A discussion with a good friend led me into thinking more deeply into portfolio sizing. More than picking long term winners it is more critical to allocate capital in proportion to the opportunity set or valuation discount. Often cited as the key reason why most mutual funds do not outperform the market. Primary reason being they hold 50-60 positions or many 1.5-2% positions which do not move the needle either ways and hence hug the index performance. Overlay the costs of management, we have a right mix high cost indexing which is bound to lose money for retail investors; Why is the design like this not just in emerging markets but across developed markets too is a question for the regulator not for the investor.
Meanwhile, several 'intelligent' investors have taken advantage of this misruling to bet heavily when the odds are in favor. As Mohnish mentions in 'Dhandho Investor', the heart of position sizing lies strictly in Kelly's criterion although many don't acknowledge or admit to it. It, apparently, has applications not only to stock market investing but also to casino games such as blackjack. Both Munger and Mohnish have mentioned on several occasions that 'stock market is a pari mutuel system (horse race), where odds are in favor of investors who bet heavily when the odds are in favor'.
In Kelly's words bet size = edge/odds; Assuming an average investor has 4 positions that have expected IRRs of 26%, 4 positions that have eIRRs of 20% and 2 positions that have eIRRs of 15%, we find that position size for the first 4 positions is 70%, the next 4 positions is 66% and the last 2 positions is 60%. Once we normalize across positions, first 4 positions have 10.5% weight, next 4 have 10% weights and the last 2 have 9% weights. workings are as follows:
One not so obvious observation is that probability of the upside is far more important than the quantum of upside. One needs to bet heavily, if one is reasonably confident of the upside although quantum of upside may not established precisely based on various valuation methodologies. In other words, if we change the downside to 100%, but keep the probability of downside constant, Kelly's formula throws out a position size of 60% instead of 70%
Kelly's Formula in practice:
Moat school vs Value school
Addendum by a dear friend and ex-Gothamite:
The number of stocks in you portfolio is inversely proportional to the amount of time and resources you have to research your picks. The deeper you research your picks the higher the concentration should be in your portfolio. If you are limited by research time, skills and resources its better to have a diversified portfolio."
Meanwhile, several 'intelligent' investors have taken advantage of this misruling to bet heavily when the odds are in favor. As Mohnish mentions in 'Dhandho Investor', the heart of position sizing lies strictly in Kelly's criterion although many don't acknowledge or admit to it. It, apparently, has applications not only to stock market investing but also to casino games such as blackjack. Both Munger and Mohnish have mentioned on several occasions that 'stock market is a pari mutuel system (horse race), where odds are in favor of investors who bet heavily when the odds are in favor'.
In Kelly's words bet size = edge/odds; Assuming an average investor has 4 positions that have expected IRRs of 26%, 4 positions that have eIRRs of 20% and 2 positions that have eIRRs of 15%, we find that position size for the first 4 positions is 70%, the next 4 positions is 66% and the last 2 positions is 60%. Once we normalize across positions, first 4 positions have 10.5% weight, next 4 have 10% weights and the last 2 have 9% weights. workings are as follows:
| Idea 1 | |
| Minimum IRR | 26% |
| 2 x | |
| in 3 yrs | |
| Return | Probability |
| 100% | 80% |
| -50% | 20% |
| Edge | 0.700301 |
| Odds | 100% |
| Position Size | 0.700038 |
One not so obvious observation is that probability of the upside is far more important than the quantum of upside. One needs to bet heavily, if one is reasonably confident of the upside although quantum of upside may not established precisely based on various valuation methodologies. In other words, if we change the downside to 100%, but keep the probability of downside constant, Kelly's formula throws out a position size of 60% instead of 70%
Kelly's Formula in practice:
Moat school vs Value school
- Based on Dhandho Investor, Greenblatt used to run 6-8 stock portfolio (Moat School)
- Eddie Lampert (Sears holdings) used to run 3 to 15 stock portfolio (Moat School)
- Buffett held 40% of his networth in Amex and has widely written about it in his ARs (Moat School)
- Mohnish holds 10% each in each of his positions and remaining in cash waiting for the fat pitch (Moat School)
- Klarman holds max of 25 positions and a max of 10% in each of his positions (Value/Distress asset/absolute orientation)
- Walter Schloss max of 100 positions (Value orientation)
In conclusion, based on some of the data moat investors can afford to invest in between 10 to 15 stocks with 80% invested in top 10 ideas; while Value investors/Distress investors probably given the obscure nature of their investments may have to invest in 25 or more investments to diversify away some of the bankruptcy risks associated with distress investing.
Addendum by a dear friend and ex-Gothamite:
" Our firm followed a concentrated portfolio with a rule that not more than 20% of portfolio should be allocated to a single idea (20% for high conviction ideas). Portfolio size was between 8 to 10 stocks. Statistically the benefits of diversification reduce drastically after adding 8 stocks to the portfolio.
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