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Risk, Reward, and Profitability

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The Nature of Risk and Opportunity

Trading literature is filled with vast amounts of information about market knowledge: fundamentals, Central Banks, events, economic developments and technical analysis. This information is believed necessary to provide the trader with the right information to improve their trading decisions.

On the other hand, the trader believes that success is linked to that knowledge and that a trade is good because the right piece of knowledge has been used, and a bad trade was wrong because the trader made a mistake or didn’t accurately analyse the trading set-up.

The focus in this kind of information leads most traders to think that entries are the most significant aspect of the trading profession, and they use most of their time to get “correct” entries. The other consequence is that novice traders prefer systems with high percent winners over other systems, without more in-depth analysis about other aspects.

The reality is that the market is characterized by its randomness; and that trading, as opposed to gambling, is not a closed game. Trading is open in its entry, length, and exit, which gives room for uncountable ways to define its rules. Therefore, the trader’s final equity is a combination of the probability of a positive outcome – frequency of success- and the outcome’s pay-off, or magnitude.

This latest variable, the reward-to-risk ratio of a system, technically called “the pay-off” but commonly called risk-reward ratio, is only marginally discussed in many trading books, but it deserves a closer in-depth study because it’s critical for the ultimate profitability of any trading system.

To help you see what I mean, Figure 1 shows a game with 10% percent winners that is highly profitable, because it holds a 20:1 risk-reward ratio.

A losing game is also possible to achieve with 90% winners:

So, as we see, just the percentage winners tell us nothing about a trading strategy. We need to specify both parameters to assess the ultimate behaviour of a system.

The equation of profitability

Let’s call Rr the mean risk-reward of a system.  If we call W the average winning trade and L the average losing trade then Rr is computed as follows:

Rr = W/L

If we call minimum P the percent winners needed to achieve profitability, then the equation that defines if a system is profitable in relation to a determined reward-risk ratio Rr is:

P > 1 / (1 +Rr) (1)

Starting from equation (1) we can also get the equation that defines the reward-risk needed to achieve profitability if we define percent winners P:

Rr > (1-P) / P (2)

If we use one of these formulas on a spreadsheet we will get a table like this one:

When we look at this table, we can see that, if the reward is 0.5, a trader would need two out of three winning trades just to break-even, while they would require only one winner every three trades in the case of a 2:1 payoff, and just one winner every four trades if the mean reward is three times its risk.

The lessons learned from analysing these equations are:

Let’s call nxR the opportunity of a trade, where R is the risk and n is the multiplier of R that defines the opportunity. Then we can observe that:

  1. If you spot an nxR opportunity, you could fail, on average, n-1 times and still be profitable.
  2. A higher nxR protects your account against a drop in the percent of gainers
  3. You don’t need to predict the price to make money because you can be profitable with 10% winners or less.
  4. As a corollary to 3, the real money comes from exits, not entries.
  5. The search for higher R-multiples with decent winning chances is the primary goal when designing a trading system.

A high Rr ratio is a kind of protection against a potential decline in the percentage of winning trades. Therefore, we should make sure our strategies acquire this kind of protection. Finally, we must avoid Rr’s under 1.0, since it requires higher than 50% winners, and that’s not easy to attain when we combine the usual entries with stop-loss protection.

One key idea by Dr. Van K. Tharp is the concept of the low-risk idea. As in business, in trading, a low-risk idea is a good opportunity with moderate cost and high reward, with a reasonable probability to succeed. By using this concept, we get rid of one of the main troubles of a trader: the belief that we need to predict the market to be successful.

As we stated in point 3 of lessons learned: we don’t need to predict. You’ll be perfectly well served with 20% winners if your risk reward is high enough. We just need to use our time to find low-risk opportunities with the proper risk-reward.

We can find a low-risk opportunity, just by price location as in figure 3. Here we employ of a triple bottom, inferred by three dojis, as a fair chance of a possible price turn, and we define our entry above the high of the latest doji, to let the market confirm our trade.  Rr is 3.71 from entry to target, so we need just one out of four similar opportunities for our strategy to be profitable.

Finally, we should use Rr as a way to filter out the trades of a system that don’t meet our criteria of what a low-risk trade is.

If, for instance, you’re using a moving average crossover as your trading strategy, by just filtering out the low profitable trades you will stop trading when price enters choppy channels.

Conclusions:

  • Risk-reward is the parameter that allows the assessment of the opportunity value of a trade.
  • The higher the opportunity, the less the frequency of winners we need to be profitable.
  • Therefore, we can assess an opportunity just by its intrinsic value, regardless of other factors.
  • That frees us from seeking accurate entries and set the focus on trade setup and follow-up.
  • We just need to use the familiar market concepts, for instance, support and resistance, to design a robust trading system, by filtering out all trades that don’t comply with the risk-reward figure.
  • Trading becomes the search for low-risk opportunities, instead of trying to forecast the market.

Appendix:

Example of Rr Calculation:

As we observe in Fig 3, the risk is defined by the distance between the entry price and the stop loss level, and the reward is the distance between the projected target level defined by the distance from the Take profit level to the entry price:

Risk = Entry price– Stop loss

Reward = Take profit – Entry price.

Rr = Reward / Risk

In this case,

Entry price  = 1.19355

Stop loss = 1.19259

Take profit = 1.19712

Therefore,

Risk = 1.19355 -1.19259 = 0.00096

Reward = 1.19712 – 1.19355 = 0.00357

Rr = 0.00357 / 0.00096

Rr = 3.7187

©Forex.Academy

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