Portfolio Analysis In R: Risk-Contribution Analysis

Do you know where the risk in your portfolio is coming from? Well, of course, you do. After all, you designed the portfolio and so the asset weights reflect the risk contribution. A 50% weighting in stocks translates into a 50% contribution to risk for the portfolio overall, right? That’s a reasonable first approximation, but it’s a crude estimate and one that’s prone to error as market conditions change—particularly for a strategy that holds a mix of asset classes. For a precise profile of the relative contributions from each piece of the portfolio—an essential piece of intelligence for risk management—we’ll have to go deeper into the analytical toolkit.

The reasoning for decomposing portfolio risk into its constituent parts is straightforward: the relationship of risk across assets is in constant flux through time. As a result, correlation and volatility are changing. The main takeaway: your portfolio’s risk profile may differ from your assumptions—perhaps radically so at time. The only way to know if your estimates match reality is to routinely run the numbers and make periodic adjustments to the asset allocation when appropriate.

An exaggerated example tells us why this facet or risk management is essential. Let’s say that you’ve designed a portfolio with an 10% allocation to emerging market stocks on the assumption that 10% of total portfolio risk will be driven by these assets. Because of shifting relationships with other assets, however, it turns out that the risk contribution from emerging markets rises to twice your assumption after three months—20%. The problem is that this change might not be obvious without formally modeling the risk-contribution factor.

Let’s dig into some details with a real-world example. As in previous installments in this series (see list of articles below) we’ll use our standard sample portfolio (unrebalanced in this case), which consists of 11 funds for testing a global mix of assets, spanning US and foreign stocks, bonds, REITs and commodities, based on the following target allocations:

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