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Money Management Systems
Introduction
• Technical signals are useful for entry, but technical
understanding of risk is even more important.
• Remember the law of percentages and how difficult it
is to recover from losses.
• Investing and trading are a matter of determining and
controlling loss of capital.
• Entry is easy; best exit is difficult.
• Money management consists of a number of ways to
measure and to protect from the risk of loss either in
individual trades or in complete systems.
• How many of your trades are losers?
• What’s the typical percentage loss on a losing
trade?
• How many of your trades are winners?
• What’s the typical percentage gain on a
winning trade?
Expected Return
• Let’s say you determine that 40 percent of the
time a trade loses, and it loses 1 percent. Sixty
percent of the time, the trade wins, and
winning trades are up 1.5 percent. With these
numbers, you can calculate your per-trade
expected return, like this:
.40 × –.01 + .60 × .015 = –.004 + .009 = .005
• On average, then, you would expect to earn a half a percent on every
trade you make.
How to calculate the
probability of ruin
• Trader’s advantage
• trades win 60 percent of the time and lose 40
percent of the time. In that case, the trader’s
advantage would be: 60% – 40% = 20%
C is the number of trades in an account.
Valuing volatility
• Expected return gives you an idea of how
much you can get from a trade on average,
but it doesn’t tell you how much that return
might vary from trade to trade
• The wider the range of returns that a strategy
has, the more volatile it is.
• There are several ways to measure volatility.
One common one is standard deviation.
In the derivatives markets, volatility is
measured by a group of numbers
• Delta is a ratio that tells you how much the option or future
changes in price when the underlying security or market
index changes in price. Delta changes over time.
• Gamma is the rate of change on delta. That’s because a
derivative’s delta will be higher when it is close to the
expiration date, for example, then when the expiration date
is further away.
• Vega is the amount that the derivative would change in
price if the underlying security became 1 percent more
volatile.
• Theta is the amount that a derivative’s price declines as it
gets closer to the day of expiration.
Considering opportunity costs
• Opportunity cost is the value you give up
because you choose to do something else. In
trading, each dollar you commit to one trade
is a dollar that you cannot commit to another
trade. Thus, each dollar you trade carries
some opportunity cost, and good traders seek
to minimize this cost.
• The underlying idea is that you should never
place all of your money in a single trade, but
rather put in an amount that is appropriate
given the level of volatility. Otherwise, you risk
losing everything too soon.
Money Management Styles
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Fixed fractional
Gann
Kelly Criterion
Martingale
Monte Carlo simulation
Optimal F
Fixed fractional
• Fixed fractional trading assumes that you want to limit
each trade to a set portion of your total account, often
between 2 and 10 percent. Within that range, you’d trade a
larger percentage of money in less risky trades and at the
smaller end of the scale for more risky trades.
Example- This means that if you have decided to limit each trade to 10 percent of your
account, if you have a $20,000 account, and if the risk of loss is –$3,500, your
trade should be:
Fixed ratio
• The fixed ratio money management system is
used in trading options and futures.
• It was developed by a trader named Ryan Jones,
who wrote a book about it.
• In order to find the optimal number of options or
futures contracts to trade, N:
N is the number of contracts or shares of stock that you should trade, P is your
accumulated profit to date, and the triangle, delta, is the dollar amount that you would
need before you could trade a second contract or another lot of stock.
Gann
• William Gann developed a complicated system
for identifying securities trades. Part of that
was a list of rules for managing money, and
many traders follow that if nothing else.
• The primary rule is: Divide your money into
ten equal parts, and never place more than
one 10-percent portion on a single trade. That
helps control your risk, whether or not you
use Gann.
Kelly Criterion
• emerged from statistical work done at Bell
Laboratories in the 1950s.
• The goal was to figure out the best ways to
manage signal-noise issues in long-distance
telephone communications.
• Very quickly, the mathematicians who worked
on it saw that there were applications to
gambling, and in no time, the formula took
off.
Cont’
Kelly Criterion
• To calculate the ideal percentage of your
portfolio to put at risk, you need to know
what percentage of your trades are expected
to win as well as the return from a winning
trade and the ratio performance of winning
trades to losing trades.
Kelly % = W – [(1 – W) / R]
•
W is the percentage of winning trades, and R is the ratio of the average gain of the
winning trades relative to the average loss of the losing trades.
Example for Kelly ratio
• a system that loses 40 percent of the time
with a loss of 1 percent and that wins 60
percent of the time with a gain of 1.5 percent.
• Kelly formula percentage to trade is:
.60 – [(1-.60)/(.015/.01)]= 33.3 %
- Interpretation : As long as you limit your trades to no more
than 33% of your capital, you should never run out of
money.
Many traders use a “half-Kelly” strategy!!?
Martingale
• The martingale style of money management is common
with serious casino gamblers, and many traders apply it as
well. It’s designed to improve the amount of money you
can earn in a game that has even odds. Most casino odds
favor the house.
• Day trading, on the other hand, is a zero sum game,
especially in the options and futures markets. This means
that for every winner, there is a loser, so the odds of any
one trade being successful Day trading, on the other hand,
is a zero sum game, especially in the options and futures
markets. This means that for every winner, there is a loser,
so the odds of any one trade being successful are even. The
martingale system is designed to work in any market where
the odds are even or in your favor.
Martingale
• Under the martingale strategy, you start with
a set amount per trade, say $2,000. If your
trade succeeds, you trade another $2,000. If
your trade loses, you double your next order
(after you close or limit the first trade) so that
you can win back your loss.
• (You may have heard gamblers talk about
doubling down? Well, this is what they are
doing.)
Martingale
• Under the martingale system, you will always
come out ahead as long as you have an infinite
amount of money to trade. The problem is that
you can run out of money before you have a
trade that works. The market, on the other hand,
has almost infinite resources because of the huge
volume of participants coming and going all over
the world. That means that you have an
enormous disadvantage. As long as you have a
disadvantage, thoughtful money management is
critical.
Monte Carlo simulation
• If you have the programming expertise or buy the right
software, you can run what’s called a Monte Carlo
simulation. In this, you enter in your risk and return
parameters and your account value, let the program run,
and it returns the optimal trade size.
• The system is not perfect — it is only a model that can’t
incorporate every market situation that you’ll face and it
has the fractional trade problem that the other systems do.
But it has one big advantage:
- It can incorporate random changes in the markets in ways
that simpler money management models cannot.
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www.analycorp.com
Optimal F
• The Optimal F system of money management was
devised by Ralph Vince.
• The idea is that you determine the ideal fraction
of your money to allocate per trade based on
past performance.
• This is the maximum percentage to invest any
capital account in the trading system.
• If your Optimal F is 18 percent, then each trade
should be 18 percent of your account — no more,
no less.
Calculation of Optimal f
• The optimal f percentage =
(percentage of wins x (profit factor +1) - 1) /
profit factor
Where:
Percentage of wins is the percentage of winning trades
Profit factor is the ratio of total gains over total losses
Example:
Optimal f = (.097 x (10.988 + 1) - 1) /10.988 = 1.46%
F is a factor based on the basis of historical data, and the risk is the
biggest percentage loss that you experienced in the past.
Example : Optimal F
• Using these numbers and the current price,
you can find the contracts or shares you need
to buy. If your account has $25,000, your
biggest loss was 40 percent, your F is
determined to be 30 percent, and you’re
looking at a stock trading at $25 per share,
then you should buy 750 shares.
Notes on Optimal F
• Some traders only use Optimal F in certain
market conditions, in part because the history
changes each time a trade is made, and that
history doesn’t always lead to usable
numbers.