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I am coming across a problem I can't seem to wrap my head around, and I am not sure I am using the right words so cannot find much info in it!

I have a portfolio of assets, with data on historical daily prices for each asset.

I want to calculate the average correlation of my portfolio to an external metric, e.g. the housing market. I have average daily prices for the housing market over the same 24 month period.

Is is correct to calculate the individual correlations between each asset and the housing market, and then average that correlation weighted by how much of the asset I hold in the portfolio to get the average correlation of my portfolio to the housing market?

In Portfolio Theory I see that the focus in on "internal" correlations (e.g. stocks with each other) but I did not see what happens when you want to consider the portfolio as a group vs. an external metric.

Thank you for your help!

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  • $\begingroup$ How are the weights of the assets in the portfolio determined? Do they vary over time? $\endgroup$ – Alex C May 31 '19 at 14:32
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    $\begingroup$ they do - it's market based valuation. so let's say I have 1 Apple stock and 1 P&G stock their weights is determined by their market price at the close of the day for which I am calculating the weights. $\endgroup$ – AlexM88 May 31 '19 at 14:36
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    $\begingroup$ IMHO you should first compute a time series of returns on the portfolio, then compute the correlation of this with the (changes in) the external metric of interest. $\endgroup$ – Alex C May 31 '19 at 17:38
  • $\begingroup$ Thanks ! I'll look into that. The problem is there are additions to the assets over time (e.g. more investment), hence some returns might look high because its new money vs. existing returns. $\endgroup$ – AlexM88 Jun 1 '19 at 9:34
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If you take the average of the pair-wise correlations j-asset / housing, then it is like if you are holding an equally weighted portfolio composed by the assets.

Indeed, you should first build a portfolio using the market weights you computed and then calculate the correlation with the housing. This way you get a proper average cross-sectional correlation. By deciding on a different time frame and whether to roll the calculations or not, you bring into the game the time dimension.

Also, when calculating the correlation that is independent by the invested amount. You should solely consider the daily returns of the strategy.

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