As derivatives educator Rick Thachuk explains, it is
essential to approach them systematically – and to
check your system as you go along.
Binary options are a novel type of investment, so it follows
that a successful trading system will differ from those for
more traditional assets. Studying the mathematics behind the
instruments can help move the trader along the learning curve
and reveal useful insights into building and evaluating a
trading system.
Binary options on financial assets are short term
investments that return one of two possible payouts at
expiration, depending upon a condition being met in the price
of the underlying asset.
A common type is the above/below option, which locks in the
current market price of the asset as the strike price. If, at
option expiration, the asset’s price is above the
strike price in the case of a call, or below the strike price
in the case of a put, the option finishes inthemoney and the
option buyer receives the maximum payout. If not, a smaller
payout is received.
Retail trading of binary options on online platforms has
been growing rapidly in the last few years, especially among
those with little prior investment experience. Chief among the
attractions are the product’s intuitive
simplicity, the fixed risk of every trade, and the ease of
entry from both an administrative and investment point of
view.
The electronic platforms have also become more
userfriendly, with improved graphics, content in various
languages, and an expanded array of tradable assets including
Asian, European and US stocks.
For example, if the current level of the FTSE 100 Index is
6051.718, an investor can go to a website, enter the desired
investment amount, say $100, and click "Call" or "Put" to
obtain an option that expires in, say, 38 minutes. The screen
says the payout will be $185 (including the invested $100) if
the investor bets right, or nothing if wrong.
A simpler trade system
As with any asset, traders using binary options should be
systematic. Following a trading system provides objective
criteria for when to initiate a trade, either long or short,
and when to close one, either at a profit or a loss.
The unique features of retail binary options make coming up
with a trading system simpler. In most cases, binary options
can only be purchased, not sold – and the payouts are
fixed. Also, a binary option is automatically closed at expiry
and usually cannot be closed before.
Consequently, a trading system need only dictate which
particular options to trade, when to buy a call or put, and how
much to risk on the position.
For the most part, we’ll consider just the
above/below option, though many of the results can be extended
to other types of binary options.
Since retail binary options have only two possible outcomes
and require no fee or commission, their performance can be
effectively modelled mathematically.
Let’s say that you have just opened a trading
account and deposited some cash. We’ll call the
dollar value of your account VAL. You decide to invest the same
amount on every trade – we’ll call that
amount INV. In practice, this may be anywhere from $30 to
$1,000.
If the binary option finishes inthemoney, meaning that you
win, your payout is P_{W} – the loss
payout is called P_{L}. So, for example, if a binary
option has a payout matrix of 75% plus stake for a win, 10% of
stake for a loss, then P_{W} = 1.75 and
P_{L} =0.1. We’ll assume that these
payouts are fixed across all option trades that are made.
The value of your account, VAL_{t,} after t
option trades is given by:
VAL_{t } = VAL_{t1 } +
[þ_{t} P_{W} + (1 –
þ_{t}) P_{L} – 1] INV
Where VAL_{t=0 } = starting balance.
The stochastic variable, þ, can have only one of two
values: "1" meaning that the binary option finishes
inthemoney (you win), and "0" meaning that the binary option
finishes outofthemoney (you lose).
The equation above is dynamic, since the value of your
account at any time depends on the success or failure of prior
trades. Not surprisingly, there are a great number of ways that
the value of your account can evolve, even for the same ratio
of winning and losing trades, since they could occur in
different orders.
The success ratio of a trading system, SR, after t binary
option trades is simply:
SR_{t} = (
S þ_{t})/t
So, for example, if 25 out of 40 trades are winners, the
success ratio of the system is 62.5%.
Armed with our mathematical model, let’s
explore the dynamics of binary option trading, beginning with
pure guessing.
The pure guess scenario
A pure guess means that the trading system provides no value
in improving the success ratio beyond the expected value of
þ, E(þ). The expected value of þ is
determined by the type of binary option and the stochastic
nature of the asset price underlying it.
With an above/below option, E(þ) should be about 0.5
or 50%, since the percentage change of an asset’s
price is usually distributed symmetrically around zero. In
other words, an above/below binary option based on pure
guessing is equally likely to win or lose.
A barrier binary option – where the price of the
asset must rise or fall to some designated level for the option
to finish inthemoney – has an expected value of
þ that is much less than 50%, because it is much easier
to make a mistake.
An above/below binary option trading system that amounts to
guessing will not usually be profitable in the long run, since
the payouts are always structured so that the penalty for
losing is bigger than the reward for winning.
Moreover, for a given payout matrix, the speed with which
you burn through your starting balance is faster, the more you
risk on each trade – so there is a good reason to make
small bets.
Guessing is a losing game
The graph shows outcomes for a guessing strategy on
above/below binary options with a payout matrix of a
75% gain for a win, and return of 10% of stake for a
loss. Fortyfour trades, each of $50, are made, half of
which win. The expected path of the starting balance is
shown by the black, downwardsloping line, which
declines from $1,000 to $835. The blue lines show two
representative paths that the account balance might
actually follow, each with the same number of winning
and losing trades but in a different order.

In the example of 44 trades in the graph, there are over 1.7tr
possible paths that the account balance can follow, depending
on the order in which wins and losses occur. While all will
fluctuate around the theoretical account value, sometimes the
account balance can rise above the starting balance –
if the investor is lucky early on.
The dark blue line, for example, represents an account that
was up nearly 10% after nine trades, even though the success
ratio of the trade system is not high enough to sustain this
performance. If the trader erroneously believed that the trade
system was better than it actually was, he or she might have
been tempted to make bigger investments, only to be
disappointed by subsequent trades.
This suggests that traders need to make a high enough number
of trades to measure the success ratio of a trading system
correctly. Four or five trades, whether winners or losers, are
not enough to make this determination.
In practice, no trader would use a system that is expected
to provide no greater chance of success than a pure guess.
Consequently, we’ll turn our attention to a more
important consideration, the breakeven scenario.
The breakeven scenario
A binary options trading system will break even if the
accumulated payouts received after t trades are equal to the
total investment made. Formally, this means the breakeven
success ratio, SR_{BE}, can be calculated:
SR_{BE} = (
S þ_{t})/t = (1 –
P_{L})/(P_{W} –
P_{L})
Naturally, the success ratio required to break even depends
on the payout matrix offered. The table below calculates
success ratios for various payouts that are typically available
on trading websites for above/below binary options. For
example, an investor using a 75/10 payout matrix would need a
success ratio of 0.5454 to break even.
Binary option
payout


Breakeven

Win

Lose


success
ratios

85%

0%


54.1%

71%

15%


54.5%

75%

10%


54.5%

69%

15%


55.2%

81%

0%


55.2%

70%

10%


56.3%

73%

5%


56.5%

69%

10%


56.6%

65%

15%


56.7%

72%

5%


56.9%

68%

10%


57.0%

71%

5%


57.2%





Even though payouts differ markedly among options providers,
their breakeven success ratios tend to lie close together.
This is, in part, a consequence of healthy competition among
the providers.
When success ratios differ, it usually reflects the
liquidity of the underlying asset. The most attractive payouts
are typically available on forex, since that is the most liquid
market, but the payouts of any particular market may change
during the day as liquidity improves or diminishes.
As is evident from the table, the success ratios required to
break even are only marginally better than the pure guess hit
rate of 50%. For a payout matrix of 75/10, for example, only 12
out of 22 trades need be winners to reach breakeven –
just one more winner than what would be expected by
guessing.
This reinforces the earlier suggestion that evaluating a
trading system properly requires many transactions. If only one
out of 22 trades can mean the difference between a system that
breaks even and one that provides essentially no value, a great
many trades are needed to test this strategy.
It is also clear that traders should focus on options with
the lowest breakeven success ratios, being careful to remember
that payouts can vary during the day. Not only are these
contracts the most likely to break even; they should also
accumulate profits more quickly if they succeed (see
graph).
Option payout and profit growth
The graph shows the theoretical account balance
growth for a trading system that achieves a 60% success
ratio. It is based on 44 above/below binary options
trades of $50. The light blue line indicates what would
be achieved using a payout matrix of 85/0, which has
the lowest breakeven success ratio. The other two have
higher breakeven success ratios.

Implications for trading system
Some further conclusions can be drawn about how to design a
successful binary options system.
Winning trades Because of the payout
structures available, any system must generate more winning
than losing trades to be viable. This is not true of trading
systems for other assets such as stocks or commodities, where a
minority of winning trades, if they win big, can more than
offset the losses.
But the success ratio does not have to be huge. In most
cases, a system need only generate a marginally higher success
ratio than 50% to break even. Success ratios higher than
breakeven translate directly into improved profit
performance.
High volume Evaluating the usefulness of a
system requires making many trades. The more trades, the more
precisely the success ratio can be calculated, especially to
determine whether it is breaking even. This need not be costly.
As shown in the graph, a trade system that in practice provides
no better success than a pure guess would be expected to cost
just $165 after 44 trades (starting balance of $1,000 less the
ending balance of $835 with no commissions). Moreover, with the
feedback from 44 actual trades, the trader may be in a good
position to modify the system to improve performance.
Low investment Because evaluating a system
requires many trades, the amount invested on each option
relative to the starting balance must be low enough to mitigate
the danger of ruin. Even with a success ratio above breakeven,
it is still possible to suffer a string of losing trades. The
system needs to be able to tolerate this without shutting down
because of insufficient funds. Calculating the exact amount to
invest depends on the success ratio, and this is only known
after the system is run. As a starting point, the amount to
invest can be set between 5% and 10%, with the lower value
being more advisable.
Reversibility Unlike trading systems for most
other assets, an above/below binary option trade system is
reversible and this can be a useful feature. Consider a trade
system that has a very low success ratio and loses money. It
could be worth trying a simple reversal – buy a call
every time the system tells you to buy a put, and vice versa.
Reversibility is impractical for discretionary systems and is a
good reason to develop an objective system, free of personal
influence and emotion.
Rick Thachuk is president of the WLF Futures, Options and
Forex Education Network, a group of US websites that exists to
educate investors about trading opportunities. WLF does not
make money by offering binary options trading services, though
it does receive