"TAP não sobrevive se se mantiver pública", garante Pinto Luz

[cannot]

Fiz uma procura no google e encontrei o artigo aqui:
http://www.futuresmag.com/Issues/2009/A ... -ruin.aspx

O site é futuresmag.com e como eles referem no artigo as equações são de uns tais D.R. Cox and H.D. Miller, e publicadas no livro “The Theory of Stochastic Processes.”

Podes encontrar (em pré-visualização) o livro no Google books em: http://www.google.com/books?hl=pt-PT&lr ... q=&f=false

Mas como todos os livros que eles têm, algumas páginas não podes ver.

Abraço

ps - de qualquer forma para perceber o livro (~350páginas) terás que ter um forte background em estatística (pelo índice parece-me que ao nível de mestrado, pelo menos numa licenciatura em engenharia). E não é um livro directamente direccionado para aplicar à bolsa.

[salvadorveiga]

vset... qual a fonte disto ?

Diz ai o nome do book ou donde isso veio porque eu quero... um abraço

[cannot]

Olá!


vset, por acaso não tens por aí um link para uma versão mais "simpática"? tipo .pdf...

Abraço

[vset]

Monsieur Cent,

averigua lá então a veracidade das fórmulas e apita por favor.

Abraço!

[Cem pt]

Muito interessante, amigo VR, não conhecia esse estudo mas vou certamente aprofundar os conhecimentos neste ramo.

Há algumas passagens que tenho algumas reticências em aceitar de barato mas no geral trata-se de um paper que merece bastante reflexão, em especial nas sempre críticas matérias de sabermos quantificar o risco que estamos a correr nas nossas carteiras!

Abraço e thanks,
Cem

[vset]

Where:

R = risk of losing one standard
deviation
e = 2.71828, the base of the
natural logarithm
a = average, or mean return,
in this case 6%, or 0.06. a must
be a positive number, or else R is
defined as 100%.
d = standard deviation of returns,
in this case 13%, or 0.13. d must be
a positive number between 0 and 1.
Plugging in the numbers, we find that

R = e^(-(2*0.06)/0.13)
R = e^-0.923
R = 0.397

There is a 39.7% chance of losing
13% of the account from any point on
the equity curve. This trader will spend
39.7% of his time at least 13% below a
prior maximum equity high.
Now suppose this same trader wants to
calculate the probability of losing half of
his account. From Cox and Miller, the
equation is:

R = e^(-(2*a*z)/(d*d))

Where:

R = risk of losing z fraction
of the account
e = 2.71828, the base of the
natural logarithm
z = The fraction of the account that
might be lost, in this case 50%,
or 0.50
a = average, or mean return,
in this case 6%, or 0.06
d = standard deviation of returns,
in this case 13%, or 0.13
Plugging in the numbers, we find that
R = e^(-(2*0.06*0.50)/(0.13*0.13))
R = e^-3.550
R = 0.029

There is a 2.9% chance of losing 50%
of the account from any point on the
equity curve. This trader will spend 2.9%
of his time at least 50% below a prior
maximum equity high.
This equation assumes that the trader
cannot reduce the trade size as the
account value falls. The monthly standard
deviation remains at 13% of the
original account size and the average
return remains at 6% of the original
account size.
If the trader uses fixed fractional position
sizing to take smaller positions as the
account value falls, then he will reduce
his bets as the account goes down (see
“Constant vs. fixed fractional,” page
41). For example, a fixed fractional
trader might risk 2% of the current
account value on each losing trade.
This will reduce the risk of losing half of
the account because the losses will get
smaller as the account gets smaller. More
losses will be required to lose some large
fraction of the account.
We can modify the Cox and Miller
equation for fixed fractional position sizing.
In their equation, the risk of losing
one standard deviation is e^(-(2*a)/d)
and the number of times d must be lost
to lose z is given by z/d. In the equation
below, the risk of losing one standard
deviation remains e^(-(2*a)/d) and the
number of times d must be lost to lose z
is given by ln(1-z)/ln(1-d).
For fixed fractional position size, the
risk of ruin equation is:

R = e^((-2*a/d)*(ln(1-z)/ln(1-d)))

Where:
R = risk of losing z fraction
of the account
e = 2.71828, the base of the
natural logarithm
ln(1-z) is the natural logarithm of (1-z)
z = The fraction of the account that
might be lost, in this case 50%,
or 0.5
a = average, or mean return,
in this case 6%, or 0.06
d = standard deviation of returns,
in this case 13%, or 0.13
Plugging in the numbers, we find that:

R = e^(-(2*0.06)/0.13*(ln(1-0.5)/
(ln(1-0.13)))
R = e^(-0.923*(-0.693/-0.139))
R = e^-4.594
R = 0.010

[vset]

In 2003, this author lost 35% of his
account trading commodities with
a profitable long-term trend-following
system. The resulting emotion?
Fear. I dreaded how much worse
it might get and thought my system
could be broken. I wondered how likely
it was that I would lose half of my
account and wanted to calculate the
odds of further losses.
The first risk of ruin equation below
was derived with the help of a Monte
Carlo simulation. Then Colorado
State University professors Dr. Sanjay
Ramchander and Dr. Hong Miao recommended
a more complete formula
published by D.R. Cox and H.D. Miller
in “The Theory of Stochastic Processes.”
Their formula to calculate risk of ruin
was written for insurance companies, but
it also applies to traders.
An insurance company is ruined when
it loses its capital. A gambler is ruined
when he loses all his money. A hedge
fund may have to stop trading when it
loses a specific percentage of its starting
capital. Even with a good system, a trader
may decide to stop trading after losing
some large fraction of his account.
Few traders know how to calculate risk
of ruin. Many traders talk about maximum
drawdown, as if there is a maximum
limit. Obviously, once the “maximum”
drawdown has happened, further losses
are still possible. The maximum drawdown
is merely the point at which the
bad luck ended in some historical data set.
The maximum observed drawdown will
continue to increase the longer the game
is played.
Suppose an experimenter flips a coin
1,000 times and observes a string of bad
luck consisting of 10 tails in a row. Is this
the maximum possible number of consecutive
tails? No.
If the experiment continues for one
million flips, a string of 20 consecutive
tails is likely. There is no fixed
limit to the maximum number of consecutive
tails, or consecutive losses, or
maximum drawdown.
The maximum drawdown will usually
be much larger than the worst string
of consecutive losses. After a string of
losses is interrupted by a win, losses may
resume. Bear markets have rallies and
then sink to new lows. In a similar vein,
the path to ruin is rarely a straight line.
The following equations account for all
possible paths to ruin.

INSIDE THE NUMBERS

Most professional traders and hedge
fund investors know the monthly mean
and standard deviation of their returns.
These numbers are needed as inputs
to the risk of ruin equation. The mean
and standard deviation may be measured
per month, per day, per week,
per year or per trade. It is important to
measure both the mean and standard
deviation over the same time period.
Do not mix the annual mean return
with the standard deviation per trade.
Markets usually have fat-tailed distributions.
This means that extreme
events happen more often than you’d
see in a random data set. The fat tail is
often caused by variation in the standard
deviation. The risk of ruin formulae are
sensitive to standard deviation. It is dangerous
to underestimate standard deviation
because that will underestimate risk
of ruin. An increase in standard deviation
makes large losses more likely.
Monthly numbers work well in this
formula. Few traders have enough years
of data to use annual numbers. Typical
trading systems make several trades in
a month, so the monthly returns often
have a distribution reasonably close to a
normal bell curve.
For example, suppose a trader has a
mean return of 6% per month, with a
standard deviation of 13% (see “Risk of
loss,” above). The risk of losing one standard
deviation, or 13% of the account, is
given by this formula:

R = e^(-2*a/d)


(continua)