Posted by Karl Denninger
Specifically, that Goldman Sachs pulled this off without cheating in some form or fashion?
Goldman Sachs, which makes more money from trading than any other Wall Street firm, also disclosed that its traders generated $100 million or more on 35 days during the first quarter and lost money on no days. The firm set a record when it made $100 million or more on 46 days in the second quarter.
No losing days in the entire quarter?
You are free to believe that this is solely due to “superior skill.” I, on the other hand, do not believe that on a statistical probability basis the record this firm has put together over the last two years in terms of the number of winning .vs. losing days is possible simply due to superior skill – that is, without cheating in some form or fashion.
Indeed, I would liken the odds of this being a matter of pure skill (or luck) to be somewhat similar to the odds of my pulling three royal flush’s in a row at the poker table – against a full house aces each time.
It will be quite interesting to see how the future of the firm plays in terms of litigation risk and whether this “record” holds up as being as represented in the fullness of time.
A bit of math for the geeky among you… or those interested in the odds of Goldman’s “perfect trading record” being achievable.
Let’s take a simple game of chance. We flip a coin and call “heads” a winning day, and “tails” a losing day. A pure game of chance with a 50% set of odds for each “trial.”
If we perform one flip, half the time it will come up heads, half the time tails (we will ignore the tiny chance of it landing on the EDGE and balancing – not exactly zero odds of that, but close enough.)
So what about if we perform four trials? What are the odds that the coin comes up “heads” all four times?
This is easily determined as 0.5 (odds on one trial) ^ 4, or the odds times itself four times over (to the 4th power)
This comes out to 6.25%. That is, if you did 100 sets of these four flips, in about six of them you would expect to have all four comes up “heads.”
In the first quarter there were 12 full weeks and four days, for a total of 64 week days. A couple of those days, however, were holidays during which the market was closed (Good Friday, New Year’s Day, etc.) so we will call it 60 trading days. This is a reasonable estimation for any given quarter.
So what are the odds that in a pure game of chance the coin would come up “heads” all 60 times?
That would be 8.67 x 10-19, or 8.67 times in 10,000,000,000,000,000,000 attempts (if I counted my zeros correctly.)
A trillion is 1,000,000,000,000,000, or 1015; this is about 1,000 times less likely than one in a trillion.
In the “real world” we have had 234 years of history in America. There have been, on average, 240 days (approximately) of trading in each of those years, or 56,160 trading days, and there have been 936 quarters. The NYSE was founded in 1792, so in fact there haven’t been that many days on which stocks have traded in the United States, but that’s close enough.
The odds of this outcome happening in any one quarter since the founding of the nation are approximately 8.1 x 10-16 or quite significantly (by close to 100 times) less likely than a one-in-a-trillion chance.
To put this in perspective you have a 1-in-500,000 chance each year of being hit by lightning while retrieving your mail, walking your dog, or taking a hike.
In comparison to that risk in ordinary life the odds of Goldman pulling this off in a game of chance are approximately forty million times LESS than the probability either of that event happening to you in the next year (again, assuming I’ve checked my zeros correctly.)
Should such an outcome happen on the street with the outcome subject to the exchange of money (that is, a wager) the gullible would hand over the wager. A person with a bit of knowledge of mathematics and even the tiniest bit of street smarts would react to such an event by pulling his sixgun and drilling the coin-flipper, as he would be certain (within HIS knowledge of having just been robbed) that the coin was rigged.
Now certainly trading is not a pure game of chance. Indeed, quite to the contrary; trading is allegedly a game of skill in the main.
I will leave it to you, and those who investigate frauds, to determine whether the application of skill, without any sort of cheating such as front-running client orders, insider information or other forms of rigging the markets, can turn the random chance odds of 8.67 x 10-19 into an event that has, in fact, actually occurred.