Applying Meucci’s Flexible Views to Higher-Moment Portfolio Data
Summary
The document outlines a proposed portfolio framework that combines probabilities for four market states, historical asset data, simulated returns, and an investment committee’s views on distribution moments. It focuses on the difficulty of generating multivariate samples for 43 assets that match moments through kurtosis, then adjusting those samples with Meucci’s flexible-view method. The author reports that attempts to optimize a very large set of moment constraints with SciPy ran into memory problems, including when limiting the constraints to individual asset moments.
The post also asks how to recover coskewness and cokurtosis after applying views, in addition to the mean and covariance calculations shown in Meucci’s work. It does not provide a solution, demonstrate a successful simulation, or establish whether another optimizer would make the full problem tractable. Its value is in framing practical computational and statistical questions around high-dimensional moment matching for portfolio construction.
Key ideas
- The proposed framework combines market-state probabilities, historical asset data, simulated returns, and investor views on moments.
- Matching higher-order multivariate moments creates a large optimization problem as the number of assets grows.
- The author reports memory failures when trying to fit the requested moments, even with a reduced set of constraints.
- The post leaves open how to calculate coskewness and cokurtosis after applying flexible views.
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# Full Copula View using Meucci's Full Flexible View # Full Copula View using Meucci's Full Flexible View I'm currently setting up an "Investment Framework" that should allow the following steps: - Investment Committee (IC) has to decide on probabilities for 4 different market states. I have historical data for each of the distinct market states. This historical data will be probability weighted as input in step 2. - Generate 1 million data points for all 43 portfolio assets based upon the moments (up to kurtosis) of the weighted market state. This will be use as input for step 3. - The IC can now specify views on all the different moments (for example that the correlation between asset 4 and asset 17 has to be >0.8) using Meuccis Algorithm. - Once all views are created, run the algorithm and get all 4 moments as input into a portfolio optimizer. I cannot solve the following points: - Step 2: If I specify all 4 moments for 43 assets, I end up with 178'364 `(n + (n*(n+1))/2 + (n*(n+1)*(n+2))/6 + (n*(n+1)*(n+2)*(n+3)/24)` unique views for the copula. I tried to generate random multivariate distributions using the mean and covariance and then adjust the sample using Meuccis algorithm and all moments as "views" as described by him (see page 20 of his paper). Using Scipys optimizer didn't yield any results (beside an out of memory error...). I even tried using only mean, variance, skew and kurtosis (no covariance, no coskewness and no cokurtosis, but this failed as well... Is it even feasible to optimize after so many parameters? Or is it worth the time to rebuild everything and use another optimiser (like pyomo)? If we can solve this, it would allow to generate multivariate samples from existing distributions using higher moments which is an unsolved problem in math as far as I'm informed - Step 4: Meucci shows how to calculate the mean as well as covariance after the optimisation (Matlab Code). I would be interested in the coskewness and cokurtosis matrix as well. Does anybody know how to?
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