Friday, April 19, 2013

What Warren Buffett Can Teach Us About Position Sizing

Investing successfully requires an investor to make many decisions. The first and foremost decision is the amount of capital available for investing, the type of asset (e.g. mutual funds, index funds (link to index fund article, stocks, gold etc.) to invest in and construct an investment portfolio. Regardless whether allocators select investment managers or individual securities, optimal position sizing is paramount to portfolio success. Small allocations to prescient investments minimize their impact while large allocations to poorly performing investments leads to underperformance

Some investors use a simplified model to construct their portfolio where an equal weight allocation is given to all investments not taking into account uncertainty regarding which investments will perform best. The portfolio is then rebalanced on a regular basis to maintain the equal-weight allocation. This equal weighted strategy benefits from simplicity and it prevents the portfolio from being over-allocated to one particular stock. However, the drawback of this strategy includes underweighting exceptional investments and overweighting marginal ideas.

An alternative strategy is to allocate large amount of capitals to the ideas with the most potential upside. This strategy suggests investors should invest proportionally according to their return expectations. 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. Many famed value investors such as Bruce Berkowitz, Donald Yacktman, Mohnish Pabrai and Warren Buffett runs concentrated portfolio where they take up huge position in their high conviction stock picks. One method that they could use to determine the position sizing is using the Kelly Criterion. Mohnish Pabrai in his book, The Dhandho Investor (amazon link), explain exclusively on how Kelly Formula can be used for portfolio allocation and how investors can benefit from using it.

What is Kelly Criterion?
The Kelly Growth Criterion is a simple formula that determines mathematically optimal allocations to maximize long-term portfolio performance given each investment’s probability of success (“edge”) compared to the amount gained or lost (“odds”). This mathematical formula was developed by John Larry Kelly Jr 50 years ago while working at the AT&T Bell Laboratories. The formula assumes a bimodal outcome of success (“base case”) or failure (“stress case”) over a single time period:

Since the formula was developed, it has been used by bettors and investors to beat the 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

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