Economics 434 Theory of Financial Markets

Economics 434Theory of Financial Markets Professor Edwin T Burton Economics Department The University of Virginia

Administrative • Office Hours • Moved to 11:30pm-1pm Tues/Thurs • Will continue through first exam • LNEC Note-Taker • Today’s road-map • Details on mortgages • Return to ABS • Probabilistic Independence

Mortgage Loans Let’s say you want to buy a $400,000 house… what happens? One option – you write a $400,000 check, and the house is yours (unlikely). Alternatively, you could approach a bank to take out a loan to buy the house.

Mortgage Loans Based on your credit history, income, etc. they provide terms for the loan. If you accept: • You provide a down-payment (say, 20%). • They provide the remaining funds to purchase the house. • Those funds become a loan secured by the house. This is a mortgage loan.

Mortgage Loans Returning to our example – let’s say the bank offers you a 20% down, 6% annual interest rate conventional loan. You accept, and put 20% of $400,000 down = $80,000 down. The remaining $320,000 becomes a mortgage loan that you need to repay over the next 30 years.

Mortgage Loans How does this repayment work? One possibility, following the example of Treasuries: • Semi-annual payments of 6% / 2 ¢ $320,000 = $9,600 every 6 months for next 360 months • Both the $9,600 interest payment and $320,000 principal payment in month 360 Instead, most mortgage loans are self-amortized.

Mortgage Loans In our example: BOM Balance Int. Rate Interest Payment Monthly Payment Principal Payment EOM Balance Month $320,000.00 0 (now) $319,681.44 $320,000.00 1 0.5% $1,600.00 $1,918.56 $318.56 $319,361.28 2 $319,681.44 0.5% $1,598.41 $1,918.56 $320.15 $319,039.53 3 $319,361.28 $1,596.81 $1,918.56 $321.76 0.5% …………….. ………….. …………. …………….. ……. ………….. …… $1,909.02 $1,899.52 $3,808.54 0.5% $19.04 $1,918.56 359 $0 $1,918.56 $1,909.02 360 $1,909.02 0.5% $9.55

Mortgage Loans Notice that the principal decreases every month, since the monthly payments exceed the interest. As a result, the interest due each month decreases as well. However, the total monthly payment remains constant. Therefore, initial payments are mainly interest and very little principal, while final payments are mainly principal and very little interest.

Mortgage Loans How do interest and principal payments change over time?

Mortgage Loans Total Monthly Payment broken down into Interest vs. Principal

Mortgage Loans Some stats on this mortgage loan: • 360 payments of $1,918.56 each means $690,682.20 in total. • This satisfied an initial debt of $320,000.00. • Therefore: • Total Principal Payments = $320,000.00 • Total Interest Payments = $370,682.20 Not atypical for total interest paid and total principal paid to be about the same – they are exactly equal for an interest rate of ~5.25%, and close for similar rates.

Mortgage Loans Fast-forward 5 years… you have $300,000 left in principal on your mortgage loan. Also, real estate prices have increased – your house is now worth $500,000. Lastly, interest rates have dropped – to, say, 4%. Is there any way to take advantage of this situation? Yes… you can refinance!

Mortgage Loans Let’s say you take out a new mortgage for $400,000: BOM Balance Int. Rate Interest Payment Monthly Payment Principal Payment EOM Balance Month $400,000.00 0 (now) $399,423.67 $400,000.00 1 0.33% $1,333.33 $1,909.66 $576.33 $398,845.42 2 $399,423.67 0.33% $1,331.41 $1,909.66 $578.25 $398,265.25 3 $398,845.42 $1,329.48 $1,909.66 $580.18 0.33% …………….. ………….. …………. …………….. ……. ………….. …… $1,903.32 $1,896.99 $3,800.31 0.33% $12.67 $1,909.66 359 $0 $1,909.66 $1,903.32 360 $1,903.32 0.33% $6.34

Mortgage Loans So… what’s changed? • You’ve gotten $400,000 in cash now. • Your monthly mortgage payment has dropped. • Your mortgage has been extended by 5 years. Since you owed ~$300,000, you’ve essentially gotten $100,000 in cash today in exchange for paying ~$1,900 per month for 60 months starting 25 years from today. This is like getting a $100,000 loan at a 0.54% rate. (!!)

Mortgage Loans What does this whole process depend on? You must be able to re-pay your first mortgage – this is why removing the prepayment penalty is a benefit to consumers. If interest rates increase, consumers can keep their old rates, and without a prepayment penalty, as interest rates drop, consumers can lock in the new rate as well.

Mortgage Loans The new interest and principal payments over time:

Mortgage Loans New monthly payment’s interest vs. principal breakdown

Mortgage-Backed Securities Consider a bank that, today, initiates 5 conventional mortgages with the following monthly payments: • $1,500 • $2,000 • $800 • $1,200 • $2,500 What exactly does this bank own?

Mortgage-Backed Securities The bank owns 5 separate streams of cash flows:

Mortgage-Backed Securities Each row by itself represents a separate mortgage.

Mortgage-Backed Securities However, once the bank has initiated each of the five mortgages, there’s no reason to group the payments as such. Grouping the payments by row is really just as arbitrary as any other potential grouping of these future cash flows.

Mortgage-Backed Securities In fact, really what the bank owns… …is 1,800 separate securities.

Mortgage-Backed Securities This is really the backbone of asset-backed securities. Once an entity owns a set of assets, each with its own stream of future cash flows, it does not need to keep them in tact. Instead, it can group the individual payments however it wants and sell off the pieces.

Mortgage-Backed Securities Really, any potential grouping is possible:

Mortgage-Backed Securities A more natural grouping is by month:

Mortgage-Backed Securities Each individual grouping is called a “traunche.” How would these traunches differ if the underlying securities were Treasuries? They would only differ in time-to-maturity, because they would all have zero default risk. However, this changes significantly now that we are dealing with defaultable securities. Not only is there now default risk, but that risk changes from one traunche to another.

Mortgage-Backed Securities The default risk of each payment goes up with time. Low Default Risk High Default Risk

Mortgage-Backed Securities Let’s say each mortgage (and therefore the portfolio as a whole) is B-rated. Then, the ratings of the first few traunches’ will be very good (say, AAA), while the last few traunches’ payments will be poor (say, C). As a result, by grouping in this way, you’ve turned a portfolio of B-rated instruments into a set of securities with a much larger spectrum of credit ratings.

Mortgage-Backed Securities Let’s split one of these traunches even further. Traunche 1: Half of each payment after one month Traunche 2: Half of each payment after one month The owner of each security gets $4,000 after one month.

Mortgage-Backed Securities However, these payments are not guaranteed – each security-owner is taking on half of the risk of the first payment from each mortgage. Let’s say the first security purchaser wants less risk and is willing to accept a lower return, while the second security purchaser wants a higher return and is willing to accept more risk. What can you do to accommodate both potential buyers?

Mortgage-Backed Securities You can instead set the traunches up this way: Traunche 1: The first $4,000 that comes in. SENIOR DEBT Traunche 2: The second $4,000 that comes in. SUBORD- INATED DEBT You’ve now created traunches with different ratings from just one months’ payments.

Economics 434 Theory of Financial Markets