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Jericho
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Adjusted Sharpe Ratio

May 29th, 2022, 7:22 pm

Hi Guys 

Have a question on Sharpe ratio and specifically Adjusted Sharpe Ratio.  Basically my company is calculating the sharpe ratio for individual traders as follows:

Assume 6 days for the current period (for simplicity in this example) where the trader makes the following Dollar PL: 100k, -60k, 1M, 400k, -90k and -600k.  We have a dollarised ANV of 400M so our 6 daily returns are 0.025%, -0.015%, 0.25%, 0.1%, -0.0225% and -0.15%.  So for Sharpe we are taking Average of returns and annualizing to get 7.88% as per Excel.  for Annualised SD its simply STDEV(returns) * square 252 to get 2.14% so my sharpe (SR) is 3.69

I feel they should also include Skew and Kurtosis here to get a get an Adjusted sharpe ratio as per the work of Pezier (2006) - so for Skew in Excel I get 0.564.  My understanding is that the KURT function in Excel is excess kurtosis so this gives me 1.02.  So Im converting this to sample kurtosis via a formula I foun don google (Sample Kurtosis = Excess Kurtosis + 3(n-1) squared / (n-2)*(n-3) to give me 7.27 in this case.

However when I plug this into the Adjusted Sharpe RAtio formula I get a bizarre number; the formula I have is ASR = SR * (1+(Skew/6) X SR - (Kurtosis-3/24)*SR squared).

Can someone please check over my workings and method?  Im clearly doing something wrong

Bottom line is I want to use an ASR which penalises negative skew and fat tails rather than using a very general Sharpe ratio that my company is currently using - any advice offered would be appreciated as always

Thanks so much

J.
 
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Alan
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Re: Adjusted Sharpe Ratio

May 31st, 2022, 2:55 am

1. Look carefully at (7) here
2. That corrected, 6 days will probably produce nonsense anyway. I suggest at least 20 days, or better: 252 days or more. 
3. You really need confidence intervals. Run some simulations with iid drawings from the daily market empirical distribution. Draw N days say 10,000 times, to produce a sampling distribution and hence, a confidence interval for your ASR statistic.
 
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katastrofa
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Re: Adjusted Sharpe Ratio

May 31st, 2022, 10:54 am

I cannot understand finance folk's fondness for higher moments such as skewness and kurtosis. They have huge variance, especially for small samples. If one wants to penalise for negative PL, why not compare the bottom quartile or something similar? Not sure what average Jericho uses, but for small samples I'd use geometric mean. Anyway, a 6 point sample is no sample.
 
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Jericho
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Re: Adjusted Sharpe Ratio

June 1st, 2022, 8:01 am

Thanks for your answers and suggestions - I was only using n = 6 as an illustration.

In reality, what my organisation is doing is every month calculating a sharpe ratio by taking the 22 observations (business days) in any given month, taking the average of those returns and then dividing my the standard deviation.  Thats it..

My understanding is that the Portfolio manager's payout is a function of that sharpe ratio (presumably an average of the 12 different sharpes for the year)

My question was is this too simplistic - should we draw skew and kurtosis to get a better measure and if we do use confidence intervals how can we then use that to determine a trader payout?  

I hope that makes more sense and thank you again for your time
 
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Alan
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Re: Adjusted Sharpe Ratio

June 1st, 2022, 3:10 pm

You're welcome.

The purpose of the confidence intervals is to, well -- give confidence -- to any estimate of a statistic. How close is it likely to be to a putative 'true' value?

Let me play devil's advocate with respect to any trader compensation scheme based upon Sharpe ratios, adjusted Sharpe ratios, low moments, etc.

Consider the following. I'm the trader and my strategy, from Nov 2010 through Feb 2018 is to invest 100% of my capital allocation to a long position in the former XIV (Velocity Shares Daily Inverse VIX).

1.  What would have been my yearly compensation under any of the proposed rules?
2.   What went wrong?
3.  What are the lessons and fixes?
 
 
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Alan
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Re: Adjusted Sharpe Ratio

June 1st, 2022, 5:24 pm

BTW, to be clear, the direct answer to your question is, yes, Sharpe ratios are too simplistic -- esp. when a portfolio has significant optionality. There is a big literature on adjusting performance measurement stats to account for this. I had an ancient contribution myself: Semivariance and the Performance of Portfolios with Options

But the point of my XIV example is that performance statistics alone, regardless of what they measure, can be a trap. That's because, ultimately, they provide only a noisy, backwards-looking, superficial view of a trading strategy.
 
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Jericho
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Re: Adjusted Sharpe Ratio

June 2nd, 2022, 10:25 am

Thanks v much, Ill have a read of that paper, looks like the link you have shared is a summary, but the semi variance is definitely interesting.
 
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Alan
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Re: Adjusted Sharpe Ratio

June 2nd, 2022, 4:45 pm

Thanks -- I attach a scan.
Attachments
Lewis.FAJ.Semivariance.PDF
(6.09 MiB) Downloaded 127 times
 
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Jericho
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Re: Adjusted Sharpe Ratio

June 5th, 2022, 1:05 pm

Thanks Alan - Ive had a read of this.  Final question I have is given what I need to do (Calculate a sharpe ratio for a given month with 22 observations), Do you see any problems with me (i) Calculating a sharpe but using the Semi variance measure as the denominator of the sharpe as per your paper and (ii) Further adjusting the Calculated sharpe for Skewness and Kurtosis (ASR) as per the paper you attached earlier in the thread.  DO you think this will result in a sharpe ratio that has more meaning and intuition behind this?  Or should I stay with just the semi variance approach and leave it as that?

Rgds
 
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Alan
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Re: Adjusted Sharpe Ratio

June 6th, 2022, 2:12 pm

I would consider Sharpe with sqrt(semivariance), but not further adjust as that double compensates for skewness. Also I would develop confidence intervals for both regular and semivariance-Sharpe and do XIV study.