Calculating Portfolio Correlation with an External Market
Summary
The note asks how to measure the relationship between a portfolio of assets and an external series, such as housing prices. Averaging each asset’s correlation with the external metric, weighted by portfolio holdings, may seem appropriate, but the response explains that a simple average of pairwise correlations corresponds to an equally weighted portfolio.
For a portfolio with other weights, first calculate the portfolio’s daily returns using those weights, then calculate the correlation between that return series and the external metric’s returns. Correlation concerns returns rather than price levels and is unchanged by simply scaling invested capital. The analysis can use a chosen observation window or rolling windows to examine how the relationship changes over time. The short response does not specify details such as rebalancing frequency, handling missing observations, or whether the housing series is available at the same frequency as the assets, so those choices still need to be defined in an implementation.
Key ideas
- A simple average of asset-level correlations represents an equally weighted portfolio.
- To measure a weighted portfolio’s correlation, construct its return series with the intended portfolio weights first.
- Calculate correlation from daily returns rather than price levels.
- The chosen time window and use of rolling estimates affect the time dimension of the analysis.
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# Average portfolio correlation vs. external metric # Average portfolio correlation vs. external metric 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! ## Answer by Vitomir (score 1) https://quant.stackexchange.com/a/45882 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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