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BLOBY
Topic Author
Posts: 113
Joined: May 17th, 2004, 5:07 am

### Correlation linearization

Hi, I got to set a correlation constraint in my optimizer for an equity portfolio generating, but correlation is not linear and even not convex. How would you linearize correlation in order to be able to set it as a constraint ? Thx a lot.

Alan
Posts: 10319
Joined: December 19th, 2001, 4:01 am
Location: California
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### Correlation linearization

The best solution is to get a better optimizer -- one that handles non-linear constrained problems, say Mathematica,Absent that, to get a good response, I think you need to spell out:1. What exactly are the capabilities of your optimizer?2. What exactly is the (ideal) correlation constraint you want to approximate?

Posts: 23951
Joined: September 20th, 2002, 8:30 pm

### Correlation linearization

To add to Alan's point #2 is the issue of coupling between correlations in a correlation matrix. One cannot constrain single values in the matrix without running the risk of creating an invalid correlation matrix.

BLOBY
Topic Author
Posts: 113
Joined: May 17th, 2004, 5:07 am

### Correlation linearization

Alan, my optimizer is Matlab, and I just try to minimize my equity portfolio's variance under a few sectors, liquidity constraints ... and particularly a correlation (between my output portolio and an equity benchmark) constraint...Thanks again.

Alan
Posts: 10319
Joined: December 19th, 2001, 4:01 am
Location: California
Contact:

### Correlation linearization

See my previous post:1. ?2. ?
Last edited by Alan on October 28th, 2012, 11:00 pm, edited 1 time in total.

BLOBY
Topic Author
Posts: 113
Joined: May 17th, 2004, 5:07 am

### Correlation linearization

1. What exactly are the capabilities of your optimizer?=> I don't know, it's just the optimization toolbox of Matlab (fmincon function)2. What exactly is the (ideal) correlation constraint you want to approximate? => I just wanna constraint the correlation between my output portfolio return (Nav) and equity benchmark (say S&P500) return. For example, correlation between both can never go below 80%.Hope it helps.

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