Annualized Sharpe ratios and Volatilities

[Sebastian Sigl]

Good morning,

I have Monthly excess returns of two portfolios P1 and P8 over 29 years. For my master thesis I have to state the Volatilities and SR in one number, while these two numbers should be annualized. So far I have tried different approaches to calculate the needed results but I'm not sure which is the formally correct code to do so.

Here is an example of the code (for Portfolio P1) I think is correct and the data from 1990 and 1991. I know the Code Looks Kind of sloppy but I will put the calculations into loops later on.

egen Sd_P1= sd(P1), by(Jahr)
gen Sd_Annual= Sd_P1*sqrt(12)

gen SR= P1/Sd_P1
gen SR_annual= SR*sqrt(12)
egen SR_final= mean(SR_annual)

//To get my SD for P1
gen SD_final= Sd_Annual*sqrt(29)
  
 * Example generated by -dataex-. To install: ssc install dataex
clear
input float(date Jahr Monat P1 P8)
360 1990  1  -.0019377362   -.003668688
361 1990  2   .0008372813    .001459499
362 1990  3 -.00022618668   .0019396635
363 1990  4  -.0003067676   -.002378969
364 1990  5   .0004768702    .005065726
365 1990  6   .0006901055 -.00016673017
366 1990  7  -.0012268435  -.0008285865
367 1990  8  -.0027135995   -.005536701
368 1990  9  -.0011730944   -.004750926
369 1990 10  -.0017754886   .0002686236
370 1990 11   .0014749074    .005864478
371 1990 12   .0004333424   .0011803983
372 1991  1   .0016687294    .005055216
373 1991  2   .0041755983    .005791987
374 1991  3   .0020613207   .0019960906
375 1991  4    .002639579  .00008909535
376 1991  5  .00054460054    .002296731
377 1991  6  .00011390844  -.0020861127
378 1991  7 .000027179554   .0012150153
379 1991  8   .0017399964   .0015752286
380 1991  9 -.00013826239   .0004809036
381 1991 10  -.0008881435   .0013854794
382 1991 11 -.00016042936   -.002432231
383 1991 12    .000421264    .004964425
end
format %tm date

I think I am using the wrong scaling somewhere, even though the results look Kind of reasonable.

[Phil Bromiley]

You didn't get a quick answer. Thank you for providing code and sample data.

A few suggestions. Use descriptive variable names - you seem to be switching from English to German - fine if it doesn't confuse you. Many of us also just use lower case for variable names in almost all cases - saves remembering which are upper and which are lower. Remember most of us are not from your area so don't assume we understand SR and Volatility as they are used in your area.

I don't understand the sqrt(12). You are doing a standard deviation on monthly data in
egen Sd_P1= sd(P1), by(Jahr) So I can't see why the sqrt. There may be a legitimate reason for this, but egen with sd by Jahr gives you the standard deviation by year. I also wonder if the annual stockholder return is the mean or sum of the monthly returns.

[Sebastian Sigl]

Thank you for your advice phil.

I've changed the variable names to English. Volatility is the standard deviation of a certain variable. The Sharpe ratio is the generated excess return (given by P1 and P8), divided by the standard deviation of the excess return (variables P1 and P8). This means SR= Var1/sd(Var1), with Var1= P1 or P8 in this example data.

* Example generated by -dataex-. To install: ssc install dataex
clear
input float(date year month P1 P8)
360 1990  1  -.0019377362   -.003668688
361 1990  2   .0008372813    .001459499
362 1990  3 -.00022618668   .0019396635
363 1990  4  -.0003067676   -.002378969
364 1990  5   .0004768702    .005065726
365 1990  6   .0006901055 -.00016673017
366 1990  7  -.0012268435  -.0008285865
367 1990  8  -.0027135995   -.005536701
368 1990  9  -.0011730944   -.004750926
369 1990 10  -.0017754886   .0002686236
370 1990 11   .0014749074    .005864478
371 1990 12   .0004333424   .0011803983
372 1991  1   .0016687294    .005055216
373 1991  2   .0041755983    .005791987
374 1991  3   .0020613207   .0019960906
375 1991  4    .002639579  .00008909535
376 1991  5  .00054460054    .002296731
377 1991  6  .00011390844  -.0020861127
378 1991  7 .000027179554   .0012150153
379 1991  8   .0017399964   .0015752286
380 1991  9 -.00013826239   .0004809036
381 1991 10  -.0008881435   .0013854794
382 1991 11 -.00016042936   -.002432231
383 1991 12    .000421264    .004964425
end
format %tm date

To calculate the annual return you have to take the monthly returns, add 1 and multiply them, like this: (1+monthly return January)*(1+ monthly return February)…:

bys year: asrol P1, s(product) add1

What I want is to get the total standard deviation for P1 or P8 over the 29 years. I am not sure how to calculate it. Maybe calculate annual returns and get the standard deviation over this values?