# Minimum Variance Algorithm (MVA) Excel Sheet

April 5, 2013

The link below contains a spreadsheet example for computing MVA weights from multiple times series. Next week, I will try to show some different applications.

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11 Comments
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Thank you! It is easy and simpler than MCA.

I tested it and indeed does as expected – reduces the portfolio volatility. I used an ETFs set as per Ray Dalio’s “All Weather” paper.

I have a somewhat related question for you, in the same spirit of using simple heuristics to great leverage: have you considered adding a momentum component to the asset class weights calculation?

So, MVA calculates weights inversely proportional with the average covariance and inversely proportional with asset class variance. But it could add also a normalized momentum component to the weights formula. I use some form of this and it improves results above what MVA alone does.

I would be extremely interested on your thoughts on this topic.

Again, thank you so much for your great content on this blog!

hi stefan, thank you. i have explored a lot of different avenues including the ones you suggested. I had planned to share them in subsequent posts down the line. you are correct that momentum helps to improve upon performance in that context. there are many ways to go in that direction for sure.

best

david

I David,

Thanks for sharing. Brilliant.

hi Pierre, hope you are well. thank you, and good work on the shiny application, just read about that will look into it further.

best

david

Hi David,

I tested your MCA in connection with the Clusters/Risk Parity strategy you have developed and published with Michael. Substituting the risk parity for MCA does a perfect job in limiting the drawdown of the strategy. This helps avoiding UUP, which has a considerable drag on the long term performance of the strategy, and also has the inconvenience of not being a physical replication ETF.

Thanks again,

Best,

Pierre

Sorry, please read MVA instead of MCA

hi Pierre, yes there are a lot of ways to use it, and incorporating it into clusters is also a useful application. this helps to capture the best of both worlds– a good correlation model and a means of lowering volatility/variance without excluding assets–thus preserving the clusters. good suggestion.

best

david

David, why weights (covar and inverse variance) being multiplied? Would it make sense to use a linear combination? This way other weights (momentum, as mentioned above) could be added and each method could be weighted into the final results.

Also, it would be interesting to see how the weights change over time. How would dampening changes in the final weights affect risk & reward? My concern here is transaction costs, while dampened changes may be too slow to avoid increased risk.

Neat stuff, thanks for sharing your ideas.

Cheers,

Victor

David, I have one more question about the rationale for the heuristics you used here. The asset class variance shows up twice, both as a factor in the covariance and independently, while the correlation is present only once, as a covariance factor. Is there a rationale for the higher weight given the variance in this heuristics?

Hi David,

Is MVA designed to approximate the Optimized Minimum Variance Portfolio? When I run an optimization in excel with the data from the MVA sheet I get very different results.

Thanks

The excel sheet downloads the covariance formula as =_xlfn.COVARIANCE.S, which generates errors in excel 2007. Is there any practical difference in using =COVAR for the covariance calculations?