Financial institution XYZ has the following balance sheet situation (numbers in millions of $): Assets 4-year loans, YTM 8% 100 Liabilities 1-year commercial paper, YTM 5% 50 2-year CD, YTM 6% 40 Capital 10 100 100 The loans pay annual coupons at a fixed rate and trade at par (that is, price=notional=$100, and coupon = YTM). The commercial paper and certificates of deposit are zero-coupon bonds. Yields are with annual compounding. a) (5 points) Compute the duration of the 4-year loans. b) (4 points) Compute the duration of XYZ's liabilities. c) (6 points) Is the institution exposed to interest rate risk? If yes, in which direction? Compute the leverage adjusted duration gap for XYZ. d) (7 points) Suppose the central bank is forced to unexpectedly increase the level of yields through the reference rate R. What would be the expected gain or loss to the bank equity capital, as a percentage of today's value, if R is increased from 6% to 7%? Explain. e) (7 points) The institution decides to immunize its equity against changes in interest rates. To this end, it plans to sell some of its loans and replace them with some other asset. Suppose the following three zero-coupon government bonds are available in the market: 1-year maturity, YTM = 3% 3-year maturity, YTM = 4.5% 8-year maturity, YTM = 8% Which one would you purchase, and which fraction would you allocate to it in order to achieve immunization