🌰Continued from last timeIn order to further strengthen the geometric mean and volatility drag, we have ushered in a new strategy. If the single profit is 5.1%, the loss is 5%, and the winning rate is 50% (Strategy 2, position control 2), can we still maintain profitability?

(Strategy 2, Position Control 2)

🦞This strategy is a typical one caused by the volatility drag effect, and its geometric average return is very close to 0.

So what are geometric mean returns and volatility drag effects?

Volatility Drag Effect

  • The volatility drag effect means that due to the fluctuation of investment returns (i.e. volatility), the actual long-term growth rate will be lower than the expected arithmetic mean growth rate. Specifically, the greater the volatility, the greater the decline in the geometric mean return relative to the arithmetic mean return.


    This is also an important reason why our (Strategy 1, Position Control 1) will quickly return to zero, because its volatility is too large, resulting in its geometric return rate being negative, so it will eventually quickly return to zero.

    The formula for geometric mean return is:

    Suppose you have n periods of return, R1, R2, …, Rn. The geometric mean return (G) is calculated as:

    Geometric mean rate of return calculation formula

    in:

    • Ri is the rate of return in the ith period (usually expressed as a decimal, e.g. 0.1 for 10%).

    • n is the total number of periods. (If the strategy runs for thirty days, n is 30)

    • ∏ represents the composite product of all periods.

    Example:

    Assuming an investment has an annual return of +10%, -5%, and +15% over three days, the geometric mean rate of return is calculated as follows:

    1. Calculate the growth factor for each day:

      • Day 1: 1+0.10=1.101 + 0.10 = 1.101+0.10=1.10

      • Day 2: 1−0.05=0.951 - 0.05 = 0.951−0.05=0.95

      • Day 3: 1+0.15=1.151 + 0.15 = 1.151+0.15=1.15

    2. Compute composite products:

      1.10×0.95×1.15=1.20125

    3. nth power (here is the cube root) ≈ 1.0637

    4. Subtract 1 to get the geometric mean return:

      1.0637−1=0.0637 = 6.37%

    That is to say, for a strategy, its geometric mean return varies, but to put it simply, there is a roughly concentrated probability area.

    The relationship between the two

  • When the volatility of investment returns is large, negative returns have a much greater impact on the geometric mean return than positive returns. Even when the profit and loss ratio is relatively symmetrical, due to the drag effect of volatility, the long-term geometric average return will be significantly lower than the arithmetic average return, and sometimes even negative.




    In summary, the volatility drag effect directly affects the size of the geometric mean return, making it often lower than the arithmetic mean return, especially in a high volatility environment. This is why in many cases, although the investment strategy appears to be balanced on the surface, in the long run, the funds may decrease due to the volatility drag effect and eventually approach zero.

    For those who are interested in this part of knowledge, you can refer to the following books:

    • For the principles and impacts of geometric mean return, please refer to the geometric mean return section in "Investment Science". The author David G. Luenberger mentioned that the geometric mean return is usually lower than the arithmetic mean return, especially in a high-volatility market.

    • For the impact of volatility drag effect, please refer to Nassim Nicholas Taleb’s “The Nature of Randomness”, which mentions the negative impact of volatility on long-term investment returns.

    Next, I will explain in detail how to increase your geometric return while using the same strategy.

    #新人必看 #仓位管理 #盈亏比
    I am a know-it-all in the cryptocurrency world, and I hope to learn and grow with you.