Hi allThis is a really basic question but I realised I wasn't confident about my understanding of Sharpe ratio so wanted to check with you guys. Suppose I want to buy and sell EUR with GBP and I am only ever long or short 1 EUR (no more) to keep things simple.Strategy A: Buy one EUR hold it till the end of my trading window and then sell it.Strategy B: Buy and sell EUR through out my trading window with some funky top secret strategy though never holding more than 1 or less than -1.What is the Sharpe ratio of these strategies? The way I learnt it was that it is the excess return I require for a unit of volatility. What is excess return for Strategy B in this case? Is it the amount by which it outperforms a buy and hold strategy? Or is it simply 'outperformance' over zero. What is the volatility I should use? Is it the volatility of my pnl? For FX my intuition would say that its the excess return over zero (ie the return itself) that I should use. Thanks for any thoughts you may have.LS ps. I'm considering this at high frequency so I'm not bothered about differentials between risk free interest rates etc.

The formal definition of the Sharpe ratio is the excess return per unit of risk taken. You decide which bit is the excess part based on your desired return. So if you were running a cash equity portfolio it might be the portfolio alpha (ie the return in excess of the market), or if you had an absolute return strategy it might be that anything over zero is counted as excess. You have to define the return that you want and anything over this is excess. For currency, I would probably use risk-free rate of sterling, if that is your base currency, since this is the return you would hope to achieve if you didn't take any risk. You say that you are looking at intra-day / high frequency so essentially risk-free tends to zero. I think this is fine so long as you are not looking at building this up over a number of time periods. So if you just want sharpe ratio for a day then this policy works, but if you are looking at a portfolio strategy based over a number of trading sessions then it probably doesn't.The other important aspect of sharpe is that you keep your units consistent. If you are measuring your return over a day then the standard deviation (and yes, this is the standard deviation of your portfolio returns) must be factored so that it is the SD for the day. You must also ensure that you measure at even time intervals.

Thanks Maursh! I found a paper by Dempster that seems to agree with this too