Sharpe Ratio Calculation - please clarify

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hilbert
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Sharpe Ratio Calculation - please clarify

Postby hilbert » 23 Feb 2012

Can MC team please clarify how Sharpe ratio is calculated in the performance report ?

For intra-day strategies, I tried annualizing daily returns and daily standard deviations but my Sharpe ratio calculated in spreadsheet is very different from that in Strategy report.

I also used "Average monthly return'' and "Monthly Return Stddev" available in "Strategy Performance Summary" section of the performance report and tried to compute annualized sharpe ratio, but this also didn't match with Sharpe ratio computed by MC. Also tried quarterly but that also didn't match.

Posting an example here: Interest rate set to 0 in Strategy properties
Average monthly return : 41.33
Monthly Return Stddev : 106.12
Annualized Sharpe Ratio : (41.33*12)/(106.12*SQRT(12)) = 1.35.
However, MC computes Sharpe ratio as 0.39.

Attached is the screenshot. Thanks
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Henry MultiСharts
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Re: Sharpe Ratio Calculation - please clarify

Postby Henry MultiСharts » 23 Feb 2012

Hello Hilbert,

Sharpe ratio calculation has been already discussed in the following topic.

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Re: Sharpe Ratio Calculation - please clarify

Postby hilbert » 23 Feb 2012

Hi Henry,

Thanks for reply. I checked the link you mentioned, that post just gives the formula for computation of Sharpe ratio. If you see my post above, I have given an explicit example which shows problem with Sharpe ratio calculated in Multicharts.

Can you please look at the example I have given and please point out mistake, if any? Also, I read an earlier post from MC team (sometime in 2007) that MC calculates Sharpe ratio correctly but displays it incorrectly! Is this related to that problem? or I am missing something here.

Thanks.

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Henry MultiСharts
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Re: Sharpe Ratio Calculation - please clarify

Postby Henry MultiСharts » 23 Feb 2012

Hello Hilbert,

MR (average return for period (monthly))=41.33
RFR (risk-free rate of return or Interest rate)=0
SD (standard deviation of returns)=106.12
SR (monthly)= (MR - RFR) / SD=(41.33-0)/106.12=0.389 or 0.39

Why do you multiply Monthly Return Stddev by SQRT(12) to get annual Sharpe Ratio?

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Re: Sharpe Ratio Calculation - please clarify

Postby hilbert » 23 Feb 2012

Hey Henry,

Thanks again! Now I see what you guys are doing. Well, I am afraid its not the correct way to compute Sharpe.

First, Sharpe is always, always quoted as an annualized number. You can use either 'quarterly returns and quarterly std deviations' or 'monthly returns and monthly std deviations' or 'daily returns and daily std deviations' to compute the annualized Sharpe. So, Multicharts is way off here from the standard practice, since its not reporting 'annualized Sharpe number'.

First step to compute annualized Sharpe using 'monthly average return' and 'monthly standard deviation' is to multiply 'monthly average return' by number of months in a year (which is 12) and multiply 'monthly standard deviation' by square root of number of months in a year (therefore SQRT(12)). The reason to multiply standard deviation by square root lies in the underlying assumption of lognormal distribution of asset price theory - Sharpe ratio is derived using this theory only. "'Basically, volatility(=standard deviation) increases with square root of time and not linearly with time.""

An example will help. Say, you are returning 1 % every month, so in a year total return would be 12%. Assume the monthly standard deviation is 1.5% per month. For the whole year your standard deviation will not be 18% rather it will be 1.5%*SQRT(12) = 5.2%.

What Multicharts is doing now is that it is hugely under-reporting Sharpe ratios because it is not annualizing them. This is something that should be fixed. Will just need 5 minutes to change the formula in the code - and it will be done. I haven't checked other performance ratios, but maybe they are also not annualized.

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Henry MultiСharts
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Re: Sharpe Ratio Calculation - please clarify

Postby Henry MultiСharts » 24 Feb 2012

Helbert,

In MultiCharts report we calculate Sharpe ratio for the monthly period. This calculation method is inspired by Hedge Fund Returns, which is considered as industrial standard.

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Re: Sharpe Ratio Calculation - please clarify

Postby hilbert » 24 Feb 2012

Sorry but your information is wrong. All hedge funds, asset managers etc. report annualized sharpe ratios only. Let me offer you 2 examples using CTA data which is readily available.

1) http://www.autumngold.com/Advisor/Stati ... hp?id=9094

Copy the return data into excel and then you can easily compute following
Average monthly return: 1.74%
Monthly standard deviation: 9.07%
Monthly Sharpe: 1.74/9.07 = 0.19 (Multicharts way)
Annualized Sharpe: (1.74*12)/(9.07*SQRT(12)) = 0.67 (Industry Standard way)

You can see the Sharpe quoted on the report is 0.58

The reason for discrepancy is that above calculations assume 0 Risk free rate. Put in a 2.75% Risk free rate and you will get Annualized Sharpe to be 0.58, thus matching with report Sharpe on the website.

2) http://www.autumngold.com/Advisor/Stati ... php?id=124

Average monthly return: 0.56%
Monthly standard deviation: 2.28%
Monthly Sharpe: 0.56/2.28 = 0.24 (Multicharts way)
Annualized Sharpe: (0.56*12)/(2.28*SQRT(12)) = 0.84 (Industry Standard way)

You can see the Sharpe quoted on the report is 0.49. Use a Risk free rate of 2.75% and you will get a Sharpe of 0.50, very close to reported Sharpe of 0.49.

In case you are wondering if my choice of 2.75% risk free is arbitrary, please note that in both the above examples, monthly sharpe is way less that reported sharpe. if you use 'any' risk free rate not equal to 0, the monthly sharpe will reduce even further.

I hope I have been able to convince you now and you will get the formula changed in multicharts code. Trust me the industry standard way is to compute and report Annualized Sharpe only and nothing else. No offense, but I know what I am talking about here. Thanks a lot.

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Re: Sharpe Ratio Calculation - please clarify

Postby danigiu » 26 Feb 2012

Thank you Hilbert to clarify why I always got so low sharpe values in MC for the same strategy compared with TS, its a monthly value so should be multiplied by sqrt of 12 to get the annual value.I also agree that would be better to modify the code and get the annual value which I believe is much more used.

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Re: Sharpe Ratio Calculation - please clarify

Postby Henry MultiСharts » 28 Feb 2012

Hello Hilber, Danigiu,

We cannot disagree that the performance reports on some websites can contain Annualized Sharpe Ratio, but we were under impression that Monthly Sharpe Ratio calculation was more widespread in the trading software packages. For example, TS also calculates Monthly Sharpe Ratio. So we implemented it this way to provide backward compatibility of the strategy performance reports. It should not be difficult to estimate the Annual Sharpe Ratio based on the Monthly SR results.

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Re: Sharpe Ratio Calculation - please clarify

Postby hilbert » 28 Feb 2012

Hey Henry,

Since I have now got this figured out that reported Sharpe is monthly Sharpe and I can easily convert it into annual, I have no problem. My initial motivation was just to know what is going on here. Thanks for help.

Cheers,
Hilbert

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Re: Sharpe Ratio Calculation - please clarify

Postby MAtricks » 21 Feb 2014

This clears up a lot. I've ignored the MC sharpe and sortino because they were so far "off". Now it all makes sense.

Henry, I think MC should consider changing these metrics to annualized calculations.


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