# Sharpe Ratio Redux

My favourite restaurant in Singapore is near City Hall.

Nalan's serves up the tastiest vegetarian food going. Every couple of weeks I go back and find a new and interesting dish.

At lunch today my girlfriend ordered Manchurian cauliflower. Deep fried cauliflower in a Hokkien Chinese sauce which usually coats chicken.

Think you know cauliflower? Not until you try it Manchurian style.

Quirky, curious but most of all tasty.

I enjoy revisiting my assumptions.

Visits to Indonesia always throw up situations like this.

Chocolate and grated cheese sandwiches, anybody?

If you are lucky enough to visit a local Betawi wedding in Jakarta. Don't expect a bouquet thrown at the end of the ceremony.

They throw a live chicken. First one to catch it is next to be hitched!

#### Revisiting Sharpe

Recently I found myself going back over the Sharpe ratio, discovering a couple of common gotchas:

Firstly, simple (or geometric) returns cannot be used to calculate the Sharpe ratio (even if you are using the correct geometric formula). Mainly because the geometric standard deviation is dimensionless and therefore cannot be measured in dollar amounts.

Secondly, Sharpe himself revisited his formula in 1994, years after he wrote about the original 1966 'Reward to Variability' ratio (the form most commonly used today).

The original formula is,

the revised formula is

There are a couple of subtle things to note.

One, the nomenclature has changed. The original refers to a 'risk free' rate. The latter to a 'benchmark'.

Two, both equations are equivalent if the benchmark does indeed have zero volatility. In a world without a risk free asset however, the revised formula is the only way to go.

Moreover, the numerator and denominator need to be an 'apples to apples' comparison.

Strictly speaking the revised formula is the only one that should be in use.

Sharpe concludes:

[I]t is essential that the Sharpe Ratio be computed using the mean and standard deviation of a differential return.

The upshot is that the Sharpe ratio is indistinguishable from the Information ratio and most Sharpe ratios you see in the wild are wrong!