Exercise Solution 1.7

1. This is a function of the conditional distribution of the portfolio’s market value , so it is a PMMR.
2. Net cash flow is generally unrelated to portfolio market value. Accordingly, this cannot be expressed as a function of and the conditional distribution of . It is not a PMMR.
3. While beta is a function of and the conditional distribution of , additional information is required about the “market portfolio” in order to calculate beta. Accordingly, beta is not a PMMR.
4. ETL is a PMMR. If we know  and the conditional distribution of , we can calculate the conditional distribution of loss ¹L. With that, we can calculate both the portfolio’s VaR and then the expected loss conditional on that loss exceeding the VaR, which is ETL.