Under the Kelly formula, the optimal position ratio f=winning rate/net loss rate of each loss-(1-winning rate)/net profit rate of each gain, also clearly proved mathematically that if the position is not managed properly, an expected value is positive In the trading system, it is entirely possible that the actual trading result is negative due to poor positions (mainly overweight positions).
It should be added that although the Kelly formula does not explicitly mention the issue of capital leverage, in fact this formula is also applicable to the issue of capital leverage, that is, it is applicable to futures. Capital leverage is generally used more or less in futures trading. The calculation formula of capital leverage is: capital leverage value = total value of contract / total equity. For example, stock index futures is 300 yuan per point. If you If you buy long or short one lot, then the total value of this contract is 900,000. If your total equity is 300,000, then your capital leverage is 3. The purpose of using capital leverage value instead of position ratio is to apply to the situation of different margins of different products.
Here are a few practical examples to illustrate how to use the Kelly formula to control the capital leverage of transactions:
Example 1: A trading system with a winning rate of 50% and a net rate of return of 20% for each profit and a net loss rate of 10% for each loss. According to the formula, the optimal position ratio f=50%/10%-50%/20 %, which is 2.5. 2.5 is the best capital leverage ratio, that is, if you have 1 million funds, then trade 2.5 million contracts.
Example 2: It is also a trading system with a winning rate of 50%, but the net rate of return of each profit is 2% and the net loss rate of each loss is 1%, then f=50%/1%-50%/2%, that is 25, that is, 25 times leverage.
Example 3: It is also a trading system with a winning rate of 50%, but the net rate of return of each profit is 100%, and the net loss rate of each loss is 50%, then f=50%/50%-50%/100%, that is 0.5, that is, a leverage of 0.5 times (note that a leverage of 0.5 times is not a half position transaction).
It can be seen from the above example (there is a stricter mathematical proof in the recommended article in the previous blog post), the trading system with the same winning rate and consistent profit and loss ratio, the lower the value of the net profit rate and net loss rate of each transaction, you can use The higher the capital leverage ratio. This is also the reason why most trading systems rarely find that they lose money when the position ratio is too high, because most trading systems generally set stricter stop loss points and will not stop at 1 The stop loss is only when the loss of a single transaction is more than 10% under double leverage (that is, the stop loss is only when the price moves against the market by more than 10%). As in Example 3, the loss of more than 50% in a single transaction is even less. However, non-systematic traders, especially retail investors, often have a lot of people who may lose money until they lose more than 50% or even more. It is a full-position dead-load type. It can be seen from Example 3 that a full-position dead-load type (that is, a large proportion of each loss) obviously violates the optimal position ratio, and the trading performance will be poor.
What I want to emphasize is that the Kelly formula can give us a lot of guidance in the general direction of position control, but we must not simply mechanically apply the formula to set the specific position ratio.
This is because the Kelly formula was transplanted from the communication field to gambling at that time. Whether it is communication or gambling, there is no problem of forced liquidation after the floating loss is too large. For example, in gambling, the value of the profit and loss of each bet is fixed. Trading is not, the profit and loss of each transaction is uncertain, even if a system has an average net profit rate and net loss rate each time, that only represents the average level. We know that no matter how much profit you make, if you lose 100% at a time, everything is zero. Especially for wealth management funds, even if there is no 100% loss, excessive retracement will lead to a large loss of customers. The bottom line of many funds' retracement control is 20%. This is why we value the largest historical retracement of a trading system so much. We must be able to use the Kelly formula without touching the maximum retracement red line.
One way to control the risk of maximum drawdown is through position control, and more effectively through portfolio investment, especially portfolios with low yield correlation (see the previous blog post for the specific mathematical proof). But what is more tragic is that it is very common for most domestic varieties to rise and fall at the same time. We can only choose a relatively low price. For pure futures, my suggestion is a portfolio of stock index futures, industrial products and agricultural products , that is, there are at least three portfolio investments with different trading varieties and corresponding trading strategies. Whether it is the calculation of the correlation coefficient of historical data or the backtest of my real trading system combination, it is effective to show that such a portfolio is better than a single It is much less risky to trade multiple industrial commodities or just multiple agricultural commodities.