QUESTION 7. Use 4 5 and 6 to answer 7

4. [10 pts] 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? Hints: a. Since you do not know the appreciation before t=1, warm up the data generating process with 1 years worth of appreciation to generate a random t=0 appreciation (you can start the warmup itself with r=0). b. You can use either VBA or simulate directly in the spreadsheet. When testing your work, you may want to use fewer Monte Carlo simulations (say 100-300), depending on your hardware. c. is a normal random draw with mean 0 and variance 1. To generate such a random draw, use the function norm.inv(rand(),0,1). Rand()

generates a uniform random number between 0 and 1 (a random probability), and the function then returns a random draw from the normal distribution with mean 0 and variance 1. d. Since every alteration to your spreadsheet will re-compute the random variable (potentially changing your results slightly), I suggest you switch off the automatic workbook calculation by going to file>options>formulas and selecting manual. To re-compute the workbook, you MUST then press control = or F9 to update formulae... dont forget this. Also, best to set back to automatic when done with project. Apples may be different.

5. [10 pts] 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 4, 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?

6. [10 pts] Repeat 5 for Point.com. Assume transaction fees of 3%+$1,000, where the $1,000 are costs to Point. Also note that it seems that Point caps its share at very high appreciation. Since we do not know the details, assume the cap is infinite. Further, the exact share is determined in underwriting. Assume the illustrative share on their website applies.

7. [10 pts] Graph the expected return vs investment time for Unison and Point on one plot. Repeat for the Sharpe ratio and probability of a negative return. Assume a risk-free rate of 1%.