By default, everyone talks about ex post Sharpe ratios.

Take a time series, backtest, out pops a 'Sharpe ratio'.

No one says 'ex post' but that's inferred.

The implication is that what happened in the past is indicative of what will happen in the future.

Let's stop to think about the future for a split second.

Pundits predict and forecast, but the rest of us will just ponder and flounder in the ocean of possibilities before us.

Usually this 'floundering' is represented by a probability distribution function, which will say very high and low returns are not very likely.

The ex ante return probability distribution function can be described in many ways.

Perhaps it has a quarterly mean of 2%; a vol of 22%; and a skew of minus something or other .

If we sat down to generate hundreds of possible future returns and ratios we would see something along the lines of this,

a 5% chance of accruing a Sharpe of 3, and a 1% chance of a Sharpe of -8 over a future period!

Thinking about ex ante Sharpe gives us an appreciation of how wild a rollercoaster the future can be.

Compare the extremes of the distribution to the average of 0.08! Sure we might hit about average more often, perhaps 20% of the time, but it's incidental to the bigger picture.

(E.g. the math is simple: the worst loss has 100 times more downside and only a 20th less likely than the average)

It turns out that 0.08 is also the ex post quarterly Sharpe for the Nikkei 225 since the 80's, the markets are anything but average.

By simply breaking out ex post Sharpe into its constituent parts and then calculating ex ante versions, we now have a much richer idea of what's possible.

More here.