1. Download the account Case-Shiller abode amount base for Los Angeles from the St. Louis Fed (FRED II). Choose the adaptation that is not seasonally adjusted, and get all data, from about 1987 through the aftermost accessible abstracts point.
2. [5 pts] Compute the account acknowledgment r tt+1 = (H t+1 – H t)/ H t. Extra credibility if you can appearance that the consistent time alternation is stationary.
3. [15 pts] Model the change in acknowledgment as an Orenstein-Uhlenbeck action (discretized version)
Δrt+1 = r tt+1 – r t = κ (ϑ – r t) Δt + σ Δt1/2 ε
where ε is a commonly broadcast capricious with beggarly 0 and about-face 1.
a. Do this in excel, by abacus in the Analysis Tool backpack from File>Options>Add-Ins. Use OLS regression, with y= r ttt+1 – r t and x = r t Δt, and analyze the alien ambit aloft (κ, and ϑ) from your beeline corruption result.
b. To compute σ, ask the corruption to accord you the residuals, acquisition their accepted deviation, and again bisect the acknowledgment by Δt1/2
c. Since Δt = (1/12) years (monthly), your ambit will be anniversary numbers.
4. [15 pts] Actualize a set of 10,000 simulations of a account abode amount for 10 years application the blueprint and ambit in 3 above. Assume the starting amount is $800,000.
a. Since you do not apperceive the acknowledgment afore t=0, “warm up” the abstracts breeding action with 1 years’ account of acknowledgment afore t=0 (you can alpha the warmup with r=0).
b. You can use either VBA, or simulate anon in the spreadsheet. Aback testing your work, use a abate time anatomy (say 1 year) and beneath Monte Carlo simulations (say 100): 10 years’ account of 10,000 simulations may booty a while on your computer.
c. ε is a accustomed accidental draw with beggarly 0 and about-face 1. To accomplish such a accidental draw, use the action norm.inv(rand(),0,1). Rand() generates a compatible accidental cardinal amid 0 and 1 (a accidental probability), and the action again allotment a accidental draw from the accustomed administration with beggarly 0 and about-face 1.
d. Since every about-face to your spreadsheet will re-compute the accidental capricious (potentially alteration your after-effects slightly), I advance you about-face off the automated workbook adding by activity to file>options>formulas and selecting “manual.” To re-compute the workbook, you MUST again columnist “control =” or F9 to amend formulae… don’t balloon this. Also, best to set aback to “automatic” aback done with project. Apples may be different.
5. [20 pts] Suppose you capital to buy this home with 10% down, and, to lower mortgage costs, you chose to get unison.com as an disinterestedness broker to accommodate addition 10% (for a absolute of 20% bottomward and 80% mortgage). Go to unson.com to acquisition out how Accord computes its allotment of appreciation.
From your after-effects in 4, actualize a abundance administration of Unison’s return, compute their accepted acknowledgment and accepted aberration of returns, and appraisal the anticipation that Accord will lose money. Do this for the cases that the homeowner will pay aback Accord afterwards 1, 2, …,10 years (i.e., alone at annual anniversaries).
6. [5 pts] Why do you anticipate point.com computes acknowledgment from a “risk adapted basis,” that is abate than the amount of the home at origination, rather than the acquirement price/valuation at origination?
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