Many trading issues come down to risk management. In most trading styles, the trader's job is essentially to manage trading risk, focusing on exiting losing trades at the right point, and letting the market handle itself. Risk management is crucial because a few excess losses can be offset from many winning trades; it doesn't take many mistakes to completely deplete a trading advantage. We start with practical application tools for risk management and position sizing that traders on all time frames will find useful. Many large losses come from improper position sizing, and many traders do not understand the impact of trade size on the bottom line. Risk Measures, and finally a look at some less common risks that self-directed traders often overlook. Risk and Position Sizing From a practical perspective, there are three main questions to answer:
1. Where to place a stop loss order, regardless of profit or loss?
2. How to adjust stop loss and take profit over time?
3. How many shares, contracts or other units should we trade?
First, understand the risks
There are no absolutes in trading. Most trading rules are flexible, and many master traders have a rule that basically says, "Know when to break the other rules." However, there is one rule that cannot be broken - and it may be the most important rule in the world: Know where to exit a trade if you are wrong, before you enter it. The exact location of the stop loss chosen will depend on the pattern, the trader, the profit target, the time frame, the specific market, and perhaps many other conditions, but the most important thing is that the level is defined at the time of entry.
When you consider stop loss placement, it is important to ensure that your stop is placed at a meaningful location outside of the market noise range; rarely should a stop be placed too close to the market. A rough guideline is given by the average range of a single bar within the timeframe you are trading. If you place your initial stop loss closer than the range of a single average bar, you may be working within the noise level and significantly diminishing any edge you may have.
%R and Position Sizing
Once this initial level of price movement risk is known, the question of trade sizing must also be addressed. There is a vast literature covering theoretical ideas about asset allocation and position sizing for the individual trader. We will avoid these discussions for the most part and simply limit the discussion here to two points: Practical guidelines and examples that I have used successfully in my own trading Why consistent sizing is important. Many traders are familiar with the Kelly Criterion, which gives the optimal amount to bet in a game of chance, assuming some very important simplifying assumptions hold. If these assumptions are met, the Kelly formula will outperform all other methods.
However (and this is very important for real trading), if Kelly is applied to a trade where the simplifying assumptions do not hold, then all bets are off. For reference, the classic Kelly Criterion gives f, the percentage of the account risk per trade, via the formula:
f=(bp-q)/b=(p(b+1)-1)/b
in
f* is the proportion of existing funds that should be used for the next bet;
b is the odds available for betting (excluding principal);
p is the winning rate;
q is the failure rate, i.e. 1 - p;
Furthermore, and more importantly, the theoretical assumptions behind these models rarely work in short-term trading. Most optimized methods assume that each trade is independent of other trades, but many trading systems will experience a string of losses or wins in the market. Additionally, many of these optimization methods require inputs like maximum trade losses, which must be based on historical data, all of which depend on the assumption that future results will be similar to the past. If you experience larger losses in the future, and you are using an aggressive, optimized position sizing methodology, you may be in trouble. If you plan to use these methods in real trading, make sure you understand the consequences of violating any of these assumptions.
Fixed ratio method
The fixed ratio position adjustment method is simple and robust. It is not an optimization method, nor is it intended to be. Specific matters:
Define the risk of losing the trade.
Limit trading risk of losses greater than expected.
Limit the risk of a series of losing trades.
Limit the total risk of a group of highly correlated positions.
Limit the total amount of equity at risk at any one time.
Allows for easy scaling as account balances change.
Note that the focus of this process is to limit losses, not to maximize gains. This is the key to staying in the market for a long time. Professional traders know that if you fail to manage your losses, resulting in major drawdowns or even bankruptcy, your career will be over.
The rule is simple: Risk a consistent percentage on every trade. I consider anything below 1% to be very conservative, and 3% or more to be extremely aggressive. When you think about this, it is important to consider the impact of a series of four or five losing trades, or a single loss that is five times the expected maximum loss. If you are trading 3% and have a catastrophic situation where you have a 5x loss, you have only lost 15% of your capital. In reality, losses that are much larger than expected should be extremely rare, but even in such extreme cases the account will not go bankrupt. However, if you consistently use 10%, you will lose 50%; losses are inevitable in trading.
To recover from a loss, a larger percentage return is required to recover. For any D% loss, the amount needed to return the account back to breakeven can be calculated using the following formula:
Breakeven margin = D% (1-D%)
For smaller losses, the returns required to recover are only slightly larger. For example, a 5% drawdown requires a 5.3% return to recover, but a 20% drawdown requires a 25% return to break even. For a larger 50% drawdown, only a 100% gain would get you back to where you were. To put the numbers in perspective, very few traders can consistently make 25% annual gains (compounded), and the likelihood of doubling your money without excessive leverage and risk is very, very small. An effective risk management strategy will end up minimizing losses while acknowledging that they are a natural and normal part of trading.
Assumptions: A strategy with a 50% win rate, a profit-loss ratio of 1.2, a loss control of 2,000, a 100k account, and statistics after simulating 1,000 transactions
If the loss exceeds 75%, the account can be considered to be in a bankrupt state. It can be seen that with this loss control, the account will not have the risk of bankruptcy.
So what can we conclude from this? First, using pure mathematical theory, the number calculated by the expected value is very close to the average value of the terminal, and the difference can be easily explained by normal variation. Few people use mathematical expectation to verify whether the trading system has a trading edge, and most people lose nearly 90% due to market randomness and bad luck.
If the loss control amount is changed, how much impact will it have on the account? See the figure below
What do we notice here?
First, the simple understanding of some traders that “the more you risk, the more you earn” does seem to have some truth to it. As we increase the amount of money we risk per trade, the average terminal value will also increase by the average of the maximum values; risking $5,000 per trade gives us nearly 50% more profit than our initial $2,000 risk. However, this comes at a cost. The standard deviation of the terminal value increases faster than the average, as can be seen in the stable coefficient of variation. If we accept standard deviation as a measure of risk for the time being, we are taking on an extra unit of risk but are not fully compensated by higher returns. At the $5,000 risk level, we have a number of accounts that go bankrupt. A new row is added to the table showing the difference between the terminal value and the expected value. At the $2,000 risk level, the difference is very small, but it increases as the risk level increases. One reason for this divergence is that the bankruptcy limit makes testing and real trading asymmetric. If an account hits this barrier, it is removed from testing and that value becomes its terminal value; this is also a real capital constraint in trading and money management. Otherwise, the Martingale strategy (double your bet amount every time you lose) will work, but in fact, traders who use this strategy will go bankrupt if they trade long enough. As impressive as the idea that more risk means more profit is, let's assume that you decide to, as we say in the vernacular, "go crazy." You increase the risk of being a reckless person. In the end, some truths become very clear. At some point, as the risk increases, the risk of ruin starts to outweigh the possibility of increased gains.
Fixed ratio method and fixed amount method
First, at first glance, these numbers appear to be roughly equivalent. We see an increase in both the mean and median, which is expected since the fixed ratio method allows you to take on more risk as your capital grows. This is essentially a way of using accumulated trading profits to fund further risk. We notice that the standard deviation has increased significantly; the coefficient of variation does not look good. In fact, if they were directly comparable, Table 9.2 shows that we should be able to achieve an average terminal value of around $200,000. For a fixed dollar amount risk plan, the coefficient of variation is 0.35. Perhaps we are a little disappointed with the results of the fixed-ratio approach, where the risk is increased but there is no additional return compensation. In fact, the fixed ratio method has a lower Sharpe ratio to obtain corresponding returns. Digging a little deeper, we see that the average of the maximum values has increased significantly while the average of the minimum values has not had any real change. In fact the average of the minimum and lowest terminal values increases across runs, and we also see that the highest terminal value is approximately 1.7 times larger than the fixed terminal value. Figure 9.2 gives some insight into what's going on.
In Figure 9.2, the histogram also includes a normal distribution curve for comparison with the returns. We have previously established that the constant risk scenario leads to values that do look normally distributed. However, even a casual glance at the fixed fraction distribution shows that it is almost certainly not normally distributed. (In this case, the skewness of the returns is 0.95 and the kurtosis is 4.3. The Shapiro-Wilk test z-score is 8.5, providing strong evidence of non-normality. The fixed fraction distribution is log-normal.) The thing about the fixed fraction distribution is that it is no longer symmetric; the variability is concentrated in the long right (positive) tail. This is crucial: asymmetric risk is relevant for simplistic measures such as the Sharpe ratio or the coefficient of variation. In this case, the added risk of the fixed fraction is a good thing; almost all of the extra variability is a potential advantage.
Won't you go bankrupt? True advocates of fixed ratio methods often point out that it is mathematically impossible to reduce your account to zero using these methods. As your account balance decreases, you are exposed to less and less risk. If we make 250 losing trades in a row, risking 5% on each trade, our $100,000 trading account will not be completely wiped out. In fact, there will be about $0.28 left. If you consider that a 99.9997% loss is clearly better than a 100% loss, then I have nothing to say. The advantages of fixed ratio methods extend upward and reduce the possibility of decline, not that it protects you from bankruptcy itself. This is also why a 75% account bankruptcy test is set in all Monte Carlo.
How much difference does it make to use different fixed ratios?
As can be seen from the averages, the principle of "the greater the risk, the greater the reward" is technically correct. The final values in the table for the 10%, 12% and 25% risk levels, and the falling intermediate values tell a different story. We do not see the ending balance in the table, but the account balance, which becomes unacceptable, and the trading strategy starts to look more like a lottery, as we face a higher risk percentage. Do not be misled by the statistical size of the account, because the probability of these outcomes is extremely low.
There is one last important thing to consider. Many traders like to change their risk ratios, and this may be part of a trading strategy or a deliberate, disciplined decision to trade certain markets. For example, it may be that with less risk, some traders may want to approach illiquid markets with less risk. Too many individual traders make emotional decisions about risk without any real analysis, changing their risk based on their impression of how good a trade might be. If you make emotional decisions about risk, then you are almost certainly going to make suboptimal decisions. If you are going to meddle with position sizing and risk, it is important to do two things: one, understand the impact of random sizing on your trading strategy. Second, take careful notes and conduct objective analysis to add some valuable adjustment rules.
Table 9.6 shows the effect of randomly varying the bet size on each trade. The 4 percentage columns are copied from Table 9.5 for comparison, and then three other tests are performed where each bet size is a random value between 0 and 8% (~Uniform[0, 8%]). Note that in all cases, the randomly sized bets perform worse than the simple fixed fraction 4%.
The core concept of risk management is to control losses, and profit is the second goal to pursue. As the old saying goes, cut losses and let profits run.
