Financial Risk Management

CHAPTER 10Risk Contribution

RISK DECOMPOSITION OF THE GAUSSIAN VAR

So far, we have computed two risk measures: Value‐at‐Risk (VaR) and Expected Shortfall (ES) in two different frameworks: Gaussian and historical. The next step from a risk management standpoint is to think in terms of risk contribution. The idea is to allocate risk efficiently within a portfolio of financial assets.

A risk measure gives an estimate of the global or total risk exposure of a portfolio. Thanks to previous VaR and ES calculations, we know the risk exposure of our Google/Amazon portfolio—expressed as a potential loss over the next 24 hours. Although useful, this information is not enough to identify the sources of risk. We need to disentangle the total risk of our portfolio to understand where it comes from: mainly Google, mainly Amazon or both? Simply put, we aim to identify the potential risk concentration within our portfolio. This notion of risk contribution echoes with the portfolio risk profile, and is at the core of risk allocation strategies. Remember the risk reduction generated through portfolio diversification.

The risk allocation principle consists of breaking down the portfolio total risk into a sum of risk contributions by sub‐portfolios. The scope can be traders or asset managers, desks, asset classes or any other risk unit that makes sense in terms of risk exposure. This is a salient issue for financial institutions because risk allocation is linked to capital allocation, another ...