1. When we measure risk, probabilities always come into play. The same way a price is a discounted average future value, an expected loss is the average of losses. Banks have to make provisions not only for the expected but also for unexpected losses; for example you may need to build capital for losses that happen once every 100 trading days. It is customary to assume that a large portfolio will be less likely to suffer losses than individual trades. Nevertheless, this is not always the case. In order to understand this problem, consider two bonds, A and B, with identical market prices and future profiles: they both price at 100 today. Tomorrow they can stay at the same level, 100, with a probability of 99% or decrease to 90 with a probability of 1%. The loss on each bond, separately, is zero to a confidence level of 99% (because in 99 of a 100 scenarios the prices will stay level). What is the loss on the portfolio A + B at the same confidence level?

2. You have a swap contract that pays interest quarterly (same dates on both legs). The notional is $10MM. You want to hedge this contract with forwards on 3M Libor. How many of these contracts you enter, with what maturities and for what notional? (there is no initial or final notional payment on the swap - this is normal for single currency swaps)

3. Modify the bond option calculator I provided you with to price calls, puts and European or American options.

4. The risk neutral probability computed on the "bond" tab matches the model price to a market theoretical price obtained by discounting the final payoff with the curve provided in cells B7:E8. Nevertheless the market may decide to price this bond at a different level. Modify the calculator to find the spread that does justice to the market price.

5. Write a piece of research on the impact quantitative easing had, in your view, on the fixed income markets. What are the consequences of this program coming to an end? Feel free to be verbose and remember, this is a graduate course.