The Kelly formula was proposed by John R. Kelly, Jr. in 1956. It indicates the optimal proportion of bets that should be made each period in a recurring gamble or investment with a positive expected return. Kelly's formula has long been famous in "Las Vegas" and "Wall Street". Many mathematical geniuses have developed it in casinos and investments and have achieved extraordinary results. The most famous among them is probably Dr. Edward Thorp, who developed a strategy for defeating Blackjack (21 points) and used the proportion calculated by Kelly's formula to make bets (Thorp 1962); after playing in the casino, Dr. Thorp used it in His talents in statistics and probability theory are used in investment. The PNP hedge fund he founded has achieved annual returns of more than 20% in the past 30 years (Thorp 2017).

      f=（pb-q)/b

        

f = leverage ratio

b = odds (odds = expected profit ÷ possible loss)

p = probability of success

​q = failure probability (that is, 1-p)

Example:

1. Assume that when the market adjusts to around 6000, the entry success rate is 50% and the odds are 2 (expected profit 1 times, loss 0.5), then the corresponding position should be (50%*2-50%)/2=25%

2. Assume that when the market adjusts to around 6000, the entry success rate is 50% and the odds are 20 (expected profit is 10 times, loss is 0.5), then the corresponding position should be (50%*20-50%)/20=47.5%

3. Assume that when the market adjusts to around 6000, the entry success rate is 80% and the odds are 2 (expected profit 1 times, loss 0.5), then the corresponding position should be (80%*2-20%)/2=70%

4. Assuming that when the market adjusts to around 5000, the entry success rate is 100% and the odds are 20 (expected profit is 10 times, loss is 0.5), then the corresponding position should be (100%*20-0%)/20=100 %

Conclusion: The success rate has a great impact on the position. If the success rate is lower than 50%, even if there is 10 times the expected return, the position should not be higher than 50%.

PS. Buffett’s version of Kelly’s formula:

X=2p-1

p = probability of success

X=Percentage of funds invested