Consider the following Collateralized Mortgage Obligations (CMOs) with three classes of securities, Tranche A, Tranche B and Tranche Z.

Take Home Assignment Seminar course in Real Estate and Banking Attempt All three Questions. Please follow the instruction below when you submit your work. Work submitted to the wrong address will not be marked. Please send in a sof copy of your work in WORD (NOT PDF) format to my email address, \"KTSE@HKU.HK\" before 23:59 of July 9 (Sunday), 2017. Question 1: Collateralized Mortgage Obligations (40 points) Consider the following Collateralized Mortgage Obligations (CMOs) with three classes of securities, Tranche A, Tranche B and Tranche Z. Tranche A B Z Assets 10-year, 11% fixed rate Mortgages = $75,000,000 Overcollateralization = $3,000,000 Stated maturity Coupon Rate 4 years 9% 5 years 10% 10 years 11% All cash flows are annual. Amount Issued $27,000,000 $15,000,000 $30,000,000 It is expected that the mortgage pool will experience constant prepayment rate of either 0% or 10% per year depending on the mortgage interest rate level. a. Determine the market value of Tranche A, B, and Z securities if the mortgage interest rate tomorrow afer the issue of the securities increases to 15%. b. Determine the market value of Tranche A, B, and Z securities if the mortgage interest rate tomorrow afer the issue of the securities decreases to 6%. k s maurice tse 2 Question 2: Collateralized Debt Obligations (30 points) Nopay Bank is going to issue collateralized debt obligations (CDOs) against the entire issue of the 10-year risky debt of Fortune Limited as presented here: Fortune Limited Market Value of Assets Market Value of Debt and Equity Assets $100 10-yr Debt (Face = $66.8) ?? Equity ?? The risky debt is a zero-coupon bond that pays no interest. At maturity, the bond will pay the investors just the face value. The underlying assets of Fortune Limited are valued at $100 today. The volatility of asset value in terms of annualized standard deviation is estimated to be 25%. The risk free rate of interest is 5% per year compounded continuously. The entire issue of the 10-year risky debt with face value equal to $66.8 is to be placed into a debt pool. Against the debt pool, Nopay Bank will issue 10-year CDO with face value equal to $50 that pays no interest. The rest of the 10-year risky debt will be held in the debt pool as over-collateralization (equity). (a) Determine the market value of the 10-year risky debt. (b) Determine the market value of Fortune's equity. (c) Determine the market value of the 10-year CDO that pays no interest. (d) Determine the market value of the over-collateralization. (e) Determine the cost of insurance to protect the CDO investors against Fortune's default. (f) Determine the market value of Fortune's equity and the market value of the overcollateralization (equity of the debt pool) when the volatility of the asset value increases from 25% to 50%. Explain your findings with the results of part (b) and part (d) above. The Black-Scholes equation is as follows: Call Value S N (d1 ) Xe rT N (d 2 ) ln( S / X ) (r 0.5 2 )T d1 ; d 2 d1 T T k s maurice tse 3 Question 3: Real Estate Bubble (30 points) Following our discussion on stochastic rational bubble in the Hong Kong property market, repeat the same analysis for year 2015 and 2016 by looking up the relevant data from the Census and Statistics Department web site or other sources. (a) Evaluate the size of \"bubble\" for 2015 and 2016. (b) How likely the real estate bubble will burst in 2017? (c) How likely the real estate bubble will burst in the next two years, 2018 and 2019? k s maurice tse 4