Are impact weights ever equal to Covar shares? If so, explain why. If not, explain why not. Be clear and precise.
IMPORTANT FOR ANSWERING THIS:
- This question is related to Moderrn Portfolio Theory. Where you have multiple assets that are included inside of a portfolio. The question is asking whether the impacts weighted and cover shares can be equal for two assets inside a portfolio.
- When answering this please ignore the degenerative case of assets with the same impact weights, i.e., assets with an equal product of vol and weight. In the two-asset case, these assets are interchangeable from a risk perspective, when risk is based on vol and correlation. Therefore, any such risk measure will assign them the same risk. A related argument can be given in the general case of n assets.
- Also, please ignore the degenerative two-asset case when one of the assets is the risk-free asset. Here the CoVar share and the impact weight would obviously be 100% for the risky asset and 0% for the risk-free asset.