Day trading and Sharpe Ratio

[Kevin Schmit]

Sharpe Ratio assumes that your returns follow a normal distribution and that you have sufficient sample.

The second part of that statement is true, the first it not. SR assumes a few things distributionaly, normality is not one of them. It assumes that the distribution has a second moment (e.g. no Cauchy...) and that the distibution's small sample properties are such that sample first and second moment estimates are reliable. It implicitly, for sample sizes typical of markets, assumes that the distribution is symetrical (e.g log-symmetric distros). If the distro is symmetric but leptokurtotic, the small sample properties of the sharpe will be even worse than usual.

That said, the gist of your posts is spot on. I have often thought that penalizing upside semi-variance (upside sd in the denominatior of sharpe) gives a better estimate of out-of-sample performance of optimized back-tested models than either variance or downside semi-variance.

 

[destriero]

So no Sortino for you!

 

[Kevin Schmit]

A trader with with a 5:1 PL ratio would get lower Sharpe than a 3:1 even if the risk per trade is exactly the same.

Only if the profits of the 5:1 trader all come from a few outliers.

Assume binomial distribution (results are either 5 or -1 with a 50/50 split). Expectations (numerator) are (5-1)/(5+1) and (3-1)/(3+1) times number of trades in a year respectively. Sigma (denominator) is calculated as sqrt(n * p * (1 - p)) where n is number of trades in a year.

Wprk out the math.

 

[sle]

The second part of that statement is true, the first it not. SR assumes a few things distributionaly, normality is not one of them. It assumes that the distribution has a second moment (e.g. no Cauchy...) and that the distibution's small sample properties are such that sample first and second moment estimates are reliable. It implicitly, for sample sizes typical of markets, assumes that the distribution is symetrical (e.g log-symmetric distros). If the distro is symmetric but leptokurtotic, the small sample properties of the sharpe will be even worse than usual.

Lol. When I was typing the original post, I was going to say “assumption of a certain class of distribution” but decided not to go down that rabbit hole and just say the assumption as normal. This said, an assumption of normality also provides a few little benefits such as easy calculation of leverage, confidence intervals etc.

 

[sle]

I sure would not center my trading around the Sharpe - to do so I would sharply lower my profits and in no way would it give me better risk mgmt.

Sure, all ET denizen are from the Lake Wobegon and thus do much better than the average.

On a more serious note, if there is one thing that hedge fund/prop industry has figured out its how to chase high Sharpe returns that are capacity constrained. So while I might believe the mythology of great day-trading in the 90s and early 2000s, I’d be very surprised if there are many (if any) of these guys yhat are still producing. Then again, what do I know.

 

[schweiz]

Then again, what do I know.

Apparently not as much as you think you know.

 

[schweiz]

 

[sle]

Apparently not as much as you think you know.

It would be sad if i knew everything. There are few things i know fairly well (for example, how to trade options and other vol products) and there are some things that I know okay (like fixed income). Most things, even in my profession, i merely dabble.

This said, I have seen a lot of professional as well as amateur traders and can make general conclusions. I am sure there are exceptional Day traders out there that can make money day and day out (human brain is an incredible instrument) but it is a bit surprising how many of them have assembled here :|

 

[srinir]

Old David harding of Winton's article about SR critique.
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.502.6609&rep=rep1&type=pdf

I had seen in my previous life return over CVaR used. That seems to be a good measure, since it incorporates expected short fall based on history.

 

[schweiz]

it is a bit surprising how many of them have assembled here

I can only speak for myself and your description does not fit me. Like it will probably not fit more people on ET. So you cannot judge everybody because a lot of people are fake (maybe even the majority). Because using the same logic I could say you are stupid.

I posted in posting 27 two examples that show the shortcoming of Sharpe ratio. Higher returns result in lower sharpe ratio, which is not logical. Sortino is better.