Kelly Formula and Weighting Investments [ANALYSIS]VW Staff
A Reader: Do you have any recommendation on sizing of holdings? It is not a topic much covered in the investment world. In general the focus is on what to buy/sell, but not how much of it.
My reply: This is an excellent question! Many investors just blindly diversify and they never study the quality of their opportunity. In fact, you should have a question like that on your pre-investment check-list.
Obviously, the answer depends upon your assessment of the opportunity. This is where the “art” or hard-won experience comes into play. In fact, I believe a large part of Joel Greenblatt’s returns were created through heavily weighted investments at certain times vs. just consistently performing outstanding security analysis. Prof. Greenblatt knew when to push his chips out onto the table.
For example, if you read, You Can Be A Stock Market Genius (Greenblatt’s book on special situations). Please buy, read and memorize this book. There is a chapter on the Sears spin-off. In class, as well as, in the book. Prof. Greenblatt explains how Sears was going to be spun-off at about the equivalent of 1/10th the price of J.C. Penney Company, Inc. (NYSE:JCP) as shown through a comparative analysis of the two companies. Also, J.C. Penney Company, Inc. (NYSE:JCP) had much more debt then Sears at the time. In other words, the valuation discrepancy was so big you could drive a truck through it (see pages 104 to 106 in his book. A student asked, “How much did you invest in Sears?” Prof. Greenblatt’s response, “Let’s just say I loaded up the truck and then some…..”
Don’t hold me to this, but I estimate Joel put in 25% to 50% of his portfolio into Sears. The stock proceeded to go up 50% in the next few months. Joel weighted his investment.
The size of your margin of safety and risk of loss determines your bet. If you look down below in the example of the Kelly Formula, a 60% chance of winning vs. 40% chance of losing with an even pay-off means you bet 20% of your bank roll. I like to have at worse case a 40% chance of a 50% loss vs. a 60% chance of a double, I bet 10%–I under-bet. But when Enstar (ESGR) trade near $40 back in 2009, I bet 30% of my portfolio because the company was liquid, under-leveraged and growing its book value at 20% per year and the worse the financial crisis the better for its business of acquiring insurance in run-off. A very rare opportunity.
You must develop your own method but see below…………
Conclusions from a book review of Fortune’s Formula (See Below)
Fortune’s Formula is vastly better researched than your typical popsci book: Poundstone extensively cites and quotes academic literature, going so far as to unearth insults and finger-pointing buried in the footnotes of papers. Pounstone clearly understands the math and doesn’t shy away from it. Instead, he presents it in a detailed yet refreshingly accessible way, leveraging fantastic illustrations and analogies. For example, the figure and surrounding discussion on pages 197-201 paint an exceedingly clear picture of how objectives #1 and #2 compare and, moreover, how #1 “wins” in the end. There are other gems in the book, like
- Kelly’s quote that “gambling and investing differ only by a minus sign” (p.75)
- Louis Bachelier’s discovery of the efficient market hypothesis in 1900, a development that almost no one noticed until after his death (p.120)
- Poundstone’s assertion that “economists do not generally pay much attention to non-economists” (p.211). The assertion rings true, though to be fair applies to most fields and I know many glaring exceptions.
- The story of the 1998 collapse of Long-Term Capital Management and ensuing bailout is sadly amusing to read today (p.290). The factors are nearly identical to those leading to the econalypse of 2008: leverage + correlation + too big to fail. (Poundstone’s book was published in 2005.) Will we ever learn? (No.)
Fortune’s Formula is a fast, fun, fascinating, and instructive read. I highly recommend it.
There are currently only two major books about the Kelly Criterion on the market that I am aware of.1) “Fortune’s Formula“ by William Poundstone
2) “The Kelly Capital Growth Investment Criterion” by Leonard C. MacLean, Edward O. Thorp and William T. ZiembaFortune’s Formula, written by William Poundstone is the easier read. The second book, “The Kelly Capital Growth Investment Criterion”, that got just recently published is a much bigger workload to read. I would compare this duo of books with the twin sets of Graham’s “The Intelligent Investor” and “Security Analysis”. Whereby the “Intelligent Investor” is an easier read for the novice investor, and “Security Analysis” for the more advanced financial reader. The two available Kelly books should also be read in the same order, Poundstones book for the starter as an appetizer and William Ziemba’s book as the main and advanced course. Fortune’s Formula – web site for the book
http://www.fortunesformula.com/William Poundstone’s – homepage
Kelly explained @ William Poundstone’s homepage
http://home.williampoundstone.net/Kelly/Kelly.htmlWilliam Poundstone’s page @ Amazon
« Last Edit: September 05, 2011, 08:28:39 PM by berkshiremystery »
In probability theory, the Kelly criterion, Kelly strategy Kelly formula, or Kelly bet, is a formula used to determine the optimal size of a series of bets. In most gambling scenarios, and some investing scenarios under some simplifying assumptions, the Kelly strategy will do better than any essentially different strategy in the long run. It was described