Based on the Kelly formula, now we will introduce another related and interesting formula that shows an investor's maximum compound growth rate (G), if the investor is going to keep investing a fixed % f each time.
G = p*ln(1+f) + q*ln(1-f)
If we recall f = p - q, and p+q = 1, after some transformations, we can get
Gmax = 1 - H
Where H = - [ p*log(p) + q*log(q)]
In information theory, H is the famous Shannon entropy.
There are a few important takeaways from the above Gmax formula -
1. Do not participate a gamble where H = 1, because your Gmax will be 0! For example, if a gamble has p = q = 0.5. There is no need to participate!
2. The lower H, the higher the investment certainty, the higher your investment's compound growth rate in the long term. This could explain why Warren Buffet mainly invests in things he understands, because he will gain an edge in those investments which maximizes his long term compound growth rate Gmax!
3. Avoid large loss. Due to the compound rule, in the investment world, a significant loss could wipe out a string of gains before it. That's why Buffets stresses: Rule #1, don't lose money. Rule #2, don't forget Rule #1!
4. Avoid over betting, even you have higher odds of winning! This could be easily seen from the Kelly formula, the math can't be wrong!
In our next blog post, we will introduce a low math way to manage your risk.