“If you took our top fifteen decisions out, we’d have a pretty average record. It wasn’t hyperactivity, but a hell of a lot of patience. You stuck to your principles and when opportunities came along, you pounced on them with vigour.”- Charlie Munger
I find this an interesting quote to reflect. Key themes appear to be:
- Sticking to principles – faith/loyalty to the process
- Patience – a key process ingredient
- Few opportunities – seek out the fat pitches
- Pouncing with vigour – swing and swing hard at fat pitches
- Lack of Activity – Not swinging is neither lack of work nor lack of progress. Evaluating lots of swings is hard work and a lot of work.
Pouncing with vigour should be a result of at least two important elements of a good process:
- a “High +ve Expected Value”. We know that our LOW:LOW; HIGH:HIGH would lead to the highest expected value number.
- A sizing bet based on Kelly’s equation. A high expected value would lead to a high Kelly number. A high sizing bet is the “vigorous pounce”.
Here is a simple example.
Say there is a 10% chance that an investment will be a 5-bagger or yield a 500% return, a 40% chance that it will yield a 200% return, a 20% chance it will yield a small gain of 30%, 20% for breaking-even and a 10% chance for a 100% loss.
The Kelly Number Calculation:
- Event 1, the edge is E1=10% and the odds O1=6:1
- Event 2, the edge is E2=40% and the odds is O2=3:1
- Event 3, the edge is E3=20% and the odds is O3=1.3:1
- Event 4, the edge is E4=20% and the odds is O4=1:1
- Event 5, the edge for Loss L=10%
K= (E1*O1+E2*O2+E3*O3+E4*O4 – L)/(O1+O2+O3+O4)
In this case: K = (0.1*6+0.4*3+0.2*1.3+0.2*1- 0.1) / (6+3+1.3+1) = .1911. Kelly’s Bet = ~20% of our bank-roll.
Now all of this is the math/science bit. Now for the art part.
- A positive “expected value” is not sufficient. Its quality is also important. Apply the Edge/Odds concentric diagram.
- Estimating the edges/odds in real-world situations is highly imperfect. The best way to counter the uncertainty is by choosing situations whereby the estimation process of the edges and odds is both EASY and it allows plenty of room for error, so ERROR-PROOF. Which leads us to the famed “stepping over 1-foot bar” type of opportunities. Easy to accomplish and carries little risk of tripping.
- In situations where it’s not easy to estimate the edges and odds, value investors compensate by adding a margin of safety to their own imperfections and choose to bet half of the computed kelly’s estimate. They term it a “half-kelly”.
Conclusion:: A value investor thinks in terms of the “Expected Value” when choosing a bet and “Kelly formula” for sizing it.
January 13th, 2013