Smokin' Out Good Strategies

My other half and I are considering moving to Beijing.

The big smoke.

A polluted day is the equivalent to between one sixth and 21 cigarettes per day.

I don't smoke, but I'd rather a regulated cigarette than a week of breathing polluted air.

Nevertheless the analogy is helpful.

Same Old Speel

People love stories and finance is just a series of analogies.

For example, imagine bond prices are diffusing into the air like pollution does.

Maybe I got that a little wrong, asset prices aren't causing the pollution!

Remember, analogies are never exact, but helpful.

Another try, suppose, someone is trying to sell us an investment product and quotes a Sharpe ratio of 1 (i.e. we earn one dollar for every dollar of volatility risk).

Probability(Rubbish) = tdist(Sharpe * 1, 1, 1)

If they show us a year of data, there's a 25% chance of this 'strategy' being rubbish.

Multi Year Probability(Rubbish) = tdist(Sharpe * SQRT(Years), Years-1, 1)

[Good explanation here and here]

That means the ten year Sharpe of 1.1 from the previous Meb-Faber-esque timing model over 10 years is quite low! Odds are about the same as someone being arrested for drunk driving (0.5%).

The original research paper quoted a lower Sharpe of 0.73 using 40 years of data (again, who invests in any one product for 40 years?). Similar to chances of being killed by a tornado (0.002%).

Of course, there is a large assumption. How many little tweaks and similar models were brushed under the carpet on the way to publishing this strategy and its Sharpe?

In other words, let me flip a coin once, I have a one in two chance of seeing a head. Let me flip twice and I have a much better chance!!

Tweaked

How many times was the Meb Faber Timing strategy flipped before something convincing was found? It's impossible to tell.

But let's look at the different moving pieces.

A) Trading logic based on a 10 month moving average. The length of time could've been tweaked (this is alluded to in the paper)

B) Trading is executed on a monthly basis. Longer and shorter time frames are mentioned in the paper

C) Five asset classes are included plus cash. Different numbers are also included in the paper. Other combinations could have been used too, which we'll give the benefit of the doubt and ignore for now

How about we assume three different options were considered for each moving piece? Not unreasonable with modern technology (perhaps low). Let's say 27 different combinations of parameters were investigated.

We are left with a one in two hundred chance (0.002%*3^3) of the strategy being completely rubbish (or being caught drunk driving).

Not bad at all.

Of course, allow a few more tweaks and the small number grows rather quickly.

Heap on another moving part and the result will be almost definitely nonsense.

Like the coin flip example. Except you never know how many times it took to fish around for a 'winning strategy'.

In finance, as with other walks of life, laziness is a virtue.

[Big thanks to Jonathan Ng for a comment which led me to correct the formulae]