IntroF10

# IntroF10 - Econometrics The application of statistical...

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1 Econometrics The application of statistical modeling to economic problems. Differs from statistics by emphasizing non- experimental data. 2 Student Background When did you take Economics 122A ? A. Summer 2010 B. Spring 2010 C. Winter 2010 D. Fall 2009 E. Before Fall 2009 3 Probabilistic Modeling: Back to Basics Alice and Bob each have mortgages that their bank is trying to sell to investors. Based on previous experience with similar customers the bank believes that the probability of defaulting is 0.3. This means: A. If Alice or Bob take out many mortgages, they will default 30% of the time B. If a large number of mortgages were given out to people observably identical to Alice and Bob, 30% of them will default. C. Alice and Bob will behave as if a biased coin with probability of heads = 30% is tossed. If this coin comes up heads they default, otherwise they don’t. 4 Mortgage Markets Suppose the holder of the mortgage gets \$100 if the mortgage doesn’t default, and 0 otherwise. How much would an investor pay to purchase Alice or Bob’s mortgage? A. \$100 B. \$70 C. Strictly less than \$70 depending on the investor’s risk aversion.

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5 Mortgage Securities Suppose that Bob is a Professor in California and Alice is a hockey mom in Alaska, so the bank now thinks that the events that they default are independent. The bank now bundles the mortgages together into 2 securities and tries to sell them to investors. How much will the investors be willing to pay? A. \$100 B. \$70 C. The same as they would be willing to pay for the mortgages separately. D. Less than \$70, but more than they would be willing to pay for the mortgages separately. 6 Mortgage Securities Probabilities Expected Value of each mortgage = \$100·.7 + \$0·.3 = \$70 Variance of each mortgage = \$900·.7 + \$4900·.3 =\$2100 Each Security pays: \$100 with probability .7·.7 = .49 \$50 with probability 2·.7·.3 = .42 \$0 with probability .3·.3 = .09 Expected Value = \$100·.49 + \$50·.42 = \$70 Variance = \$900·.49 + \$400·.42+ \$4900·.09 = \$441 + \$168 + \$441 = \$1050 7 Mortgage Securities Independence? Suppose that mortgages fail because either the mortgage holder loses their job (which happens with probability = .222) or because house prices fall below the value of the mortgage (which happens with probability = .1 independent of people losing jobs). Now what is the expected value of Alice or Bob’s mortgage? A. \$100 B. \$70 C. \$68 8 Mortgage Securities Probabilities 2 The mortgage does not default if the holder keeps their job (event A) and the house prices don’t fall too far (event B). Since A and B are independent, the probability of no default = ( ) ( ) ( ) .778 .9 .7 PA B PA PB ∩= = •= (Since P(A)=1-.222 and P(B) = 1 - .1) Expected Value of each mortgage = \$100·.7 + \$0·.3 = \$70 Variance of each mortgage = \$900·.7 + \$4900·.3 =\$2100
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IntroF10 - Econometrics The application of statistical...

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