Minimum Variance Portfolio Suppose there are N stocks in the investmentable universe and we have a fully invested portfolio investing 100% of the capital. The Covariance matrix is denoted as ∑. We are interested in finding the portfolio with minimum variance. An investor choosing this portfolio is only concerned about the risk of the portfolio. Denoting a vector of ones by i=(1,….,1)^' , we have the following optimization problem:
$$Minimize \frac{1}{2}w'∑w$$

$$Subject to : w’ .i = w_1 + w_2 +……+ w_N =1$$

I would like to solve above problem using Lagrangian multipliers.

  • $\begingroup$ What have you tried? Google seems helpful. $\endgroup$ – Bob Jansen May 29 '16 at 12:42
  • $\begingroup$ I'm voting to close this question as off-topic because this requires more effort from the OP. $\endgroup$ – Bob Jansen May 29 '16 at 12:42
  • $\begingroup$ Bob from your perspective it requires lot of efforts, but may be someone in the forum can answer...kindly keep it open. $\endgroup$ – Atul Agarawal May 29 '16 at 12:44
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    $\begingroup$ @ Neeraj, Sir I know there are several packages in R, but I don't know much about R. I like if you can guide me from the scratch. I have 10 yrs of historical data in separate .csv file. $\endgroup$ – Atul Agarawal May 30 '16 at 2:02
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    $\begingroup$ @AtulAgarawal You have to show some effort. We can only help you on specific issue. Your question appear to be more like a complete college assignment. BE SPECIFIC what you want to ask. Donot get demotivated if your question gets closed. Just show some effort from your side and we are always here to help you. $\endgroup$ – Neeraj May 30 '16 at 12:01