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Interest rate swap doing your head?


Sophisticated Investor 2

In our earlier post, we stated that the requirements forsophistication were:

a) Knowledge
b) Experience
c) Ability to conceptualise

Here’s Dara O’Briain’s Brainteaser in full:

You and your mate aresharing a carton of 100 fries. You take it in turn to eat between 1 and 10fries. Whoever eats the last fry has to perform a humiliating dance. To avoid that, shouldyou offer to go first or second?

Now, the trick is easy once you know it. Youalways go second, and make sure that you take the number of chips that makes hislast take up to 11. So if he took one, you take 10, if he took 2 you take 9, and so on.

So after your go, the number of chips taken is in total 11 after the first 2 goes, then 22 after 4 goes, then 33, and so on, up to 99.

So on his next go, he has to take the last one.

Now, imagine that you are trying to turn this into a pub trick, to make some money betting on the outcome.

You want to play your opponent several times, with increasing stakes.  You may let him win the first couple of games, when he doesn’t realise there’s a pattern. After that, you start the betting, ‘to make it interesting’, and win back what you lost. He believes that you’ve been lucky, and increases his stakes, ‘to win back what he’s lost’.  That’s when you get him.

How might you do this?

Starting off, you take care not to show him there’s a pattern. You let him win a few games by not playing the best strategy. That’s the way to disguise the method.

Let’s suppose you have now won a couple of games using the best possible strategy. You are ahead on money, but your opponent is getting smart to the trick, and is insisting on going second. What do you do?

We’ll find out later.

(Note, if a bank were doing this, it would have brainstorming sessions, and test ideas on its staff, before trying it out on the public!)

What you could do is say “Let’s change the game. You can choose the number of chips, and you can go first! Can’t say fairer than that!”

Now you clearly wouldn’t let him have just one chip. What you insist is that the total number is more than 100.

There are now two things you need to know.

If the total number of chips is one more than a multiple of eleven, (e.g., 176+ 1 = 177, then the second player will always win if he plays the best strategy. If it is any other number, the first player wins. This can be shown easily, as the first player just removes enough chips to leave the multiple of eleven plus one. So if he doesn’t really understand the rules, you stand at least 10 chances in 11 of winning (at least because he might guess right and still make a mistake). Good enough odds for you?

OK, enough maths! The purpose of this is to show that what is quite a simple game can be converted into what is effectively a profitable con trick - but a lot of playing around is needed to develop the ‘sophistication’ to manage a winning strategy.

Almost certainly, banks’ technical staff would have played around with swaps and collars for a long time, and developed similar ideas to sneak in extra profit to their sales. Doing this improves their ability to conceptualise, which is part of the sophistication test described above.
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