I just read Irene Aldridge blog post titled “How Profitable Are High-Frequency Strategies?”.

AlthoughÂ no hard facts about the overall profitability of high frequency trading strategies are given, it got me thinking about something else. As Irene does in her blog post, she takes historical data and calculates the Sharpe rato of the absolute optimal, 20/20 hindsight, strategy based on historical data. Now of course, it’s not possible to actually have a strategy that is this good, unless you give me a time machine and let me play with that!

But is does however give an upper range value, something you could use to compare against your own models/strategies when doing back testing. The Sharpe ratio it self only gives you a number telling you how well you’re doing compared to the underlying benchmark. That is of course great when comparing two or more models against each other. But it does not tell you how much head room you have with regards to improving a specific model.

And this is where a relative Sharpe ratio would enter the picture. Take your models Sharpe rato, and divide that by the absolute maximum Sharpe ratio for the same test periode, and you have a number between zero and one. The closer that value is to the value of one, the better. I guess maybe you could also say that the more stable this value is over time, the better as well. In other words, your model can perform just as good no matter varying market conditions.

BTW Irene is the author of the brilliant book named High-Frequency Trading, a book I plan on writing a review of soon.

## 3 replies on “Relative Sharpe ratio”

While I think this can be interesting and I’ve done something similar before, I don’t think it answers the most important question. That question is if what you are getting is just lucky. You can use random portfolios to answer that question. You can learn more about this on http://www.burns-stat.com in particular the “random portfolio page” is http://www.burns-stat.com/pages/Finance/random_portfolios.html

“between zero and one” assumes your Sharpe ratio is always positive.

Regarding “between zero and one” and negative values, yes, that’s an issue.

Arguably, the Sortino Ratio is a better way of quantifying an investment’s performance than the Sharpe ratio. That’s because the Sortino Ratio does not consider upside volatility (i.e. large swings upwards in price) as bad, but the Sharpe Ratio treads upside and downside volatility equally. Anyway, if you go to http://optimizeyourportfolio.blogspot.com/2011/05/calculating-sharpe-ratio-with-excel.html there is an Excel spreadsheet to calculate the Sharpe Ratio (and can be easily adapted to the Sortino Ratio)