay attention that this
definition does not list as money management
controlling the size of an already open position,
which Van tharp allows.
Table2.
| % loss |
10 |
20 |
30 |
40 |
50 |
60 |
70 |
80 |
90 |
| % profit required to
recover |
11,1 |
25,0 |
42,9 |
66,7 |
100 |
150 |
223,3 |
400 |
900 |
Table3.
| Bet size |
k-50 DD, % |
k-99 DD, % |
Max DD, % |
Worst profit case |
k-1 profit |
k-50 profit |
k-95 profit |
| 1.00 |
5.87 |
13.25 |
18.30 |
900 |
956 |
1.215 |
21.426 |
| 5.00 |
26.86 |
52.32 |
68.17 |
484 |
654 |
2.401 |
5.346 |
| 10.00 |
48.43 |
78.36 |
89.49 |
181 |
405 |
4.501 |
22.411 |
| 15.00 |
64.77 |
92.81 |
97.48 |
71 |
237 |
6.586 |
73.936 |
| 40.00 |
98.81 |
100.00 |
100.00 |
0 |
0 |
783 |
687.933 |
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