Binary trading is bad

Some of my mechanics-studying sixth-formers were discussing Binary Options yesterday.  This worried me a little because I have always taken it for granted that Mechanics was a superior discipline to Statistics and their scary lack of statistical knowledge has made me start to reconsider this!

When I described it as ‘gambling’ they corrected me: “it’s investing”.

The way it works is that you bet (sorry, ‘invest’) that over a particular time-frame (that might be only 5 minutes) a particular share or basket of shares will rise or fall in value.  That’s it.  Now, using your superior knowledge of the markets to decide that over a period of several days/weeks/months/years a particular company will rise or fall in value is one thing, but to get through the ‘noise’ of minute-by-minute share-dealing to say that a share will rise/fall immediately is very unlikely (unless Sir Alex has given you the tip that he is about to announce his resignation!).

Forbes business magazine puts it like this: http://www.forbes.com/sites/investor/2010/07/27/dont-gamble-on-binary-options/

Quoting that article:  One particular binary option website

pays $71 for each successful $100 “trade.” If you lose, you get back $15. Let’s say you make 1,000 “trades” and win 545 of them. Your profit is $38,695. But your 455 losses will cost you $38,675. In other words, you must win 54.5% of the time just to break even.

How did Forbes know that it would be 54.5% of the time?  I reckon my non-stats sixth-formers (and Higher tier GCSE pupils) can work this out for themselves.

Let’s call the probability you win p.

In the long run you will win 71xp dollars per ‘trade’.

The probability you will lose is (1 - p) and in the long run you will lose 85 x (1 - p) dollars.

To break even your wins and losses must be equal, so we have the equation:

71p = 85(1 - p)

Solving this gives p = 85/156

Which is about 0.54487

How to present this to a class?

Slide 1:

There is a particular type of gambling that is close to being random.  You pay $100 and if you win you get your stake back and also $71 in winnings.  If you lose you get $15 back.  Should you play?

Slide 2:   (Scaffolding)

Let’s call the probability that you will win each time p. 

How much will you win each game on average?

What is the probability you will lose?

How much will you lose each game on average?

What probability do you need so you will break even in the long run?

Slide 3:  Why do you get $15 back even if you lose?  What is the point of starting with $100 in that case?

I will try it out with a KS4 Higher class in a couple of week’s time.