Global Real Estate Capital Markets Problem 1 [10 points] You want to buy a house for main residence and have the following four choices of mortgage with monthly payments. Suppose that your marginal...

Global Real Estate Capital Markets

Problem 1 [10 points]

You want to buy a house for main residence and have the following four choices of mortgage with monthly payments. Suppose that your marginal tax rate is 25% and the market index will stay 10.5% after year 5.

1. [5 points] If you hold the loan for the entire term, what is the annual effective cost of each mortgage before-tax?

2. [5 points] If you hold the loan for the entire term, what is the annual effective cost of each mortgage after-tax?

Problem 2 [10 points]

Suppose that you bought a house in Los Angeles, California in 2006Q1 and the house price was $600,000. Your LTV is 95%, so you borrow a fixed rate mortgage (FRM) of $570,000. The loan term is 30 years with interest rate 6% and monthly payments. Assuming the house price dropped 35% in Los Angeles during the period of 2006Q1 to 2009Q1.

1. [1 points] What is the value of your house at the end of 2009Q1?

2. [1 points] What is your loan balance at the end of 2009Q1 (36 months later)?

3. [2 points] Which is the better choice from economic point of view and why?

a. Keep the house and continue to pay mortgage every month

b. Default and walk away

Suppose that you borrowed a price level adjusted mortgage (PLAM) in 2006Q1 instead of borrowing a FRM and assuming that the first loan balance adjustment will occur at the end of 2009Q1 and everything else is equal.

4. [1 points] What is your adjusted loan balance at the end of 2009Q1 (36 months later)?

5. [2 points] Which is the better choice from economic point of view and why?

a. Keep the house and continue to pay mortgage every month

b. Default and walk away

6. [3 points] What is the implication for PLAM to the recent XXXXXXXXXXhousing crisis?

Problem 3 [10 points]

You decide to buy a house of $250,000 with loan amount of $200,000. The lender offers the following three SAM choices with $5,000 origination cost for each choice:

(1) $200,000; 15 years; monthly payment; 0% interest rate; 50% of appreciated value of the property in year 10. In addition, if the property value declines in year 10, the lender pays nothing.

(2) $200,000; 15 years; monthly payment; 3% interest rate; 50% of changed value of the property in year 10

(3) $200,000; 15 years; monthly payment; 5% interest rate; 25% of changed value of the property in year 10.

The housing market conditions:

a) Home price will appreciate 50% in total for the next 10 years;

b) Home price will stay the same for the next 10 years

c) Home price will decline 50% in total for the next 10 years.

Questions: If you hold the loan for only 10 years, please find out the best choice for each market condition.

Problem 4 [10 points]

ABC Bank originates a pool of containing XXXXXXXXXXyear fixed-rate mortgages with loan amount of $100,000 each. All mortgages in the pool carry a rate of 6% with annual payments. Suppose that the servicing fee is 0.5%. ABC Bank would like to sell the pool to investors via Mortgage Pass Through (MPT) security. Suppose that 100,000 shares will be issued and the market interest rate is 5.5%

Questions

1. [3 points] Assume that there are no prepayment and no default, how much an investor would like to pay for each share of the MPT security?

2. [3 points] What is the price of each share of the MPT if there are a constant annual prepayment rate of 10% and no default?

3. [3 points] What is the price of each share of the MPT if there are a constant annual default rate of 10% (assuming the recovering rate is 50%) and no prepayment?

4. [1 points] Please briefly discuss your findings

Problem 5 [10 points]

The Green Bank originates a pool of containing XXXXXXXXXXyear fixed-rate mortgages with loan amount of $250,000 each. All mortgages in the pool carry a rate of 6.5% with monthly payments. The servicing fee is 0.05% each month. The Green Bank would like to sell the pool to investors via IO/PO Strips. Suppose that they issue 150,000 shares of IO/PO Strips and the market interest rate is 6%.

Questions

1. [3 points] Assume that there are no prepayment and no default, how much an investor would like to pay for each share of the IO/PO Strips?

2. [3 points] What is the price of each share of the IO/PO Strips if there are a constant prepayment rate of 1.5% every month and no default?

3. [3 points] What is the price of each share of the IO/PO Strips if there are a constant default rate of 1.5% every month (assuming the recovering rate is 50%) and no prepayment?

4. [1 points] Please briefly discuss your findings.

Problem 6 [10 points]

Questions

1. [5 points] Suppose that there are no prepayment and no default, what are the cash flows for Class A, Class B and Class Z bonds? What is the IRR for the issuer?

2. [5 points] Suppose that there are 15% prepayment and no default, what are the cash flows for Class A, Class B and Class Z bonds? What is the IRR for the issuer?

Problem 7 [10 points]

Questions

1. [4 points] Suppose that there are no prepayment and no default, what are the cash flows for Class A, Class B and Class Z bonds? What is the IRR for the issuer?

2. [4 points] Suppose that there are 10% prepayment and no default, what are the cash flows for Class A, Class B and Class Z bonds? What is the IRR for the issuer?

3. [2 points] Please briefly discuss your findings.

Problem 8 [15 points]

1. [5 points] What is the long-standing real estate risk premium puzzle? What is the real estate mixed assets allocation puzzle? Do these puzzles really exist? Discuss the causes of these puzzles.

2. [5 points] Below are Sharpe ratios for both the financial and real estate markets. Briefly discuss their difference and explain why the real estate should have its own Sharpe ratio.

3. [5 points] Cheng, Lin and Liu (2017-JRER) develop the mixed-asset portfolio by extending the Modern Portfolio Theory (MPT) as follows,

Briefly discuss the difference between these two models and explain why the real estate should have its own asset allocation model.

Problem 9 [15 points]

1. [5 points] In practice, one of the most important factors to control for credit risk is loan-to-value (LTV) ratio. Is this a good practice? Why?

2. [5 points] Bian, Lin and Liu (2018b) derive the following LTV bias for the Interest-Only (IO) mortgage:

Describe what , , , and stand for.

3. [5 points] In a depressing market with extremely high time-on-market for real estate sellers, why are transaction prices noisy?