This analysis identifies the contribution of each position to the overall portfolio risk.
The contribution of a position to portfolio risk is the product of:
- the risk of the position's asset (standard deviation)
- the weight of the position in the portfolio
- the correlation of the position to the portfolio
The last factor quantifies the diversification benefits of the position. For example, a position that has low correlation to other positions will lower the overall portfolio risk. Its contribution to portfolio risk will be low.
The example below shows an equally allocated 25%/25%/25%/25% portfolio. The EEM position is the main contributor to portfolio risk.
In the above example all contributions are positive, however it is possible that for some assets in some portfolios to have a negative contribution. In that case, augmenting the asset weight in the portfolio will decrease the overall portfolio risk.
For the detail of mathematical formulas used to calculate risk contribution, please refer to "Active Portfolio Management", Grinold, Richard C., and Ronald N. Kahn (1999). 2nd ed. New York: McGraw-Hill, page 78.