Building a “market portfolio” has obvious benefits for portfolio design. The asset allocation is relatively objective in the sense that Mr. Market chooses the weights. History suggests this is a competitive strategy. Even if it’s not slavishly followed, market weights can be useful for guidance in portfolio design and management. But the necessary task of estimating market values can be problematic, especially if the portfolio includes so-called alternative asset classes and strategies. A possible solution: using a statistical factor model to estimate a market portfolio.

One methodology is based on principal component analysis (PCA), a modeling application for estimating factor weights. Using only returns, PCA decomposes the portfolio and spits out the weights that correspond to the “market” portfolio. Specifically, the first factor portfolio via PCA – the one with the highest variance — tends to capture the primary beta that drives risk and return for a given set of assets. The resulting mix typically corresponds with what we think of as the market portfolio.

Why might you consider analyzing a set of assets with this approach? Several reasons, starting with efficiency and simplicity. Instead of estimating market values for all the assets, which can be cumbersome and prone to error, PCA offers a clean, efficient tools for determining market-related weights. Using R, for instance, provides a quick means for generating PCA data.

For example, consider how a set of ETFs representing the major asset classes stack up. Decomposing the portfolio based on daily returns for the past year produces the following set of weights.

The results are somewhat surprising. Note, for instance, that the PCA analysis for the trailing 12 months, based on yesterday’s close (Dec. 12), gives the biggest weight (roughly 16%)  in the portfolio to VWO, an emerging-markets ETF. Domestic and foreign real estate (VNQ and VNQI, respectively) are also given relatively high weights. US equities (VTI), by comparison, receive just 6%.