The Half Kelly bet

One of the smartest and most numerate commenters on GuruFocus is the one who goes by the pseudonym "Buffetteer17". Here is Buffetteer17 recently expounding on the merits of a modified version of the Kelly formula for optimally sizing bets or investment positions:

The half Kelly bet has some interesting mathematical properties. For risk management purposes, the nice property is that it cuts your risk of temporary loss (i.e., volatility) by a large amount while reducing your return expectation only a little. The other important property of the half Kelly bet is that it gives a large margin of safety in the risk estimate. If you are off by a factor of two on your risk of loss estimate, a full Kelly bet will reduce your return expectation to zero. But a half Kelly bet will leave you with 2/3 of the return expectation. Not surprisingly, underbetting is far, far safer than overbetting.

With the full Kelly bet, your probability of temporary loss is a linear function of the amount of loss. For example, you stand a 90% chance of losing 10%, an 80% chance of losing 20%, a 50% chance of losing 50%, etc. Not many investors are comfortable with the prospect of a 50% probability of losing 50% of their money. With the half Kelly bet, your probability of temporary loss is a quadratic function of the amount of loss. For example, you stand a 81% chance of losing 10%, a 64% chance of losing 20%, a 25% chance of losing 50%, etc.

Your expected gain with the half Kelly bet is reduced by 25%. For example, if your expected gain is 40% with the full Kelly, it is 30% with the half Kelly, if your expected gain is 30% with the full Kelly, it is 22.5% with the half Kelly, and if your expected gain is 10% with the full Kelly, it is 7.5% with the half Kelly.

The quarter Kelly bet is even safer. You cut your volatility by a quartic factor while reducing your return expectation by half. For example, you stand only a 6.25% of losing half your money. If you can find enough uncorrelated bets to get all your money invested, you can still invest 100% of your stake with a high safety factor with multiple quarter Kelly bets. The rub, of course, is that it is hard to find truly uncorrelated bets during a market crash like 2008.

In his brief book The Dhando Investor, Buffett wannabe Mohnish Pabrai devoted a chapter to the Kelly formula before concluding that, rather than follow it exactly, he was motivated by it to aim for a 10x10 portfolio (ten positions each comprising 10% of his portfolio). According to notes on his annual investor meeting earlier this year, Pabrai has moved further away from the Kelly formula, to a 3-5-10 set up, where he will only allocate 3% or 5% to most positions, and only occasionally allocate 10% to one idea under extraordinary circumstances.

A problem I have with this gets to a key difference between investing in stocks and betting. Stocks have their own idiosyncratic risks and potential upsides, and the more of them you own, generally, the less informed you will be about them. Better to dig deep and bet big on a handful of stocks with high upside potential, in my opinion, than to broadly diversify as Pabrai is doing. Even broadly diversified index investors got their heads handed to them last year. Idiosyncratic risks aren't the only ones out there, and in over-diversifying to eliminate them, you also diversify away the idiosyncratic high potential returns associated with individual stocks.

Mohnish Pabrai: A Super Salesman, not a Super Investor

Mohnish Pabrai is clearly savvy at self-promotion (as I noted elsewhere last year) and a consummate salesman, judging by the hundreds of millions of dollars of assets he's gathered. I think it's clear by now though that he's not a great investor. If it's not, these notes on Pabrai's 2009 Chicago investor meeting, compiled by Miguel Barbosa of Simoleon Sense may be instructive. Reading them, you'll be reminded that Pabrai used to use shares of Berkshire Hathaway as a "placeholder for cash", which made absolutely no sense; that he ignored his own advice about avoiding retailers (not to mention his alleged preference for small caps) when he invested in Sears; and that he has belatedly realized that a highly-leveraged, subprime lender (Compucredit, on which Pabrai took a 72% loss¹) might not do well during a credit crunch.

A couple of years ago, I sent a copy of Pabrai's book, The Dhando Investor², to a friend of mine who works in the Southern California office of a firm that was initially established as the family office for a Gilded Age family, and now handles the finances for other wealthy families. At the time, I figured my friend's firm might be interested in looking at Pabrai as a candidate for its stable of outside investment managers, but now I think a better role for Pabrai would be as a salesman for a wealth management firm (though perhaps one with a lower minimum asset requirement than my friend's firm).

If I were Pabrai, I would quietly approach some leading wealth management/family office firms about them absorbing Pabrai's assets under management and bringing Pabrai on to gather assets for the firm from affluent Indian Americans. Pabrai could probably add more value to his wealthy clients as an excellent salesman than as an investor.

¹Pabrai also doubled down on a subprime mortgage lender, Delta Financial Corporation, after the securitization market seized up in August of 2007. He held his stake until that company went bankrupt.

²Pabrai's brief book actually contains some interesting stories about entrepreneurship (Pabrai was an IT entrepreneur before becoming a hedge fund manager), but Pabrai himself ignored some of the lessons in those stories. For example, Pabrai wrote about the ethnic Indians whose businesses were expropriated by Idi Amin, and despite this, Pabrai invested in an oil company based in Hugo Chavez's Venezuela.

Pabrai's New Buys

In a recent post ("Mohnish, How Are You Feeling?"), we linked to Mohnish Pabrai's annual investor letter in which he wrote that he had invested in a number of businesses in the commodities sector in 4Q08. On Seeking Alpha, Davy Bui lists Pabrai's new positions (Hat Tip: The Guru Five):

Pabrai's new positions can be summed up as a bunch of commodities with a hint of financials. New mining stakes include Horsehead Holding Corp (ZINC), Teck Cominco (TCK) and indirectly, Leucadia National (LUK). He also moved into the agriculture space with Potash (POT) and Cresud SA (CRESY). He also added a good-sized position in Goldman Sachs (GS), which received a well-publicized capital boost from Pabrai's acknowledged idol, Warren Buffett. Pabrai completely divested his WCG position and massively reduced stakes in Buffett's Berkshire, Cryptologic (CRYP), CompuCredit (CCRT) and Fairfax Financial (FFH).

Alloy Steel Update

Ugly tape for Alloy Steel International (OTC BB: AYSI.OB) on a down day. Looks like a flat-lining EKG. No company-specific news today, but there have been some tentatively positive indicators related to the metals sector recently¹. Picked up a few more shares today at .29.


¹E.g.,

- Temasek, the $134 billion Singaporean sovereign wealth fund, recently hired Chip Goodyear, former CEO of blue chip miner BHP Billiton, as its new chief (Wall Street Journal: Temasek Shakes Up Its Top Ranks -- Ho Ching Out, 'Chip' Goodyear In at Singapore Fund; a Commodity Push?)

- China bought a stake in (over-levered) blue chip miner Rio Tinto (BBC: China takes a stake in Rio Tinto)

- The Baltic Dry Index was up 147% year-to-date as of February 17th (Bloomberg: "Shipping Index Surge Signals Commodity Currency Gains"). It's up about 166% as of today (but still down steeply from its 2008 highs).

On the other hand, the continuing global recession is obviously bearish, and as reader Sivaram noted in a recent comment thread ("Mohnish, How Are You Feeling"), Mohnish Pabrai mentioned in his annual investor letter that he has turned bullish on the commodity sector, which, given his recent track record, could be considered a bearish indicator.

Coming Soon

The titles of a few posts I have on deck, but haven't finished yet:

- TBT or not TBT

- More on Mohnish

- Some Bullish and Bearish Indicators on Commodities

- Penny Ante Arbitrage

"Mohnish, How Are You Feeling?"

According to Mohnish Pabrai, this is what most of his investors were asking him after he lost 60% of their money last year. For his answer, see the excerpt below from his annual letter to his investors, dated January 16^th:

I did hear from a few of you in the last few weeks. While some calls and emails expressed concern over our performance numbers, the surprising thing for me was that the overwhelming majority of you were focused on asking, “Mohnish, how are you feeling?”

Well, I am actually feeling pretty good. And as Q408 unfolded, my spirits remained elevated – mainly because I remained focused on intrinsic value and was drooling over the incredible opportunity set and valuations. I was in turbo mode trying to read huge piles of 10Ks, 10Qs, annual reports, industry reports, listening to conference calls etc. – so I could pull the trigger while the prices were still incredible. And several triggers were pulled in November and December. We bought into an incredible array of assets at remarkable prices.

While it was indeed tough to watch the severe drops many of our holdings took in Q408, keeping my focus on intrinsic value, rather than fixating on the quoted market value of various positions was fundamental to staying level headed.

Pabrai isn't the only professional investor who's expressed similar sentiments when asked about his outlook recently, but I don't get this, for a couple of reasons. First, if someone asked me how I felt about the money I lost last year, "pretty good" wouldn't be my answer; "nauseous" would be -- and I just lost my own money. If I had lost 60% of the money entrusted to me by hundreds of other investors, in addition to nausea, I'd feel some remorse.

Second, it's one thing to tout the great opportunities you see in a beaten-down market, but it raises an obvious question: did you have any dry powder to take advantage of them, or have you been forced to sell your beaten-down positions to buy stocks you think are even cheaper? At least Bruce Berkowitz was candid enough to acknowledge (on a recent conference call) that that's what he's been doing, for the most part (selling cheap to buy cheaper). If that's been the case with Pabrai too (and I assume it is, considering that Pabrai has allegedly used Berkshire Hathaway stock as a "placeholder" for cash), then his zeal for current bargains ought to be tempered by some regret for not keeping more cash on hand to take advantage of them.

About the image above:

In his book The Dhando Investor: The Low Risk Value Method to High Returns, Pabrai offers the story of the end of Abhimanyu, a hero of the Hindu epic The Mahabharata, as metaphor for the difficulty of selling a stock. In an nutshell: Abhimanyu uses a technique he overheard¹ from Krishna to penetrate the spiral chakravyuh battle formation of his enemies, the Kauravas. Unfortunately, he never learned how to break out of the chakravyuh, so he has no exit strategy. He fights valiantly, one against many, and kills a number of Kauravas, but ultimately gets killed. I believe the image above², from a Geo Cities site, depicts this.


¹Please see the second comment by Ravinsu for elaboration.

²Replaced as per Ravinsu.