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The St. Petersburg Lottery (In Reverse)

‘The St. Petersburg Lottery’ is based on a theoretical lottery game that has an infinite payoff.  You pay a fixed fee to enter the game of chance in which a coin is tossed until a tail appears.  Each time a head appears, the pot is doubled and, at the end of the game, you win whatever is in the pot.

If the first bet is for $1, this means that, with 50/50 odds in the first round, you can win $1.  The next time around the probability is 25% but you can win $2.  When the probability is 1/8th you can $4 and so forth.  Knowing how the game is played, what would be a fair price to enter the game?

What we know about the game is that only unlikely events (low probabilities) yield high prizes.  When famed mathematician Bernoulli addressed this problem, he conjectured that people tend to neglect unlikely events

While mathematicians have since conducted experiments to counter Bernoulli’s claim, stock market practitioners have served only to prove his point through spectacular failure.

One famous hedge fund comprised former Vice-chairman and head of bond trading at Salomon Brothers, John Meriwether, Nobel Prize Winners in Economics, Myron Scholes and Robert Merton, as well as principals such as Eric Rosenfeld and Larry Hilbrand.

The fund began with just over $1bn of investor capital and operated strategies that were almost a reverse of the St. Petersburg Lottery.  Rather than seeking extraordinarily high returns with low probability, the fund engaged in strategies that would return very small capital amounts with very high probability.

The premise of the fund’s investing strategy was that long-dated bonds issued a short time apart would tend to become identical over time.  However, the rate at which these bonds approached this price would be different, and high-liquidity bonds such as US Treasury Bonds would approach the long-term price more quickly than illiquid bonds.

The firm reported annualized gains of over 40% initially but, as the capital grew, management decided to engage in non-directional strategies which demanded they take highly leveraged positions to make a significant profits and which were outside their area of expertise.

In 1998 the hedge fund had just under $5Bn in equity and had borrowed an astounding $124Bn.  It’s derivative positions off-balance sheet had a value of approximately $1.25 Trillion.  These comprised interest rate derivatives as well as equity options. 

The strategy employed was in many respects similar to selling out-of-the-money options naked.  The payouts were small, the chance of a large loss was small BUT, if the large loss were to occur, it could be devestating.  And it was!

The fund reported losses in mid-1998 that were compounded by Salomon Brothers exiting the arbitrage business and by the Russian Financial Crisis in which the Russian government defaulted on government bonds.  As the value of bonds diverged due to heightened selling in Japanese and European bonds in favor of US Treasury bonds, the fund lost $1.85Bn in capital.   By September the equity stake in the hedge fund was just $600M.

As the company liquidated securities to cover debt, fear mounted that other funds would liquidate their own debt leading to a chain reaction as prices fell.  Ultimately, the New York Federal Reserve Bank stepped in ahead of a proposed bailout by Goldman Sachs, AIG and Berkshire Hathaway.  In the end, losses were tabulated at $4.6Bn.

In the current market, relative value proponents argue that the Federal Reserve is lowering rates so substantially that returns on cash are unattractive, that Treasury yields are too low to warrant investment, that credit is unappealing and that equities are therefore the place to be.

Although the equity yield/bond yield ratio is below the level that has historically signalled equity outperformance, it would be highly unusual for the bear market to last just one  month.  A massive unravelling of leveraged plays will likely still occur according to latest research reports.  The yen carry trade alone is an example where hedge funds borrow yen at low rates in order to invest the borrowed capital elsewhere to produce higher returns.  The expectation is that currency fluctuations will not negate the gain.

The past has demonstrated time and again how exotic financial strategies that are neck-deep in leverage  and premised on a relative value argument have proven disastrous for aggressive high-yield seeking, high-risk tolerant investors.  In contrast, the tried and true method of seeking absolute value and conducting due diligence with the intent of finding securities on sale with high intrinsic value, high cash levels, low relative debt, 15% returns on equity, and low PEGs has consistently proven a winner over time. 

Although we may consider creative option strategies, we should always know the premise on which we are applying a strategy to a specific stock.  In general, the application of a more aggressive strategy to a fundamentally solid stock offers greater opportunity to ride out the storms because we know that the internal strength of the company will be sufficient to produce a rebound long-term.  This knowledge injects us with confidence that our patience will be rewarded while we engage in adjustments.  Without following this methodology, fear can dominate and irrational, emotional decision-making can follow.  In this market, it is vital that we have strong conviction in every trading decision because the market volatility will certainly test our resolve.


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  1. sage words


  2. The following statement you make is fundamental and so appropriate

    “we should always know the premise on which we are applying a strategy to a specific stock. In general, the application of a more aggressive strategy to a fundamentally solid stock offers greater opportunity to ride out the storms because we know that the internal strength of the company will be sufficient to produce a rebound long-term”

    I try to follow Phil’s LTP to find these fundamentally strong stocks because who knows how many more storms we have to ride out!

    Your newsletters are always informative and interesting, thanks.


  3. Thanks so much raffy and xian!


  4. Sage- as always, fascinating and informative. I’ve read “When Genius Failed” but wondering if you recommend other histories of the LTCM story? My reading of that history was that LTCM employed a strategy that required stupendous leverage in order to be profitable, which seems (to me) to be forever inadvisable.


  5. Sage – Excellent post. I’ve also read Lowenstein’s Book “When Genuis Failed” His autobiography of Warren Buffett “Making of an American Capitalist” is one of the best bios I’ve ever read and gives a good account of his involvment in the LTCM disaster. If I remember right Buffett wasn’t involved since he was on a rare fishing excursion in Alaska with Bill Gates and he couldn’t be reached by phone.