Download the monthly Case-Shiller house price index for Los Angeles from the St. Louis Fed (FRED II). Choose the version that is not seasonally adjusted, and get all data, from about 1987 through the last available data point.

A) Create a set of 3,000 simulations of a monthly house price for 10 years using the equation and parameters in 3 above. Assume the starting price is $800,000. Do you think 3,000 simulations is enough?

B) Suppose you wanted to buy this home with 10% down, and, to lower mortgage costs, you chose to get unison.com as an equity investor to provide another 10% (for a total of 20% down and 80% mortgage). Go to unison.com to find out how Unison computes its share of appreciation. Assume transaction fees of 3.9% all in, of which 3% are lender profit. From your results in part A, compute their annualized expected return and standard deviation of returns, estimate a Sharpe ratio and the probability that Unison will lose money. Do this for the cases that the homeowner will pay back Unison after 1, 2, ...,10 years (i.e., only at yearly anniversaries). Note that technically Unison has an option to purchase a share of your home, so that their losses are limited to 100% of their initial investment. Do you see any trends over time? How does this investment compare to one in, say, a stock/option investment?

Any help is very much appreciated! :)