📡If there is a strategy that gives you a 50% chance of doubling your single profit, and a 50% chance of halving your assets and losing 50% (Strategy 1, Position Control 1), would you choose such a trading strategy? From the perspective of probability theory understood by ordinary people, this is a high-quality strategy. Because the money earned from his profit is far greater than the money lost, and with a 50% probability, his weight is a positive number.
📢Then my subsequent experiments will be carried out under the following conditions: the initial capital is 10,000, and when the funds are less than 100, we will consider it bankrupt.
Strategy 1, Position Control 1
The following are the simulation results I conducted using the code. The horizontal axis is time in days, the vertical axis is money, and the starting capital is 10,000.
After many simulations, most simulation results showed bankruptcy occurred on the 22-23 days, with the longest being bankruptcy on the 28th day, but without exception the final destination was zero.
🔔From the results, it can be seen that this strategy and position are undoubtedly wrong. What are the reasons? You can discuss it in the comment section.
Strategy 1, Position Control 2
📻 Let's change to another strategy. A single transaction will make a profit of 10% or a loss of 5%, and the probability is also 50% (Strategy 1, Position Control 2). The initial capital is also 10,000. When the capital is less than 100, we will consider it bankrupt. If it is a profitable strategy, I will only issue it for 30 days.
🎺From the figure, we can see that the same profit and loss ratio and the same winning rate lead to different results. From the perspective of ordinary people's probability theory, why do the weights are the same and lead to different results?
💡 is actually a classic misunderstanding involving the difference between geometric mean return and arithmetic mean return, commonly known as the fallacy of "profit and loss symmetry". Assuming that assets double every time you make a profit and halve every time you lose, and the winning rate is 50%, many people may think that the final assets should keep growing, but the actual situation is that in the long run, the geometric average growth rate of assets is negative, and assets will eventually tend to zero.
reason:
Geometric mean: Long-term returns are closer to the geometric mean than the arithmetic mean. Even if there are the same gains and losses, the impact of losses is greater.
Volatility drag: Volatility will reduce the long-term growth of assets. Although the magnitude of each profit or loss is the same, the low rate of return caused by volatility will gradually reduce assets. (We will verify this in the next issue)
