### Not Quite Being Lucky

Often, there is an element of luck when it comes to trading. Even if your analysis is spot on, the timing is very difficult. A famous example from the real world can be found in Michael Burry, the storied US investor who correctly predicted the 2008 housing bubble from Michael Lewis’ bestseller “The Big Short”. He had to face down a revolt among his investors that nearly chased him out of the very trades that would land him in the history books. Burry’s financial backers balked at a steady stream of expensive payments made to keep his trades in play as the markets dithered.

There is a way for traders to compensate for luck – risk management. Overlooking this essential component of the strategy is how an incredibly lucky trader – someone who can frequently call trades correctly – may still lose money in the aggregate. Conversely, using risk management effectively is how a poor win rate can still translate into profitability.

How is it that a lucky trader can lose money overall? Consider a person who profited on 8 trades out of 10, making 10 dollars per trade. On the two remaining trades, however, 50 dollars were lost each time. On net, this will leave the trader 20 dollars poorer. In this special report, we will show how an unlucky trader can still be profitable, and what you can do to optimize risk management.

### The First Random Walk – Understanding the Sequence

A random walk simulation was used to mimic someone trading 100 times in a row. Each random walk has a few parameters: starting account balance, the maximum risk a person is willing to take per trade as a percentage of the account balance (which stays the same as the trader makes or losses money), the risk-reward ratio (how much the trader wants to make relative to how much is put at risk), and finally the trader’s luck (the chance that a given trade in the sequence is profitable).

The first random walk is shown on the chart below. It simulates a trader that starts with a $2k account, risks 1% per trade, has a risk/reward (RR) ratio of 1:1 (meaning that the first trade risks losing $20 to make a profit of $20), and has 50% luck. Being lucky about half of the time had a predictable outcome. The ending balance ($1990) was nearly identical to where it started ($2000) after one hundred trades.

### Study Limitations

It should be noted that this is a study computed with code and has no margin of error or human emotion factored into it. This means that no matter what, it assumes the trader being modeled always sticks to the game plan perfectly. It also assumes that trades can be seamlessly closed – with a profit or loss – at the designated settings with absolute precision. In the real world, stops may not always be executed at the specified price, resulting in some slippage. These simulations also assume 100 trades were taken, which will not match everyone’s level of activity. With that in mind, this is more of a demonstration of the importance of risk management rather than a one-size-fits-all trading system.

### The Second Random Walk – Reducing Luck

What happens when we take the same sequence but make our hypothetical trader unlucky, leaving everything else unchanged? With 25% luck, disaster strikes. Someone with a risk/reward ratio of just 1:1 would see their account balance cut almost in half after 100 trades ($1137). As we will find at the end of this journey, however, an increase in the risk/reward ratio can compensate for worse luck.

### Simulating Hundreds of Thousands of Trades to Find Optimal Risk/Reward Ratios

To find ideal risk/reward ratios for given levels of luck, these random walks were run many times to find statistically meaningful interpretations. In this study, one cycle constituted 100 trades conducted 100 times. That is a total of 10,000 trades per cycle! With each cycle, the risk/reward ratio automatically rose by 0.05, starting at 1. The program is coded to keep doing this until 100% of the trades are finished at or above the starting account balance.

So, what does this look like for someone lucky about half of the time? Well, in the image below, we can see that the optimal risk-reward ratio is on average 1.6 (meaning that with a starting balance of $2k the strategy aims to make $32 in profit while risking $20 on the first trade). The latter two will adjust alongside the evolving account balance to maintain a 1.6 RR ratio, making sure the risk remains at 1% per trade.

The code ended up increasing the risk/reward ratio 6 times. Including the starting point, the cycle ran 7 times. In other words, 70k trades were conducted to find the optimal RR ratio. To further optimize this study, another 10 rounds of random sequences were used. This means that roughly 770,000 trades were placed to find the optimal risk/reward ratio for 50% luck! It is not exactly 770,000 because sometimes the RR ratio was above/under 1.6.

When someone is lucky half of the time, and they use a 1.6 risk-reward ratio, we can expect an average ending balance of $2734 (36.7% return, which remains constant no matter what the starting account balance size is) after 100 trades. In the lower half of the image, there is a normal distribution of outcomes. There were a couple of outliers, with an account topping $4.5k. A few others were above $3.5k.

### The Optimal Risk/Reward Ratio Curve

What about other levels of luck? In this study, I used the following: 50%, 40%, 33%, 25%, 20% and 10%. Optimal RR ratios are displayed in the chart below for a given luck level. As expected, lower levels of luck required higher risk/reward ratios to compensate. When you are lucky 40% of the time, an ideal RR ratio for a sequence of 100 trades seems to be 2.45.

At 2.45, a total of 30 cycles were simulated for a given random sequence. Just like before, an additional 10 were performed to help optimize this study. Combining all these sequences, roughly 3,300,000 trades were placed to find the optimal risk/reward ratio for 40% luck.

Someone lucky just 10% of the time can still make a profit. However, this would demand the daunting task of maintaining a 21.47 risk/reward ratio.

### Is Trading Success Based on Luck?

Now, let us revisit the earlier scenario of a trader that is lucky just 25% of the time. Using a 1:1 risk-reward ratio, they lost almost half of their account. Using the optimal risk/reward ratio of 5.3 suggested in our analysis, their ending balance becomes $2844, a 42.2% return. Do traders have to be lucky to be profitable? Absolutely not. Success comes down to risk management.

* All random walks simulated with Python

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