How is the formula for MCTR expressed?

The formula for the Marginal Contribution to Risk (MCTR) is expressed as the asset beta relative to the portfolio multiplied by the portfolio's standard deviation. This is because MCTR quantifies the risk that an additional asset contributes to the overall risk of the portfolio.

Asset beta reflects the sensitivity of an asset's returns relative to the overall market. When calculating MCTR, multiplying the asset's beta by the portfolio's standard deviation indicates how much risk the asset adds to the portfolio on a marginal level. This provides insights into the contribution of each asset to the total portfolio risk and is essential for effective risk management and asset allocation decisions.

The calculation does not involve simply using the standard deviation of the portfolio or the variability of returns independently, as these metrics do not account for the relationship between the asset's risk and the portfolio's risk. Similarly, the weight of assets in the portfolio divided by total assets does not reflect the risk contribution of those assets to the overall portfolio. Instead, MCTR focuses specifically on how individual assets change the risk profile of the existing portfolio based on their beta and the standard deviation of the portfolio's returns.