(Leverage and Sovereign Default): You have $100 in your pocket with which you can buy a risky sovereign bond. The risk-free rate is 3%. With a probability of 0.5, the government, which issued the bond, will default, and the rate of return on the sovereign bonds is -10%. With a probability of 0.5, the government will not default.

a) (10 marks) Assuming that investors are risk-neutral, compute the promised interest rate on the risky-sovereign bond.

b) (10 marks) What is the sovereign spread in the previous question ? What is the risk-premium on the sovereign bond?

c) (20 marks) Suppose that you borrow $100 from a bank and leverage your investment in the sovereign bond with the borrowed fund. After the return on the sovereign bond has been realized, you need to pay back $100+$3 (interest) to the bank. One unit of sovereign bond sells for $100.

(i) Compute the return on your investment when the sovereign government defaults. (ii) Compute the return on your investment when the sovereign government does not default. (iii) In the event of sovereign default, are you going to default on your debt to the bank ? Provide an explanation why you are going to or not to default on your debt.