Determine the optimal supply quantity q and the optimal

Question

Its comprised of three questions: Collateralized Mortgage Obligations, Pre-Sale Market Analysis, Real Estate Bubble

Question 1: Collateralized Mortgage Obligations

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

Assets 10-year, 11% fixed rate Mortgages = $75,000,000 Overcollateralization = $3,000,000
Tranche	Stated maturity	Coupon Rate	Amount Issued
A	4 years	9%	$27,000,000
B	5 years	10%	$15,000,000
Z	10 years	11%	$30,000,000
All cash flows are annual.

It is expected that the mortgage pool will experience constant prepayment rateof 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 after 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 after the issue of the securities decreases to 6%.

Question 2: Pre-Sale Market Analysis

Consider the supply decision of MFIN Limited, a residential real estate developer facing future price uncertainty. Let q be the number of residential units to be built. The variable cost C(q) is equal to c/2 * q². The fixed cost of construction is equal to B.

The developer can pre-sell some units (h) in the presale market at price pftoday and sell the rest of the supply quantity (q - h) at the spot market priceat the end of the construction period. The presale revenue generated will be held as cash only with zero rate of return.The future spot price is uncertain and is represented by p(~) as follows:

p(~) = p + ε

where p is the expected (mean) future spot price and ε is the forecast error which has mean equal to zero and variance equal to σ_p². That is,

E(p(~)) = p and Var(p(~)) = σ².

The developer is risk averse with the degree of risk aversion given by λ_s.

(a) Determine the optimal supply quantity q* and the optimal pre-sale quantity h*.

Now consider the demand side of the market with a representative short-term investor facing the same market conditions as MFIN Limited. The investor, like the MFIN Limited, is risk averse with degree of risk aversion given by λb. Similarly, the investor determines the optimal pre-sale demand quantity (qb) by maximizing the certainty-equivalent profit with respect to the expected future spot price.

(b) Determine the optimal demand quantity (q_b*).

(c) What is the market-clearing pre-sale price today?

Question 3: Real Estate Bubble

Following our discussion on stochastic rational bubble in the Hong Kong property market (from slide 34 onward), repeat the same analysis for year 2014 and 2015 by looking up the relevant data from the Census and Statistics Department web site or other sources.

(a) Evaluate the size of "bubble" for 2014 and 2015.

(b) How likely the real estate bubble will burst in 2016?

(c) How likely the real estate bubble will burst in the next two years, 2017 and 2018?