# Efficient Market Hypothesis

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Thorp’s original fund, Princeton Newport Partners, ran for 19 years (November 1969 to December 1988) and had an average annualized compounded gross return of 19.1 percent (15.1 percent after fees). It is not return, but rather the extraordinary consistency of return, that sets Thorp apart. Princeton Newport Partners compiled a track record of 227 winning months and only 3 losing months (all under 1 percent) – an extraordinary 98.7 percent winning percentage. To calculate the probability of this achievement if markets were efficient, we make the simplifying assumption that the average win and average loss were equal. (This is a very conservative assumption since, in fact, Thorp’s average win was significantly higher, which implies that the probability of Thorp achieving his win percentage by chance will be even lower than the estimate we derive.) Given the assumption that the average win and loss are about equal, the probability of any single trader achieving 227 winning months (or better) out of 230 is equivalent to the probability of getting 227 or more heads in 230 coin tosses, which is approximately equal to an infinitesimally small 1 out of 1 x e63. Even if we assume 1 billion traders, which is a deliberate exaggeration, the odds of getting at least one track record equivalent to or better than Thorp’s would still be less than 1 out of 1 x e62. To put this in context, the odds of randomly selecting a specific atom in the earth would be about a trillion times better. (The estimated number of atoms in the earth is 1 x e50)

There are two ways of looking at these results:

1. Boy, Thorp was unbelievably lucky!

2. The efficient market hypothesis is wrong.

“Hedge Fund Market Wizards” by Jack D. Schwager

giofranchi

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Thorp’s original fund, Princeton Newport Partners, ran for 19 years (November 1969 to December 1988) and had an average annualized compounded gross return of 19.1 percent (15.1 percent after fees). It is not return, but rather the extraordinary consistency of return, that sets Thorp apart. Princeton Newport Partners compiled a track record of 227 winning months and only 3 losing months (all under 1 percent) – an extraordinary 98.7 percent winning percentage. To calculate the probability of this achievement if markets were efficient, we make the simplifying assumption that the average win and average loss were equal. (This is a very conservative assumption since, in fact, Thorp’s average win was significantly higher, which implies that the probability of Thorp achieving his win percentage by chance will be even lower than the estimate we derive.) Given the assumption that the average win and loss are about equal, the probability of any single trader achieving 227 winning months (or better) out of 230 is equivalent to the probability of getting 227 or more heads in 230 coin tosses, which is approximately equal to an infinitesimally small 1 out of 1 x e63. Even if we assume 1 billion traders, which is a deliberate exaggeration, the odds of getting at least one track record equivalent to or better than Thorp’s would still be less than 1 out of 1 x e62. To put this in context, the odds of randomly selecting a specific atom in the earth would be about a trillion times better. (The estimated number of atoms in the earth is 1 x e50)

There are two ways of looking at these results:

1. Boy, Thorp was unbelievably lucky!

2. The efficient market hypothesis is wrong.

“Hedge Fund Market Wizards” by Jack D. Schwager

giofranchi

You are preaching to the choir.  However, the assumption that the average normalized loss is equal to the averaged normalized gain is not well founded.  At one time Thorp levered up and got into a position arbitraging AT&T stock against the when issued stock of the baby bells when AT&T was broken up.  That trade was the biggest ever that had taken place on the NYSE. The probability of that not going through was not zero, although very low.  If the government had changed it's mind at the last minute, the fund would have been wiped out.

Even so, his results do not support the efficient markets theory strong or weak form as stated.  What actually has been happening is that markets generally are becoming increasingly efficient as information access improves.

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What actually has been happening is that markets generally are becoming increasingly efficient as information access improves.

S&P500 Shiller P/E at 23, with all the western world engulfed in debt, just because Central Banks are printing money as never before… I think that, if we go back in history, very few times the markets had been less efficient than they are today. Time will tell.

giofranchi

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What actually has been happening is that markets generally are becoming increasingly efficient as information access improves.

S&P500 Shiller P/E at 23, with all the western world engulfed in debt, just because Central Banks are printing money as never before… I think that, if we go back in history, very few times the markets had been less efficient than they are today. Time will tell.

giofranchi

By efficient I meant tighter spreads  between all sorts of trades and strategies.  The profit margins of hedge funds have been narrowing in recent years.  For example, the sweet spot of Thorp's trades was convertible bond arbitrage.  That trade is far less profitable now than then.

Even the risk of a catastrophic  crash may be less than in earlier decades because of central bank intervention.  In my opinion, the US market would have been on track to a loss of 90% of its market value as happened in the 1930's except for massive intervention  by the Feds.

Never the less, a loss of 57% of market value by the S&P 500 hardly could be called efficient.  I'm not saying that markets are efficient, merely that they seem to me to be somewhat less inefficient than they used to be.  There should always be opportunities however because of the herding tendency, short term focus and aversion to volatility that we all have.  :)

A Schiller PE of 23 isn't inefficient by the Fed Model of pricing for equities.  But I hope we all know where this will lead.  At some point the worm will turn, inflation will kick in with a vengeance, interest rates will increase a lot, and the stock market will tank.

That may happen a lot sooner than Mr. Market thinks.

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