The Nature of risk and opportunity

To help us in the task of exploring and finding a sound trading system, we’ll examine the features of risk and opportunity.

In the article Are Forex Exchanges Casinos in Disguise, we saw that the nature of the trading environment is mostly random. Traders have the illusion of control because they choose their trades (the lotto bias), but the real truth is randomness or luck is at least as essential for the outcome of their trades as their skills.

We have seen that, even when the trader has an edge, his bias for the law of the small numbers makes him think the system is not sound.

Below we show five possible trading histories of a perfectly good trading system, which presents a 5% edge over a coin toss, trading in an initial account of 10,000 dollars using a constant 300-dollar risk.

Fig 1 – 5 Different Trading paths of a System with 5% edge

Everybody would love a trading system like this! Right? But let’s put a magnifying glass over the first 100 trades.

Fig 2 – First 40 trades if the Featured System

By looking at Fig 2, we can see some shocking facts. Even when all these trading histories were from the same system with 5% edge, we observe that some paths experience large drawdowns, and all but one of the curves show almost no profits after 100 trades.

The blue equity curve had a nice run up to higher than 40% gain in trade Nr 62, and then it almost completely lost all that profit after 38 more trades. We can see also, that one of the possible equity curves moves underwater virtually all the 100 first trades.

If we look attentively at the different paths on fig 1, we see that, although there is a continuous equity growth, the drawdowns continue appearing. This is not to show that many traders would reject this system before the end of trade Nr 100, or even, before trade Nr 40.

This demonstration is to show that the sensation of controlling anything is an illusion. Also, the idea that somebody can forecast the markets is also illusory. We can only evaluate scenarios and create an opportunity by assessing the potential rewards and its risk.

If you still do not believe in the randomness of the markets, I’ve taken the 1-minute close of the EURUSD for April 2019 and plotted five different equity curves (Using Monte Carlo Resampling), including a real buy and hold curve assuming one mini-lot bet. I dare you to guess which is the buy and hold curve one and which the ones cooked by the resampling process.

Fig 3 – EURUSD 1-minute Equity Curve together with Five Similar Resampled Curves

The preceding discussion is to state one clear fact: It is very hard to design a sound trading system depicting per cent winners higher than 50%. Usually, high-per cent winners are achieved at the expense of over-optimisation, low reward-to-risk ratios, and, worse, using dangerous martingale methods, one of the main causes of account “deaths” in Forex.

People in Forex expend their time trying to forecast the markets when this is futile while ignoring one key trading element which they can control: The reward and its risk.

In the figure below, you will see 20 equity curves of a game with 10% winners and 90% losers. I want you to look at an extreme case to realise that per cent winners is not the only variable. We have to take into account the reward-to-risk ratio (in this case it is a 15:1 reward ratio, but a 10% winner system begins being profitable starting from an R/r =11.

Fig 4 – A Game with 10% winners and an R/r = 15

Do you get the implication of these curves above?

It means that if you’re able to build a system with a mean reward-to-risk ratio of 15 you can trade without forecasting anything. getting just 10% of winners cannot be called “forecasting”! Of course, there is no need to go to this extreme. What I mean is, we can build systems focused on the Reward to risk ratio and let the other parameters as “improvements! on the main parameter.

Let’s see the equity curves an achievable system with less than 40% of winners and a reward-to-risk ratio of 2, which bets a constant $100 on every trade:

Fig 4 – A Game with 39% winners and an R/r = 2

Risk and Reward

We’ll call risk the amount of money we agree to lose to get a profit. From now on, let’s call this cost R. We will evaluate the opportunity as a multiple n of R.

The ideas we can take from the above exercises are:

If we spot nR opportunit¡es we can fail n-1 times and the strategy is still profitable.

opportunit¡es we can fail times and the strategy is still profitable. A high n is the best protection against a drop in the %gainers of our system.

is the best protection against a drop in the %gainers of our system. Therefore a high n makes a trading system more robust

makes a trading system more robust There is no need to try forecasting price changes to make money

If there is no need to predict, since real money comes from high n through well-chosen entries, exits and stops, not per cent winners.

through well-chosen entries, exits and stops, not per cent winners. Opportunities with high n and decent winning chances is the main goal when designing a trading system.

We should look at the reward ratio nR as a kind of insurance against a potential drop in the per cent of winners, and make sure our systems inherit that kind of safe protection.

Finally, we must avoid nxR’s below 1, since it forces our system to be right more than 50% of the time, and, as we have seen above, it is very difficult to attain.

Now, I feel we all know far better what we should seek as traders: Good opportunities with reduced cost and a reasonable likelihood to happen.

Final note: The real buy-and-hold EURUSD is the blue curve.

Images were drawn using my personally developed Python code.