The aim of risk attribution is to specify the contribution of each security to the overall risk of the portfolio. Simply summing the risk of each individual security will not equate the portfolio’s risk because it does not account for the role of correlation. Securities that are highly correlated with the portfolio are riskier than ones that are uncorrelated. In the former case, the security tends to co-move with the rest of the portfolio, thus offering little diversification. A negative correlation, by contrast, actually reduces risk, since it acts as a hedge for the rest of the portfolio.
We use a measure called Marginal Contribution to Total Risk (MCTR) for risk attribution. It basically says that the riskier positions are the ones that have all three characteristics:
- Larger allocations
- Higher individual volatilities
- More correlation to the rest of the portfolio
Conversely the less risky positions have opposite properties:
- Smaller allocations
- Lower individual volatilities
- Less correlation (preferably negative) to the rest of the portfolio
The mathematical formulation is complex and involves finding the resulting change in portfolio risk from an incremental change in the allocation of a single security (with all others kept constant). A nice property of MCTR is that it adds to the total portfolio risk.
Our risk attribution widget performs the above calculations and represents the contribution to portfolio risk, using stacked bars. For more information on the risk attribution visualization, please refer to the help document.
Knowing the contributions to risk is important to help investors ascertain if there are some positions representing too much or too little risk.