Question is based on a research paper The Impact of Federal Housing Policy on Housing Demand and Homeownership: Evidence from a Quasi-Experiment by Morris Davis, Stephen Oliner, Tobias Peter, and Edward Pinto (as presented at Baruch Real Estate Seminar on November 26, 2018).

On 1/26/2015, to promote homeownership, FHA reduced its mortgage premium by 50 bp, from 1.35 percent of loan balance to 0.85 percent. The paper uses this event to estimate the sensitivity of housing demand to interest rate. But how important is a 50bp premium cut? Is it equivalent to the same 50bp reduction in interest rate? We will answer this question using the data from the original paper, for an average mortgage in their data sample.

Ann borrowed $199,755 to buy a $207,000 house (that is pretty high LTV!) using a fully amortizing fixed rate 30-year mortgage with monthly payments. The closing costs of 1.75 points are added to the loan balance (thats not like we used to calculate mortgages, but that was the case in the data). The mortgage payment is calculated based on this larger balance, while the mortgage insurance is 1.35% of the original $199,755 balance. She also pays 1.2% property tax and 0.35% house insurance premium (both based on the value of the house). The monthly payment we are interested in consists of the mortgage payment, mortgage insurance payment, property tax, and house insurance.

The table below summarizes the information we have and calculates the total loan amount after the points are added, as well as the total monthly payment as explained above. Compute total loan and payment using the information in the first seven lines of the table and make sure your answers match the last two lines.

1. Compute the payment if the annual mortgage insurance premium falls by 50bp

2. Compute what should be the mortgage interest rate (it was 4% in part 1) that would lead to the same payment as in part 2 if the insurance premium stays the same as in part 1 (i.e. 1.35%). Enter your answer in percent, but without percent sign.

House price Loan amount Interest rate Upfront premium (points) Annual Mortgage Insurance Premium Taxes Insurance 207000 199755 0.04 0.0175 0.0135 0.012 0.0035 203251 $1462.45 Total loan Monthly payment