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 in-the-money 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 user-friendly, 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 in-the-money, 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_t-1 + <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 in-the-money (you win), and “0” meaning that the binary option finishes out-of-the-money (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 in-the-money – 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. Forty-four trades, each of $50, are made, half of which win. The expected path of the starting balance is shown by the black, downward-sloping 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 break-even scenario.

The break-even 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 break-even 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.

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 break-even – 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 break-even 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 break-even success ratio. The other two have higher break-even 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 break-even 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 break-even, 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