# Position Sizing Like Warren Buffett

Investing as defined by Warren Buffett is laying out money now to get more money back in the future after taking into account inflation. Investing successfully requires an investor to make many decisions. The investor must determine where to put his money into, the general stock market prices and where it is expected to head. The investor then needs to determine the valuation of individual companies and construct an investment portfolio. To get a good return from the market, the allocation of portfolio to different stocks play a important role. Small allocations to prescient investments minimize their impact while large allocations to poorly performing investments leads to underperformance.

There are many ways to allocate the portfolio. Some investors choose the method of equal weighting where a fixed proportion (e.g. 5%) is allocated to each stock regardless of how undervalued the stock is. The portfolio is then re-balanced on a regular basis to maintain the equal-weight allocation. Another approach is to allocate large proportion of the portfolio to the stocks with the highest potential returns. Portfolio constructed using this strategy will tend to be concentrated with most of the portfolio being invested in a few high conviction stocks. The advantage of this methodology is matching prospective return to investment size, We see such concentrated portfolio in investors such as Bruce Berkowitz and Warren Buffett where they could be using Kelly Criterion to determine the position sizing.

What is Kelly Criterion?
There is a mathematical formula called the Kelly criterion that tells one exactly how much of one's portfolio to bet on a given opportunity if the goal is to maximize the long-term compound rate of return. This was developed by John Larry Kelly Jr 50 years ago. The formula assumes a bimodal outcome of success ("base case") or failure ("stress case") over a single time period

The formula is given as such:
Kelly Criterion = Edge/Odds

The formula was initially developed to figure out the best ways to manage signal-noise issues in long-distance telephone communications The mathematician who developed this saw other applications in areas such as gambling. There is an outstanding book called Fortune's Formula, by William Poundstone which tells the story of how mathematician Edward O. Thorp used the Kelly criterion to win at blackjack, and then make a fortune in the stock market.

How to compute the amount to invest/bet on a stock?
Let's assume somebody offers you the following odds on a \$1 bet and your bankroll is \$10,000.
80% chance of winning \$21
10% chance of winning \$7.5
10% chance of losing it all
According to Kelly Criterion, the edge is equal to 80% x 21 + 10% x 7.5 + 10% x -1( because we have lost our money)=16.8+0.75-0.1=17.45
Odds= Maximum money that we can win= 21
So edge/odds=17.45/21 x10,000= 8309. So you can bet \$8309 on the bet.

The Dhandho Investor written by Monish Pabrai documents evidence that Buffet thinks like a Kelly investor, citing Buffett bets of 25% to 40% of his net worth on single situation. He cited the example of the Salad Oil Scandal where Buffett invested 40% of his net worth into American Express. The book give insights into Mr Buffett's thinking and reasoning. The same thoughts and approach was shared by his partner, Charlie Munger. In a speech at the University of Southern California's Marshall School of Business, Charlie Munger said:
The wise ones bet heavily when the world offers them that opportunity. They bet big when they have the odds. And the rest of the time, they don't. It's just that simple. -Charlie Munger

In conclusion, the Kelly Criterion is one of the many methods that can be used for position sizing. This method is valuable to investors given the systematic, repeatable process and mathematically optimal portfolio structure. When used conservatively, the formula will maximize portfolio growth by allocating capital to the most advantageous investments given both prospective return and risk.

For more detail on how Kelly Criterion is by Buffet in investing in a stock, I recommend reading http://www.infobarrel.com/What_Warren_Buffett_Can_Teach_Us_About_Position_Sizing

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