A Collateralized Loan Obligation (CLO) has assets equal to a portfolio of syndicated loans with a market value of $100 million. The duration of these loans is 3 years and the convexity of the loans is 10 years2 . The CLO's liabilities consist of a senior tranche and an equity tranche. The senior tranche has just been issued and has a 5-year maturity and a principal of $90 million. It pays semiannual floating-rate coupons equal to the 6-month default-free interest rate (e.g., the 6-month SOFR OIS rate). Assume the amount of equity tranche is sufficient to make the senior tranche essentially default-free. (a) (10 points) What is the market value and duration of the senior tranche? What is the market value and duration of the equity tranche?(b) (10 points) What is the convexity of the equity tranche?(c) (10 points) Use duration and convexity to approximate the change in the value of the equity tranche if there is a 50 basis point (0.5%) parallel shift upward in the term structure of interest rates