How to plot the mean-variance frontier in Stata?

[Jae Li]

Hi Statalists,

I would like to plot a mean-variance frontier for 10 decile portfolios but there are little resources in the Stata forum, so I wonder if there any Stata expert who is able to show me with an example of how to achieve that?

Many thanks for your help and hope to hear from you!

* Example generated by -dataex-. To install: ssc install dataex
clear
input float(exret_m ret_m rf mktrf smb hmlff P ym)
    .0790334       .0833334 .0043  .0047  .0411 -.0094 1 439
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 -.017113637    -.014213637 .0029  .0261 -.0215 -.0173 1 499
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 -.001412082 -.000012082035 .0014 -.0298  .0185   .004 1 504
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  -.04408973     -.04268973 .0014  -.008  .0104  .0413 1 509
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  -.03258663     -.03118663 .0014 -.0089  .0349 -.0418 1 511
  -.02101051    -.019610513 .0014  -.144   .063 -.1045 1 512
    .0223661       .0236661 .0013    .05  .1159 -.0514 1 513
-.0024049655   -.0012049653 .0012  .0482 -.0233  .0807 1 514
  -.01556255     -.01456255  .001  .0292  -.019 -.0197 1 515
  .006281037     .007281038  .001 -.0488   .042  .0062 1 516
  .015713431     .016713431  .001 -.0749 -.0387  .0187 1 517
 .0019898457    .0029898456  .001 -.0004 -.0403  .0281 1 518
  -.05482463     -.05392463 .0009  .1581  .0037  .0302 1 519
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   .05519151      .05589151 .0007  .0181 -.0257  .0165 1 522
   .06797187      .06877187 .0008 -.0059 -.0422  .0024 1 523
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  .014553398     .015353397 .0008  .0297 -.0329 -.0099 1 526
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   -.0383866    -.036586598 .0018 -.0162  .0063  .0131 1 540
   .11345788      .11555788 .0021  .0546  .0304  .0194 1 541
   .29228136      .29458135 .0023 -.0158  .0025 -.0132 1 542
 .0011352196    .0034352196 .0023 -.0307   .002 -.0117 1 543
  -.08277602     -.08037601 .0024 -.0125   .022 -.0158 1 544
  .018194526     .020594526 .0024  .0002  .0365  .0166 1 545
  .010804472     .013404472 .0026  .0436 -.0032 -.0132 1 546
   .02835132      .03115132 .0028   .017  .0001 -.0277 1 547
end
format %tm ym

[Attaullah Shah]

The dataset you have posted does not have a variable that records variance. Second, you have not specified which variable shall you use to build the mean-variance portfolio. The first step in building the frontier would be to find mean returns, then variance and then try a series of weights that would be used to create different return and variance combination. These combinations would be used in building the frontier. My website has some material on finding portfolio standard deviation, see this page http://www.opendoors.pk/StataHelp/po...atrix-in-stata
You can also see the help file of mvport package, I think there are some options in this package to build the efficient frontier.

ssc install mvport

[Jae Li]

Attaullah Shah Dear Professor Attaullah Shah,

Thank you very much for your reply and attached website!

I'd like to use monthly stock returns to build the mean-variance portfolios. I have over 20000 US common equity returns in one column in my dataset. From your example of the website, there are 4 individual stock return columns. However, in my case, how should I make the variance-covariance matrix from only one column of their stock returns? Also, how should I assign the stocks equal weight?

Moreover, I have read the help file of -mvport- package and intend to use the command -efrontier- to draw the frontier, but how to adjust my large amount of stock returns to do it? If I reshape them from long to wide, the Stata indicates the memory is insufficient to do that. Any ideas you may have?

Many thanks for your time and looking forward to hearing from you soon!

Best regards,
Jae

[Alberto Dorantes]

Dear Jae:
To reshape your dataset from long to wide, you need Stata SE or STATA MP since STATA IC only allows for 2,048 variables. However, if you have Stata SE and a dataset with 20,000 returns, and then you want to estimate the efficient frontier using these 20,000 returns, the command efrontier will not be able to do this. The reason is the limitation of the size of matrices in Stata, which is 11,000x11,000 for Stata SE/MP. You might need to program the efficient frontier in Mata.

Anyway, I am attaching a document about the efrontier command. It has general explanations and also some examples.
I hope this help.

Regards... Alberto

[FatimaZohra SABRANE]

Dear Attaullah Shah, the link you sent in #2 is no more available. Could you share an updated one please?
Also, in the attached file of Alberto Dorantes, the efrontier command should only be followed by returns (that are less than one). In my case, the returns are 100% each, and I already have the weights of each 'asset'. Is there a way to plot the mean-variance frontier based on weights instead of returns?
Thank you

[Attaullah Shah]

I forgot to post an updated link, the post was moved to this link https://fintechprofessor.com/2020/01...ata-and-excel/