# Mean Variance Optimal Portfolio

**URL:** <https://discourse.julialang.org/t/mean-variance-optimal-portfolio/6607>\
**Category:** Finance and Economics\
**Tags:** question\
**Created:** [October 22, 2017, 10:35am UTC](https://discourse.julialang.org/t/mean-variance-optimal-portfolio/6607 "2017-10-22T10:35:57Z")\
**Posts on this page:** 7\
**Page:** 1

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**Author:** ![adwelch](https://avatars.discourse-cdn.com/v4/letter/a/c77e96/32.png) [@adwelch](https://discourse.julialang.org/u/adwelch)\
**Post date:** [October 22, 2017, 10:35am UTC](https://discourse.julialang.org/t/mean-variance-optimal-portfolio/6607/1 "2017-10-22T10:35:57Z")

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Hello, I have n risky assets and no risk free asset and risk aversion parameter is 4(gamma). I want to use mean-variance criteria to compute optimal portfolio weights. From historical data, I have expected return data or data matrix on n risky assets, r = […] (r is a two dimensional Python array where each row represents an asset and column represents net returns). I also estimated mu and variance-co-variance matrix sigma from historical data. I would like to convert my python code to Julia code to compute the mean, variance and optimal portfolio weights. Can anyone please suggest me how can I write it on Julia. Here I have Python code.

```julia
gamma=4
n=r.shape[1]
mu=r[:,0:n].mean
sigma=cov[r:,0:n]
onematrix=ones(n)
numer1=dot(onematrix.transpose(),inv(sigma))
numer2=dot(numer1,mu)-gamma
denominator=dot(numer1,onematrix)
numer3=dot(numer2,inv(denominator))
result=mu-numer3
weight=(1.0/gamma)*dot(inv(sigma),result)
return weight

```

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**Author:** ![Tamas\_Papp](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tamas_papp/32/25949_2.png) [@Tamas\_Papp](https://discourse.julialang.org/u/Tamas_Papp)\
**Post date:** [October 22, 2017, 10:44am UTC](https://discourse.julialang.org/t/mean-variance-optimal-portfolio/6607/2 "2017-10-22T10:44:30Z")

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> [@adwelch](#):
>
> I am a new user of Julia

I you are a new user, you should probably make an effort to learn the language. The example about should be very straightforward to translate to Julia. See, in particular, [algebra](https://docs.julialang.org/en/latest/manual/mathematical-operations/) and [arrays](https://docs.julialang.org/en/latest/manual/arrays/).

(is this [homework](https://discourse.julialang.org/t/homework-policy/2342/17)?)

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<div class="post-metadata">

**Author:** ![adwelch](https://avatars.discourse-cdn.com/v4/letter/a/c77e96/32.png) [@adwelch](https://discourse.julialang.org/u/adwelch)\
**Post date:** [October 22, 2017, 3:23pm UTC](https://discourse.julialang.org/t/mean-variance-optimal-portfolio/6607/3 "2017-10-22T15:23:30Z")

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No, its not homework. Just have been trying to practice few of my R and Python work into Julia. So here what I have tried on Julia:  
gamma=4,  
n=length[:,1:end]  
mu=mean(r[:,1:end])  
sigma=r[:,1:end]  
onematrix=ones(n)  
numer1=transpose(onematrix).\*inv(sigma))  
numer2=numer1.\*mu-gamma  
denominator=numer1.\*onematrix  
numer3=numer2.\*inv(denominator))  
result=mu-numer3  
weight=(1.0/gamma)\*inv(sigma)\*result  
println( weight)

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<div class="post-metadata">

**Author:** ![Tamas\_Papp](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tamas_papp/32/25949_2.png) [@Tamas\_Papp](https://discourse.julialang.org/u/Tamas_Papp)\
**Post date:** [October 22, 2017, 3:29pm UTC](https://discourse.julialang.org/t/mean-variance-optimal-portfolio/6607/4 "2017-10-22T15:29:07Z")

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You may get better help if you post a _self-contained minimal working example_ that highlights where you got stuck. The above code is not that, but a couple of comments:

1. `length` may denote a variable, but it is also a function in Julia, use something like `lengths` or `len` (cf `c(...)` in `R`). Or did you mean `length(...)`?
2. You can use `'` for transpose.
3. You can use Greek letters (try typing `\mu` and press `TAB`), your code will be much more compact.
4. If `n` is an integer, `ones(n)` will give you a vector of `1.0`s. Use `I` for the identity matrix.

Also, please delimit your code with ```julia … ```.

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<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [October 22, 2017, 3:35pm UTC](https://discourse.julialang.org/t/mean-variance-optimal-portfolio/6607/5 "2017-10-22T15:35:13Z")

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> [@adwelch](#):
>
> So here what I have tried on Julia:

I can’t run that example because I do not know what any of the variables are. Please give a full example otherwise we can’t help. One thing I do see is that `mu=mean(r[:,1:end]` had a syntax error because it’s missing a `)`. Since you didn’t describe what your error is, I assume that might be it?

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**Author:** ![Paul\_Soderlind](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/paul_soderlind/32/1753_2.png) [@Paul\_Soderlind](https://discourse.julialang.org/u/Paul_Soderlind)\
**Post date:** [October 22, 2017, 4:17pm UTC](https://discourse.julialang.org/t/mean-variance-optimal-portfolio/6607/6 "2017-10-22T16:17:49Z")

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Hi,

“chapter” 3 of these (fairly easy) tutorials shows one way of doing these calculations:

[https://github.com/PaulSoderlind/FinancialTheoryMSc](https://github.com/PaulSoderlind/FinancialTheoryMSc)

/Paul S

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<div class="post-metadata">

**Author:** ![adwelch](https://avatars.discourse-cdn.com/v4/letter/a/c77e96/32.png) [@adwelch](https://discourse.julialang.org/u/adwelch)\
**Post date:** [October 23, 2017, 1:23am UTC](https://discourse.julialang.org/t/mean-variance-optimal-portfolio/6607/7 "2017-10-23T01:23:48Z")

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Prof. Soderlind, thank you so much. Your web site is a great resource for Macro-finance and for Julia. My humble appreciation and respect to you.