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.
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
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
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
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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