2. Bond Valuation and Arbitrage Suppose that on January 1, 2020 you observe the following market information regarding the prevailing prices for three zero-coupon bonds:

Bond A, which will pay $100 on January 1, 2021, has a price of $95.24;

Bond B, which will pay $100 on January 1, 2022, has a price of $85.73;

Bond C, which will pay $100 on January 1, 2023, has a price of $75.13.

(a) What is the term structure of spot rates (r1, r2, and r3) on January 1, 2020?

(b) There is a fourth bond, Bond D, which is a level coupon bond, with a coupon rate of 5% per year, $100 face value, and three years remaining to maturity (annual coupon payments). What is its price on January 1, 2020?

(c) Suppose one year later, that is, on January 1, 2021, you find that the price of Bond B and Bond C rise to $94.34 and $87.34, respectively. What will be the market price of Bond D? What will be its yield to maturity?

(d) Continuing part (c), suppose on January 1, 2021, you observe that the price of Bond D is $100. Suppose shorting assets is costly. Specifically, if you short $K of an asset, you have to pay a brokerage fee of $0.00005K² . Can you form an arbitrage portfolio to make a profit on January 1, 2021? If yes, what is the maximum amount of arbitraging profit you can make on January 1, 2021? Please describe the exact arbitrage strategy and the corresponding cash flows in each year.