lequant40
commented
4 years ago Hi !
Yeah, this problem is unsupported because there are 2 different assets with the same return (2.4%). This prevents the portfolio maximizing the return to be unique, and poses difficulties to the vanilla critical line algorithm of Markowitz.
In his book Portfolio Selection, Markowitz state that "one way to handle this is to alter the [returns] slightly". In your case, it would mean deciding for 2.41 % v.s. 2.40% for one of the two asset for example.
Cheers,
Roman
PS: Implementing a proper solution to allow for assets with identical returns is on the top of my to-do list, so, eventually, this error will not appear anymore, but I cannot commit on any timeline. Meanwhile, I will keep this Git issue opened as you are not the first one who notices this behaviour.
PPS: Now, speciafically for your example, I might have two remarks:
- I noticed you used optimizationMethod: 'maximumTargetVolatility' in the function; may I ask from where you found this example ? Because starting with v0.0.9 release, I should have removed all references to maximumTargetVolatility from the documentation and/or examples
I also noticed that in the covariance matrix, variances are <= 5.3% while the desired max volatility is 5.5%; maybe this is just a toy example, but maybe there is something wrong in variance / volatility calculations (volatility = square root of variance) ?My bad, I read the matrix too quickly, it seems you are rather going for a low volatility portfolio, not the reverse.
grantackerman1
X ref. from https://github.com/lequant40/portfolio_allocation_js/issues/7, to better separate issues.
Thanks Roman. That did the trick! Now I'm running into a different issue and would greatly appreciate any help:
I'm using the function below I created in Google Sheets, but am getting a #ERROR! that says "Error: unsupported problem detected (line 5838)". My goal is to calculate mean variance weights given an expected return stream, a covariance matrix, a target volatility, min weights, and max weights:
function computeWts(rets, cv, targetVol, minWts, maxWts) { return (PortfolioAllocation.meanVarianceOptimizationWeights(rets, cv, {constraints: {optimizationMethod: 'maximumTargetVolatility', maxVolatility: targetVol, minWeights: minWts, maxWeights: maxWts}})); }
The arguments I'm passing are below (and are all in cells in Google Sheets):
rets: 4.7% 5.0% 6.1% 4.0% 5.4% 2.0% 2.2% 2.4% 2.4% 3.6%
cv: 2.3% | 2.5% | 3.3% | 1.7% | 2.3% | -0.4% | -0.3% | -0.3% | 0.1% | 1.7% 2.5% | 2.9% | 3.8% | 1.9% | 2.5% | -0.4% | -0.3% | -0.3% | 0.2% | 1.9% 3.3% | 3.8% | 5.3% | 2.3% | 3.1% | -0.5% | -0.3% | -0.4% | 0.3% | 2.9% 1.7% | 1.9% | 2.3% | 1.4% | 1.8% | -0.3% | -0.3% | -0.3% | 0.0% | 1.1% 2.3% | 2.5% | 3.1% | 1.8% | 4.0% | -0.1% | 0.0% | 0.2% | 0.7% | 1.8% -0.4% | -0.4% | -0.5% | -0.3% | -0.1% | 0.2% | 0.2% | 0.2% | 0.2% | -0.1% -0.3% | -0.3% | -0.3% | -0.3% | 0.0% | 0.2% | 0.4% | 0.2% | 0.3% | 0.0% -0.3% | -0.3% | -0.4% | -0.3% | 0.2% | 0.2% | 0.2% | 0.3% | 0.2% | 0.0% 0.1% | 0.2% | 0.3% | 0.0% | 0.7% | 0.2% | 0.3% | 0.2% | 0.5% | 0.4% 1.7% | 1.9% | 2.9% | 1.1% | 1.8% | -0.1% | 0.0% | 0.0% | 0.4% | 2.0%
targetVol: 5.5%
minWts: 3% 3% 3% 0% 0% 0% 0% 3% 0% 0%
maxWts: 35% 35% 35% 35% 35% 35% 35% 35% 35% 35%
_Originally posted by @grantackerman1 in https://github.com/lequant40/portfolio_allocation_js/issues/7#issuecomment-676556595_