1. Application of data analytics in loan pricing - A mortgage-backed security (MBS) is a bundle of mortgages sold as a financial asset. Price of this asset - same as other financial assets - depends on the expected return on the MBS. To simplify things, assume expected return on MBS is a function of two factors:
   • interest rate of the underlying mortgages (IR)
   • default rate of portfolio (DR)

Expected Return on MBS=(1-DR)IR-DR

In this question we will calculate return on Bank A's MBS. Bank A has 1,000,000 prime and 1,500,000 sub-prime mortgages. To calculate DR we randomly choose 1000 prime and 1000 subprime loans.

1. Comment on this sampling approach. Is it a good sample to calculate bank's default rate? (5 points)
2. Following table shows # default, and IR in each sample. What is the expected return on an MBS composed of only prime loans? What is the expected return on an MBS composed of all the bank loans, randomly chosen and bundled? (10 points)

Sample	# observations	# default	IR
Prime	1,000	10	5%
Non-Prime	1,000	15	6%

3. What should be the IR on the sub-prime portfolio so that return on a sub-prime MBS will be 6%? (5 points)