The structured products division of your investment bank is planning to create a set of products representing claims on its portfolio of commercial loans. The value of each of the loans has an annual variance 2 and any two loans have a correlation of (0 < < 1). The bank plans to offer three types of claims on the value of the loan portfolio at time T. The claims differ in the seniority of their claims to the value of the underlying portfolio. Tranche 1 pays the value of the underlying loan portfolio, up to a maximum of D1, and is paid first; tranche 2 pays the excess value of the loan portfolio after tranche 1 has been paid, up to a maximum of D2; tranche 3 pays the residual value of the portfolio after the claims of the first two tranches have been satisfied.

Now suppose that there is a fixed number of loans in the portfolio, N. You announce that you will hold the toxic tranche 3, while selling on tranches 1 and 2 to investors; this announcement is intended to reassure investors. After making this announcement, you realize that you can choose the portfolio of loans in such a way as to alter the correlation between different loans: you can choose either a low correlation L or a high correlation H.

i. Which correlation will you choose? Why?

ii. Which correlation would the investors choose, if they could, and why?