Summary Buffett (BRK.B) stated he would have a portfolio of 4-5 securities if he were managing smaller sums of money ($50 million, $100 million, or $200 million). Most value investors who use a focused approach significantly outperform the market. The secret to this approach is the Kelly Growth Formula for portfolio allocation. “If I were running $50, $100, $200 million, I would have 80 percent in five positions, with 25 percent for the largest. In 1964 I found a position I was willing to go heavier into, up to 40 percent. I told investors they could pull their money out. None did. The position was American Express after the salad oil scandal. ” -Warren Buffett; 2008 Berkshire Hathaway (NYSE: BRK.A ) Annual Meeting Source: Dang Le, “Notes from Buffett meeting 2/15/2008,” Underground value blog , February 23, 2008; also cited in The Kelly Capital Growth Investment Criterion by Edward Thorpe, William Ziemba, Leonard Maclean ” Back in the 1960s I actually took a compound interest rate table and I made various assumptions about what kind of edge I might have in reference to the behavior of common stocks generally. I knew from being a poker player that you have to be heavily when you’ve got huge odds in your favor (he concluded as long as he could handle price volatility, owning as few as three stocks would be plenty). I knew I could handle the bumps psychologically because I was raised by people who believed in handling bumps. So I was an ideal person to adopt my own methodology.” –Charlie Munger; D*mn Right! By Janet Lowe Introduction Today I briefly wanted to illustrate the concept of a focused investing approach. I remember when I started investing nobody ever seemed to have a methodology as to how many stocks to have in their portfolio or how to decide which amount/percentage to place of each stock in a given portfolio. Obviously there was the academic theory of diversification taught in most finance classes that advocated 50-100 stocks, but it continued to puzzle me that it was so difficult to find information on a more focused approach. In this article I’ll attempt to outline the parameters of a focused strategy that I use, and also list several resources on focus investing to hopefully save everyone time as finding all of this research was quite time consuming for me. Academic Theory, Diversification, and Value Investing Focus “The Berkshire-style investors tend to be less diversified than other people. The academics have done a terrible disservice to intelligent investors by glorifying the idea of diversification. Because I just think the whole concept is literally almost insane. It emphasizes feeling good about not having your investment results depart very much from average investment results. But why would you get on the bandwagon like that if somebody didn’t make you with a whip and a gun?” — Charlie Munger, 2005 There are no winners in the short-term, relative performance derby. Attempting to outperform the market in the short term is futile…The effort only distracts a money manager from finding and acting on sound long-term opportunities…As a result the clients experience mediocre performance…Only brokers benefit from the high level of activity. – Seth Klarman; quote taken from James Montier’s Value Investing Most universities and institutions teach that a diversified approach to investing is the best way to minimize risk and still obtain good results in the market. The majority of the investment community believes this, and most mutual funds own anywhere from 50-100 stocks with few exceptions. This approach typically leads to a return that is equal to or less than the S&P 500 and also causes most mutual fund performance to fall in a very narrow range. There is no incentive for the average fund manager to deviate from the norm as even one year of performance that is significantly less than his or her peers would probably result in the mutual fund manager being fired or severely reprimanded. Investment management companies reinforce this behavior as investment companies performing in-line with their peers don’t suffer significant losses of assets under management even if their long run performance is abysmal. A study by Randy Cohen et al. (2009; quoted in Montier’s Value Investing) the obsession with relative performance is one of the key sources of underperformance among active fund managers. Although 80-90% of fund managers underperform the S&P 500 averages in a given year, it is interesting to note how much the performance of fund managers top picks deviate from the average. Cohen’s study focused on the top 25% of “best ideas” among active managers and noted active fund managers “best ideas have a long-term average return of 19% per year vs. a market return of 12% over the same period. Best ideas were determined by portfolio allocation and looking at manager’s most significant holdings in size, especially those differing from weights in a typical index fund. If active managers followed a more focused approach and invested a larger percentage of their investable funds in their “best ideas,” both the managers and their clients would be a lot wealthier. In contrast to the diversified approach I described above that is praised by most academics and mutual fund managers there is a school of thought in the value investing community labeled “Focus Investing” by Robert Hagstrom of Legg Mason . This approach advocates putting your investable funds into a few securities and is based on a formula known as the Kelly Growth Criterion. As noted above, Warren Buffett advocates holding four to five securities using this approach and his partner Charlie Munger advocated an even more extreme approach, holding just three securities. This approach is often misunderstood, and there were a few questions on this topic at the Berkshire annual meeting this year. The main question was generally why Berkshire held so many securities and wasn’t “more focused.” Although at first glance this may appear to be true, let’s dig a little deeper to see just how focused the portfolios are. Despite holding roughly 50 stocks, Berkshire’s portfolio is still very focused with 63% of the portfolio invested in four securities (AXP, KO, IBM, WFC), and 82.10% invested in the top ten holdings (in addition to the four previously mentioned, positions five through ten are: WMT, PG, USB, DVA, MCO, GS) as of 3/31/2015. Although at first glance this focused investing approach may seem very risky, Joel Greenblatt tells a different story in his book You Too Can Be a Stock Market Genius noting that, “owning just two stocks eliminates 46 percent of the nonmarket risk of owning just one stock. This type of risk is supposedly reduced to 72 percent with a four stock portfolio, by 81 percent with eight stocks, 93 percent with 16 stocks, 96 percent with just 32 stocks, and 99 percent with 500 stocks.” Greenblatt seemed perplexed at why an investor would add hundreds of stocks to his portfolio to reduce risk by 3 percent. ROBERT HAGSTROM’S STUDY: DOES THE TYPICAL FOCUSED PORTFOLIO OUTPERFORM? ” The deleterious effects of such improbable events can best be mitigated through prudent diversification. The number of securities that should be owned to reduce portfolio risk to an acceptable level is not great, as few as ten to fifteen different holdings usually suffices.” — Seth Klarman, Margin of Safety In their study “Focus Investing: An Optimal Portfolio Strategy Alternative to Active versus Passive Management, ” Joan Lamm-Tennant, Phd., and Robert Hagstrom concluded that while a portfolio consisting of 15 stocks gives an investor a 1-in-4 chance of beating the market (S&P 500 index); a 250 stock portfolio reduces those odds to 1-in-50. Their study was based on 12,000 randomly assembled portfolios constructed with the following parameters: 3,000 portfolios with 250 stocks 3,000 portfolios with 100 stocks 3,000 portfolios with 50 stocks 3,000 portfolios with 15 stocks When sorting the ten year data, they found that 63 portfolios from group #1 (250 stocks) beat the market returns, 337 from group 2 (100 stocks) beat the market, 549 from group #3 (50 stocks) beat the market returns, and 808 from group #4 (15 stocks) beat the market’s return over the time period studied (1987-1996). Although the data below will show that the average portfolio returned less than the S&P 500 over that period (a particularly well performing period for large cap stocks), it also shows that as you reduce the number of stocks in a given portfolio, the probability of beating the returns of the S&P 500 increases. KELLY GROWTH CRITERION AND PORTFOLIO ALLOCATION “It is known that the great investor Warren Buffett’s Berkshire Hathaway actually has had a growth path similar to full Kelly betting.” – Scenarios for Risk Management and Global Investment Strategies; Rachel and William Ziemba “Discussion of Buffett’s concentrated bets gives considerable evidence that Buffett thinks like a Kelly Investor, citing Buffett bets of 25% to 40% of his net worth on single situations. — The Kelly Capital Growth Investment Growth Criterion: Theory and Practice, ” World Scientific Publishing Company, 2011; written by Thorpe, Maclean, and Ziemba. When I first started investing the most difficult topic for me was deciding how much of my portfolio to invest in a given position. This changed when I stumbled upon the Kelly Growth Criterion while reading through Ed Thorpe’s classic book on blackjack Beat the Dealer , after it was mentioned in Ben Mezrich’s book Bringing Down the House , which was later turned into a movie called “21.” The Kelly Growth Criterion is a probability based model that teaches one how much of his bankroll he should wager in a given situation, whether it’s gambling at a casino or investing in the stock market. Ed Thorpe mentions the Kelly Growth Formula in his classic book on Blackjack, “Beat the Dealer,” which became the foundation for the MIT Blackjack team as shown in the book Bringing Down the House: The Inside Story of Six MIT Students Who Took Vegas for Millions by Ben Mezrich. Interestingly enough the Kelly formula was not developed by J.L. Kelly (who it is named after) but rather by the incredible genius Claude Shannon as detailed in the excellent , Fortune’s Formula: The Untold Story of the Scientific Betting System that Beat the Casinos and Wall Street , by William Poundstone. After the formula was developed and published by Shannon another Mathematician, J.L. Kelly realized the formula could be applied to gambling, and the Kelly Growth Formula for gambling/investing was born. The formula is simply expressed as: 2p – 1 = X, where 2 times the probability of winning minus 1 equals the percentage of one’s bankroll that should be bet. For example, if the probability of beating the house is 55 percent, you should bet 10 percent of your bankroll to maximize profit. If the probability of beating the house is 70 percent you should bet 40 percent, etc. Kelly Growth: Application “We might invest up to 40% of our net worth in a single security under conditions coupling an extremely high probability that our facts and reasoning are correct with a very low probability that anything could change the underlying value of the investment.” – Warren Buffett; Letters to Investment Partners In his excellent book The Dhando Investor, Mohnish Pabrai outlines the application of the Kelly Growth Formula to Buffett’s 1964-67 investment in American Express (40% of partnership assets). Pabrai estimates the odds of this bet in a conservative case would be: Odds of 200% or greater return in three years – 90 percent. Odds of breakeven return in three years – 5 percent. Odds of a loss of up to 10 percent in three years – 4 percent. Odds of a total loss on the investment – 1 percent. Using the above odds, the Kelly formula would advocate betting 98.3 percent of assets on American Express according to Pabrai. Buffett invested an amount (40%) under the maximum suggested and placed a few other bets with the remaining 60% of assets. Pabrai gives several examples of ideal portfolio allocation in Dhando Investor, and also notes that several other famous value investors (Joel Greenblatt and Eddie Lampert) seem to be using a Kelly Approach. As noted above, Buffett’s ideal portfolio allocation places 25 percent of assets into the best idea, with the remainder allocated to four investments. Although Buffett has never advocated the Kelly formula, it seems that he uses it or some variation in his portfolio allocation. Kelly Growth: Target Investments “Good jockeys will do well on good horses, but not on broken down nags.” — Warren Buffett In a recent presentation for the website Singular Diligence , Tobias Carlisle did an excellent job describing and summarizing the ideal investment targets under a Kelly approach. On a side note, if you haven’t read Tobias Carlisle’s books Deep Value , and Quantitative Value , you are missing out — they are two of my all-time favorites. Carlisle suggested that the Kelly approach favors investments with the following characteristics: Stable, low risk targets. Reasonable valuation (free cash flow yield 8-10%) Growing bigger in the next 3-5 years. High Quality businesses High Quality Management. To summarize, one should focus on buying companies with wide economic moats at affordable prices. In addition placing large bets when pessimism is at a maximum (See Buffett’s 1964 AXP Investment) is also advantageous. Conclusion “If you are a professional and have confidence, then I would advocate lots of concentration. For everyone else, if it’s not your game, participate in total diversification. If it’s your game, diversification doesn’t make sense. It’s crazy to put money in your twentieth choice rather than your first choice.” — Warren Buffett (NYSE: BRK.B ); The Kelly Capital Growth Investment Criterion by Edward Thorpe, William Ziemba, Leonard Maclean “Of course, Charlie and I can identify only a few Inevitables, even after a lifetime of looking for them… Considering what it takes to be an Inevitable, Charlie and I recognize that we will never be able to come up with a Nifty Fifty or even a Twinkling Twenty. To the Inevitables in our portfolio, therefore, we add a few “Highly Probables.” – Warren Buffett; 1996 Berkshire Hathaway Letter to Shareholders In conclusion, if one has the time and resources a focused approach to portfolio management is ideal. Since I started my investment partnership I’ve consistently had 40-50% of AUM in 4 companies: Directv (NASDAQ: DTV ), Markel (NYSE: MKL ), Express Scripts (NASDAQ: ESRX ), and Davita (NYSE: DVA ); the only time the top 4 changed (added MasterCard (NYSE: MA ) to replace DTV) was when DTV was acquired by ATT. This approach can be frightening at times as your portfolio is exposed to any volatility driven by the largest positions, but in the long run the results are incredible. Appendix Examples of Modern Day Focus Investing in Practice Allan Mecham; Arlington Value Management Nelson Peltz; Trian Capital Chuck Akre; Akre Focus Fund (MUTF: AKREX ) Hennessy Focus Fund (MUTF: HFCSX ) Lou Simpson; SQ Advisors, LLC Tom Bancroft; Makaira Partners Resources: Recommended Reading Fortune’s Formula: The Untold Story of the Scientific Betting System that Beat the Casinos and Wall Street , by William Poundstone Probabilistic Reasoning by Amos Tversky and Daniel Kahneman Skin in the Game Heuristic as Protection Against Tail Events by Nassim Taleb and Constantantine Sandis Understanding Uncertainty by Dennis V. Lindley Scenarios for Risk Management and Global Investment Strategies by Rachel and Bill Ziemba The Kelly Capital Growth Investment Criterion by Edward Thorpe, William Ziemba, Leonard Maclean An Introduction to Probability Theory and Its Applications, Volumes 1-2 , by William Feller The Mathematics of Gambling by Edward O. Thorpe The Unfinished Game: Pascal, Fermat, and the Seventeenth-Century Letter that Made the World Modern by Keith Devlin The Dhando Investor by Mohnish Pabrai The Warren Buffett Portfolio by Robert Hagstrom More Than You Know: Finding Financial Wisdom in Unconventional Places by Michael Maubossin In an Uncertain World: Tough Choices from the Brink by Robert Rubin Judgment Under Uncertainty: Heuristics and Biases (Edited by Daniel Kahnemann, Paul) Value Investing by James Montier Margin of Safety by Seth Klarman Quantitative Value by Wesley Gray and Tobias Carlisle Deep Value by Tobias Carlisle Theory of Gambling by Richard Epstein Theory of Poker by David Sklansky Singular Diligence website ( singulardiligence.com ); Tobias Carlisle Kelly Criterion in Blackjack, Sports Betting, and the Stock Market by Edward Thorpe (available at edwardothorpe.com ) Beat the Dealer : A Winning Strategy for the Game of Twenty-One Bringing Down the House: The Inside Story of Six MIT Students Who Took Vegas for Millions by Ben Mezrich. Against the Gods The Remarkable Story of Risk by Peter L. Bernstein Winning Decision: Getting it Right the First Time by Paul Shoemaker and Edward Russo Disclosure: I am/we are long MKL, BRK.B, DVA, MA, ESRX. (More…) I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.
