|For this exercise you will need to download single-family home prices by cities from Zillow (https://www.zillow.com/research/data/)Links to an external site.. Please download the series called ZHVI Single-Family Homes Time Series. You will need the time series of prices in Boston only for the month of March from the year 2010 onward. You can use for this exercise any software, but Excel will be sufficient.
1. Calculate the realized annual net returns for the house prices in Boston. (2 points)
2. Calculate the average realized net return and its standard deviation from 2010 to 2020. (2 points)
Assume now that the annual mortgage cost is 4%. Moreover, you expect that the house prices in Boston will increase at the annual pace of the average return you calculated in question 2.
3. Is it worthwhile to borrow to buy a house in Boston? Why? (2 points)
4. How does the return on your levered investment vary with the leverage, D/E? Provide the formula and a plot. (2 points)
5. How does the standard deviation of your levered investment vary with D/E? Derive the formula. Compare it with the standard deviation of house price returns. Explain the difference between these two standard deviations. (6 points)
6. What will be your realized returns on your house if the house prices in Boston increase by 10% between March 2019 and March 2020? (2 points)
7. What will be your realized returns on your house if the house prices in Boston decrease by 25% between March 2019 and March 2020? (2 points)
8. Now assume that you are a pessimist and expect that the house prices in Boston will grow at an average pace equal to the last realized return. Would you borrow to buy a house then? (2 points