A Bank has determined that there is a 5% probability that a given loan will be $

Question

A Bank has determined that there is a 5% probability that a given loan will be $20,000 underwater a year from today. The loan’s balance in one year will be Bal12 = $352,600. Now assume that the mean and standard deviation of annual real estate returns in this area are 5% and 10%, respectively. Using the tables on page 90 of your notes, which of the following choices gives you closet guess at the competitive market value of the home for which the loan has been formed?

Answer and equation using financial calculator?

a. $398k o ...solve for solve for [I] Down Payment vs Likelihood of Loan Being underwater z score (outcome mean) (std dev) Example: Local Real Estate Market With Convert z-score Convert %chance Annual mean return- 5% to %chance to Z-score Annual sdev of return 10% chance chance z-score underwater underwater z score 3.0 0.13% 0.62% 2.5 -2.06 2.28% 2.0 1.65 1.5 6.68% 10.0% -1.0 15.87% 15.0% -1.04 -0.5 30.85% 20.0% -0.84 50.00% 25.0% -0.67 15% 5% 5% 15% 25% 30.0% 0.52 CDaniel Greiner 2017 90

Explanation / Answer

Lets say competitive market value on whic loan has been formed = X

Now, it is 5% probability that given loan will be $20000 underwater and loan’s balance in one year will be Bal12 = $352,600. so market value after one year =$352,600 - $20000 = $ 332,600

Lets say Annual mean return of the market is r%

so Here 5% probability is there that market value will be only 332600

so rate of return should be (r - 5)/10 = -1.65

r = 5 - 1.65 * 10 = -11.5%

so X * ( 1 - 0.115) = 332600

X = $375,819 or nearly equals to $ 376k

so option b seems correct in this case.

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