Calculating Sharpe Ratio

[winnertakesall]

Can somebody confirm this? Let's say I have a hypothetical return of average 1% per month and that my monthly return standard deviation is also 1%. Then most of the monthly return is somewhere between 0 to 2%. The annualized Sharpe ratio would then be SQRT(12)*1/1 = 3.46. That's quite a high ratio given that my strategy only returns 12% per year. So is that right?

 

[traider]

Can somebody confirm this? Let's say I have a hypothetical return of average 1% per month and that my monthly return standard deviation is also 1%. Then most of the monthly return is somewhere between 0 to 2%. The annualized Sharpe ratio would then be SQRT(12)*1/1 = 3.46. That's quite a high ratio given that my strategy only returns 12% per year. So is that right?

Your formula is correct, so probably your values plugged in are wrong. Returns are clear cut so your stdev is probably wrong.

Easier way, take daily returns
Calculate std dev of this data series

Multiply by SQRT(256) = 16
That is your sharpe ratio.

 

[winnertakesall]

That was a just a hypothetical average return and standard deviation. But I do understand now why HFT typically has higher Sharpe ratio. Just the sheer number of trades (even with just a little bit alpha) can achieve smooth monthly earnings.

 

[jbusse]

First, here is the theory. In the world of spherical horses, whenever you sell the stock you get the proceeds of the sale and can turn around and buy another asset. That's what self-financing is really all about.

In real life, of course, that's a bit more tricky due to various issues. Primarily that you have to post the generated cash as collateral, creating a funding discrepancy - cash as collateral usually generates less interest than your long margin interest. Borrow rates, that you have mentioned, are part of your stock-specific risk and have to be accounted for in the strategy returns as opposed to financing. Again, in the world of big players, you frequently get negative borrow rates on easy to borrow names because of funding discrepancies.

However, the self-funding assumption still sort-of holds for the grownup players in this business. First, let's take an example. If you trade a futures on S&P, you have some exposure to the interest rate since you are implicitly financing some index arbitrageur out there. However, if you turn around and sell Dow Jones futures against it, you only going to have a tiny exposure on the margin amount. Now you can see how a market neutral combination of futures is self-financing, right? Similar to this example, most quant funds trade all securities on swap, which makes them effectively funding neutral (besides some tiny bid/offer).


Does that make sense?

Very nicely explained.

In theory, the math for the numerator of the Sharpe ratio in the context of a market neutral strategy works out to:

(Long - risk free) - (Short - risk free) = Long - Short, as risk free cancels out.

 

[sle]

Can somebody confirm this? Let's say I have a hypothetical return of average 1% per month and that my monthly return standard deviation is also 1%. Then most of the monthly return is somewhere between 0 to 2%. The annualized Sharpe ratio would then be SQRT(12)*1/1 = 3.46. That's quite a high ratio given that my strategy only returns 12% per year. So is that right?

Sharpe ratio does not tell anything about the return on capital, but rather it’s an indicator of signal to noise. If you are uncertain about the numbers, go ahead and calculate sharpe ratio on dollar PNL, you should get similar value.

 

[nonlinear5]

Sharpe ratio = (Average Portfolio Return - Risk free rate of return) / STDEV of returns

The formula that you cite is from the original formulation, published in 1966. Sharpe has revised it in 1994 to this:

Sharpe ratio = (Average Portfolio Return - Risk free rate of return) / STDEV(excess returns)
If the risk free rate is 0, the 1994 version reduces to the 1966 version.

From my research, it looks like the 3 month T-bills rate is considered the risk free rate of return. My question is do I need to determine the T-bill rate for each time period in the calculation?

Yes, if you want to be precise, you should use a separate risk-free rate for each period. For a simplified method, assume risk free rate to be 0, which reduces the formula to:
Sharpe ratio = Average Portfolio Return / STDEV of returns

Then you need to annualize it, as suggested in the previous posts.

 

[fan27]

Finally getting around to adding Sharpe Ratio to my platform. One more question.

Assume I had the following returns:
2015: 12%
2016: 18%
2017: 19%
2018: 23%
2019 (YTD): 4%

How should I handle 2019 since the year has not completed and it introduces a misleading deviation in returns. Should I do something like (365/CurrentDayOfYear) * 4% to extrapolate the YTD return to a yearly value?

thanks

 

[sle]

How should I handle 2019 since the year has not completed and it introduces a misleading deviation in returns. Should I do something like (365/CurrentDayOfYear) * 4% to extrapolate the YTD return to a yearly value?

What you should do is look at periodic returns (daily, weekly, monthly, whatever you think is applicable), calculate the Sharpe ratio for that return periodicity and then rescale it to the annualized form. E.g. if you have daily data

annualized_sharpe_ratio = sqrt(252) * mean(daily_returns)/stdev(daily_returns)

PS. There is a lot of little things that surround S/R that are worth implementing too, like confidence intervals given the sample size, Sharpe decay rate etc

 

[fan27]

What you should do is look at periodic returns (daily, weekly, monthly, whatever you think is applicable), calculate the Sharpe ratio for that return periodicity and then rescale it to the annualized form. E.g. if you have daily data

annualized_sharpe_ratio = sqrt(252) * mean(daily_returns)/stdev(daily_returns)

PS. There is a lot of little things that surround S/R that are worth implementing too, like confidence intervals given the sample size, Sharpe decay rate etc

Excellent...thanks!

 

[winnertakesall]

How do you calculate Sharpe decay rate?