1. Warm-up Problems Random variable X equals 0 with probability 0.4, 4 with probability 0.5, and -10 with probability 0.1. –What is E[X]? –What is E[X | X ≤ 1]? N(2,4) is a normal random variable. What is E[3+N(2,4)]? Suppose an HIV test gives a negative result for an HIV- individual 99% of the time. If 1% of the population is infected, how many false-positives will you have if you test 1000 people?

2. Previous Approach 1.List alternatives 2.For each alternative a)Describe cashflow stream b)Calculate NPV 3.Choose alternative with largest NPV

3. New Approach 1.List alternatives 2.For each alternative a)Describe average cashflow stream b)Calculate average NPV 3.Choose alternative with largest average NPV

4. New Approach 1.List alternatives 2.For each alternative a)List possible scenarios and their probabilities I.Describe cashflow stream II.Calculate NPV b)Calculate E[NPV] 3.Choose alternative with largest E[NPV]

5. Simulation Example: Mortgage Backed Security Consider a pool of 100 extremely risky mortgages. Each mortgage has an independent 50% probability of defaulting. If a mortgage defaults it creates losses U[20k,70k] for investors. Suppose this pool of mortgages into 2 tranches (or slices). The equity slice absorbs the first $2.1m in losses, and the mezzanine slice, absorbs the rest.