I’ve been reading a book called How Not to Be Wrong: The Power of Mathematical Thinking by Jordan Ellenberg
The author recounts a classic stock advisor scam that goes like this …
One day, you receive an unsolicited newsletter from an investment advisor, containing a tip that a certain stock is due for a big rise.
A week passes, and just as the Investment advisor predicted, the stock goes up.
The next week, you get a new edition of the newsletter, and this time, the tip is about a stock whose price the adviser thinks is going to fall.
And indeed, the stock craters.
That’s good, but it gets even better …
Ten weeks go by, each one bringing a new issue of the remarkable newsletter with a new prediction, and each time, the prediction comes true.
On the eleventh week, you get a solicitation to invest money with the investment advisor naturally with a hefty commission to cover the keen view of the market so amply demonstrated by the newsletter’s ten-week run of golden picks.
Sounds like a pretty good deal, right?
Surely the Investment advisor is onto something — it seems incredibly unlikely that a complete duffer, with no special knowledge about the market, would get ten up-or-down predictions in a row correct.
Let’s unpack the parable from 2 perspectives.
First, let’s calculate the “null hypothesis” odds that a non-gifted stock-picker is right 10 weeks in a row.
For simplicity, we’ll outboard weeks in which a stock doesn’t change from week to week and assume that a stock moves either up or down from week to week.
Since a “moving” stock either goes up or goes down, a non-gifted picker has a 50% chance of getting each prediction right,
So, the chance of his getting the first two predictions right is 1 in 4 = 25% … 50% x 50% … or 50% “squared”.
His chance of getting the first three right is 1/8 = 12.5% … 50% “cubed” – i.e. raised to the 3rd power .
Running the streak out 10 weeks, the odds of a non-gifted stock picker getting 10 consecutive right calls is 1 in 1024 … about 1/10th of a percent.
Pretty long odds, so it seems reasonable to reject the “null hypothesis” and to assume that an advisor who nails 10 straight calls does, indeed, have a Midas touch … right?
Not so fast.
Here’s how the scam works …. from the adviser’s perspective.
Flashback to the first week.
That first week, you weren’t the only person who got the advisor’s newsletter.
To make the math easy, let’s assume that he sent out 10,240 newsletters.
But, they weren’t all the same.
Half of them (5,120) were Version A (like your’s), predicting a rise in the stock.
The other half – also 5,120 – were Version B and predicted exactly the opposite … that the stock would drop.
The 5,120 people who got Version B from the advisor never heard from him again.
But you, and the 5,119 other people who got Version A — the correct pick — got another tip next week.
Of those 5,120 newsletters, half say what yours says and half say the opposite.
And after that week, there are still 2,560 people who’ve received two correct predictions in a row.
And so on.
After the tenth week, there are going to be ten lucky people who’ve gotten ten straight winning picks from the “gifted” investment advisor — no matter what the featured stocks did.
The math is simply the reverse of the probabilities calculated above … if the odds of 10 consecutive winning picks is 1 in 1,024 … then sending out 10,240 initial newsletters cascades down to 10 “winners” at the end of the 10 weeks.
It’s simple arithmetic.
The gifted investment advisor is more of a “grifter” investment adviser.
As long as he can keep mailing costs low (beware bulk rate posted advice) … and converts a high number of the folks who personally witnessed his “gift” to fee-paying customers … he can make some serious money … more because of his gift of math than his gift of stock picking.
Think about that the next time you witness results that seem too good to be true …