# How can I select the least correlated portfolio of assets?

Can anyone explain the process and the calculations needed to select a portfolio of liquid futures assets with the least correlation? Given a set of returns for a series of assets, how do I select the best subset such that I minimize their correlation with each other?

• This could be better phrased, and I think you would get the answer you want, while helping people answer it. Perhaps- "Given a set of returns for X series of assets, how can I select the best Y assets such that I minimise their correlation with each other?" or similar?
– user407
Feb 15, 2011 at 13:10
• Yes, that's more clear! Feb 16, 2011 at 6:49
• Although this question is vague, the following more recent question is very similar but more specific. Aug 21, 2011 at 1:29

Since you are asking for low correlation of the assets, I'm guessing that you are really trying to get a low (or minimum) volatility portfolio. If that is the case, then the steps for one approach are:

• estimate the variance matrix of the universe of assets
• use a portfolio optimizer to select the minimum variance portfolio given your constraints

This assumes that you don't have preferences in terms of expected returns of some assets over others. That seems to be implied from your question.

You don't indicate the size of your universe. If it is large, then you'll want to use a factor model or shrinkage model rather than the sample estimate to estimate the variance matrix.

• Thanks so much for your answer. How do I go about estimating the variance matrix? My assets are currency pairs and cross pairs. Given a set of data series for the pairs i am using, do I calculate the standard deviation and square it? After do I calculate the correlation combination between each pair? I got the idea from this video...is this correct? youtube.com/user/bionicturtledotcom#p/u/235/35NWFr53cgA Sorry for the newbie question! May 8, 2011 at 21:24

The question is somewhat vague (lacking a well-defined objective), so this advice may not apply.

Be mindful that you may be simultaneously considering multiple futures contracts that contain overlapping underlying constituents (e.g. futures that track the EuroStoxx 600 and DAX). If you are using a risk model, the idiosyncratic risk may not, in fact, be uncorrelated across constituents. This phenomenon is true for other 'composite' assets, such as ETFs, as well.

Dan diBartolomeo, of Northfield, motivates this concept clearly in his 1998 paper:

I would start by looking at calculating the efficient frontier. which maximizes return given a specified risk.

Here is the Wikipedia article which specifies how you would do the calculation:

http://en.wikipedia.org/wiki/Modern_portfolio_theory

-Ralph Winters

Mean-Variance optimization is the standard finance answer to this question.

However, solutions can be costly since the weights will likely be dispersed across many instruments raising fixed transactions costs. I would consider Sparse PCA as another solution where you can specify cardinality constraints on the number of securities in your basket to better manage the transasctions costs vs. diversification trade-off