1. You observe the following rates:

z01	4.00%
z02	4.50%
z03	4.80%
f12	5.00%
f13	5.10%

Supposing you could borrow (short sell) up to $100 million, derive the most profitable arbitrage that generates positive cash flows today and zero net cash flows in the future. Be concise in your answer. E.g., At time t, Buy $x of Bond X, sell $y of Bond Y, etc..

2. An investment manager wishes to establish a fund that will be worth $80 million in 4 years time. She plans to follow a duration-matching approach using a 3-year zero-coupon bond and a 5-year bond paying a coupon rate of 12% pa. The 5-year bond pays coupons annually. Both bonds are currently priced to yield 6% pa. How much should she invest in the 3-year bond? How much should she invest in the 5-year bond?