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Forum List » Guru News and Commentaries Guru News, Stock picks and commentaries Position Sizes, Kelly Criterion and Prudent Capital Allocation
Posted by:
Tannor Pilatzke
(IP Logged) Date: March 6, 2014 05:26PM
- The chance of ruin is small. Because the Kelly system is based on proportional bets, or relative bets and losing all of your capital is theoretically impossible. A small chance of a significant loss remains.
- It is arguably the best system to reach a specified goal within the lowest period of time.
Assume you can participate in a coin toss game where heads pays $2 and tails costs $1. You start with a $100 bankroll and can play for 40 rounds. What betting strategy will give you the greatest probability of the most money at the end of the 40th round? 100% ???
Now if we plug the values into the formula we find: F = 0.50 – (0.5/2) F = 0.25 or 25% of capital We can rearrange the formula to end up with Edge/Odds = Where Odds = $2 0.5/2 = 25% This style of betting is rather counterintuitive at first glance but upon thinking about it for a few moments, we realize this is because of the probability distribution and chance of continual (parlay style) losses in the short-run. Mohnish Pabrai (Trades, Portfolio), PIMCO, Warren Buffett (Trades, Portfolio), Legg Mason and a few others seem to utilize the Kelly system in various unique respects. Buffett has not officially stated he used the system although he had the following to say during an interview with business students:
Pabrai on the other hand talks about the Kelly formula extensively through out The Dhandho Investor and recommends using a more conservative approach of a 1one-fourth Kelly, one-third Kelly or one-half Kelly, that is dividing the recommended total capital allocation by two, three or four. This is due to an important factor of over-betting and the loss of wealth it can cause as well as to subdue the emotional effects of losses. Because probabilities are usually estimates and are not known and the effects of over betting are worse than under betting, it is best to be conservative and bet less than Kelly suggests.
The following picture illustrates the distribution of 40 coin flips using a range of We can see that when we over bet it leads to complete ruin while if we under bet we are potentially leaving money on the table or in the market. Kelly System is a parlay style betting system and requires an investor to maximize A quick illustration of why to use GeoMean. Imagine we had five years of data.
The arithmetic average would be 19.6% annually. Is this measurement truthful? No it is actually very misleading as most of us can probably see based on the 2012 returns of a 60% loss. The Geometric mean would be roughly 7% over five years, or a difference of 12.6% in expected value. (
Both theories suggest that an investor’s utility, (as a function of investment return) is relative to proportionate wealth. Meaning the more money we have the less likely a small gain or loss is to effect us. The less money we have the more utility the returns and losses have. These theories introduced by Kahneman and Tversky also introduce us to the evidence that humans are hard wired to be loss averse. Imagine for a second about winning $1000 and losing $1000 tomorrow. The dollars that are lost effect us Cognitive biases aside, lets review an example that can be applied to the
First thing is first, before capital allocation should even be considered, the investment should have passed our investment checklist. The downside is minimal, it is a business that is within our circle of competence and we understand it very well. We know how the cash flows are likely to change or what they are to be in 5-10 years time. The business is priced at a discount from intrinsic value. It is a business we would be willing to commit a large portion of capital to. The management is honest, able and sound. The business has a durable moat that is expanding.
We find that a gas station goes on sale at the end of 2006 for $500,000. Should we buy? Well yes.
Although this is a great return, it is dependent upon how much we invested proportionate to what was available. If a 51% return is achieved on only 3-5% of the portfolio, a total portfolio return of only 1.5-2.5% is achieved. If 60% of the portfolio was invested, the total return would be about 30%. A difference of 27.5% excess return.
The Kelly system would suggest we invest 92% of our f = 0.95 – (0.05/1.55) The return of 50% would then be translated into a total return of 11.5% - 23%.
Mr. Buffett bought his Washington Post (WPO) stake for about $6.15 per share in 1973 and had believed the business to be worth $25 per share. Let us imagine now that the business will grow intrinsic value by about 10% annually ($25 x 1.1 x 1.1 x 1.1 = $33.28). A sale of the business will be made in three years when intrinsic value reaches 90%, or roughly $30 per share. Odds of making 4 times of better return in three years = 80% Odds of making 2-4 times or better return in three years = 15% Odds of breaking even to 2 times = 4% Odds of total loss = 1% How much bankroll would Kelly tell us to allocate?
F = 0.99 – (0.01/3.68) = 98.7% Take 1/2 , 1/3 or ¼ Kelly and we end up with a suggested range of 24.675% to 49.35%.
But do not be fooled. There is no “perfect” system to avoid all loses. All we can do is minimize losses, maximize gains, and everything but it doesn’t guarantee that you won’t lose sometimes. The point is not to use the stated Kelly allocation amount and mathematical models when determining investments. Spend your time reading annual reports, analyzing businesses and looking to find bargains that you believe to be in the 95%+ of Kelly recommended capital allocation.When you find these types of bargains, “ Guru Discussed:
Warren Buffett:
Current Portfolio,
Stock Picks Mohnish Pabrai: Current Portfolio, Stock Picks Stocks Discussed: WPO,
BRK.A,
BRK.B,
SPY,
IWM,
SPX,
Re Position Sizes Kelly Criterion and Prudent Capital Allocation Posted by:
Tannor
(IP Logged) Date: March 7, 2014 04:16PM
No problem Cesc and thanks for reading. Guru Discussed:
Warren Buffett:
Current Portfolio,
Stock Picks Mohnish Pabrai: Current Portfolio, Stock Picks Stocks Discussed: WPO,
BRK.A,
BRK.B,
SPY,
IWM,
SPX,
Re Position Sizes Kelly Criterion and Prudent Capital Allocation Posted by:
skyaboveyou
(IP Logged) Date: March 7, 2014 06:09PM
Guru Discussed:
Warren Buffett:
Current Portfolio,
Stock Picks Mohnish Pabrai: Current Portfolio, Stock Picks Stocks Discussed: WPO,
BRK.A,
BRK.B,
SPY,
IWM,
SPX,
Re Position Sizes Kelly Criterion and Prudent Capital Allocation Posted by:
Tannor
(IP Logged) Date: March 7, 2014 07:31PM
Yes any negative possibility would be considered losing, a break even would be in theory be a negative expected value based on opportunity cost. The probabilities are subjective to begin with based on the analyst's research. The Kelly system shouldn't be used explicitly as Mohnish has recently said in 2009, he does not follow the Kelly approach stickily but does utilize a similar concentration allocation method. This is due to the changing odds and inability to make continual bets. The point being, focus on concentration and load up when the odds seem very favorable, this is also the reason behind under-betting using a 1/4 or 1/3 kelly. Guru Discussed:
Warren Buffett:
Current Portfolio,
Stock Picks Mohnish Pabrai: Current Portfolio, Stock Picks Stocks Discussed: WPO,
BRK.A,
BRK.B,
SPY,
IWM,
SPX,
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