Mean-Variance optimization

Strandi · December 8th, 2011, 6:47 pm

Hi everyoneI just came across some strange behavior in a mean-variance optimization.When you change the cell "E6" (correlation between commodities & hedge funds) to -1 the efficient frontier looks totally strange and the numbers for the expected return/standard deviation make no sense. Normally I would say that a portfolio consisting of 50% commodities and 50% hedge funds should be the MVP (2.5% StdDev).Do you have any explanation or do you find any error in my spreadsheet?Thanks in advance!

acastaldo · December 8th, 2011, 6:57 pm

correlation of -1 => the matrix V is singular => the standard solution formula using V^(-1) blows upthe intuition: if two assets are perfectly negatively correlated you could eliminate all risk and (if the returns are different) make infinite money by taking an infinitely sized (and still riskless!) long-short position

Strandi · December 8th, 2011, 7:04 pm

Thanks, good to hear that the standard formula blows up and that it is not necessarily my spreadsheet :-)But strange enough the formula also blows up when the correlation = -0.8 - any idea why?

SebastianJansen · December 10th, 2011, 12:39 pm

i havent looked at your spreadsheet, but if you say you havent done anything wrong, my first guess would be that the matrix could be nearly-singular in your calculation;are you checking such problems in your calculation? Had some trouble when doing minvar optimization via matlab with near-singular / singular matrices... some optimization toolboxes where unable to come up with rather useful results when covar matrix was not singular but had values extremly close to 0

Traden4Alpha · December 10th, 2011, 12:59 pm

QuoteOriginally posted by: StrandiThanks, good to hear that the standard formula blows up and that it is not necessarily my spreadsheet :-)But strange enough the formula also blows up when the correlation = -0.8 - any idea why?Chances are, you've made the matrix that can't be a valid correlation matrix (that is, no dataset could ever produce a correlation matrix with the correlation values you have and E6=-0.8). In other words, E6=-0.8 is inconsistent with the other unchanged correlation values in your matrix. For example, if commodities correlate positively to equities and equities correlate positively to hedge funds, then commodities CAN'T strongly negatively correlate to hedge funds.Look up positive semidefinite matrices.

Strandi · December 11th, 2011, 3:05 pm

Thank you for your comments! Very appreciated!@Traden4Alpha You could be right - when I change some of the other correlations to something around 0, than it works.I'll look positive semi-definite matrices up!@Sebastian No, I haven't checked for singularity...might be worth doing so Cheers!

martingull · December 22nd, 2011, 7:58 am

QuoteOriginally posted by: Traden4AlphaQuoteOriginally posted by: StrandiThanks, good to hear that the standard formula blows up and that it is not necessarily my spreadsheet :-)But strange enough the formula also blows up when the correlation = -0.8 - any idea why?Chances are, you've made the matrix that can't be a valid correlation matrix (that is, no dataset could ever produce a correlation matrix with the correlation values you have and E6=-0.8). In other words, E6=-0.8 is inconsistent with the other unchanged correlation values in your matrix. For example, if commodities correlate positively to equities and equities correlate positively to hedge funds, then commodities CAN'T strongly negatively correlate to hedge funds.Look up positive semidefinite matrices.Very well explained!