## Why is the mortgage prepayment a risk:Why does the CPR change when the mortgage rates change?

## Why is the mortgage prepayment a risk?

QUESTION 1

If the current spot rate curve is upwardly sloping, will the swap yield curve also be upwardly sloping and vice-versa? Explain why.

QUESTION 2

According to the book, “When the swap spread is large, for instance, speculators may bet on the fact that the spread will shrink in the future by taking a short position on the Treasury bonds and enter in a fixed-for-floating swap, as a fixed rate receiver”. The operative word here is “speculators”. The authors did not use the word arbitrageurs. Why is this not an arbitrage? Explain the source of violation of the arbitrage conditions.

QUESTION 3

A fixed income futures contract is not the same as the forward contract for the same underlying asset, the same notional amount and the same contract maturity date. There are many reasons for it. Explain two more reasons beyond the main mark-to-market and counterparty risk issues. (Hint: reading the basic contact details might help.)

QUESTION 4

Similar to the Panels A & B of Figure 6.4 in the book for the collar strategy, draw diagrams of these long strategies on 3-month T-bills (both panels for each strategy):

Straddle with a strike price of $97 for both the call and the put Strangle with a put strike of 96 and the call strike of 98.

You can look up the definition of straddle and strangle on the web as much as you want, you cannot copy an online diagram, you have it make your own graphs in Excel.

QUESTION 5

Does a forward rate predict a spot rate in future? Why or why not?

QUESTION 6

What is the shape of the current spot yield curve and what about that shape has some investors worried? What did the Fed do most recently which resulted in that shape?

QUESTION 7

Why is the mortgage prepayment a risk? What is so bad about getting your lent money back sooner?

QUESTION 8

Why does the CPR change when the mortgage rates change?

QUESTION 9

Calculate two forward curves (up to the largest maturity possible given the spot data below) one starting from t = 0.5 and the other from t= 3. Calculate both discount rates and annual interest rates (semiannual compounding) and plot both curves in one graph.

t Z 0.25 0.9891 0.5 0.9798 0.75 0.9713 1 0.9633 1.25 0.9553 1.5 0.9473 1.75 0.9392 2 0.931 2.25 0.9227 2.5 0.9143 2.75 0.9059 3 0.8973 3.25 0.8888 3.5 0.8801 3.75 0.8714 4 0.8627 4.25 0.8538

4.5 0.845 4.75 0.8361 5 0.8272 5.25 0.8182 5.5 0.8093 5.75 0.8003 6 0.7913 6.25 0.7823 6.5 0.7733 6.75 0.7643 7 0.7554 7.25 0.7465 7.5 0.7376 7.75 0.7287 8 0.7199 8.25 0.7111 8.5 0.7024 8.75 0.6938 9 0.6852 9.25 0.6767 9.5 0.6683 9.75 0.6599 10 0.6516

QUESTION 10

Using the spot curve given in Question 9, estimate the swap curve and plot it.

QUESTION 11

You will receive $5,000,000 on June 1, 2018 as part of your inheritance from your great- grandfather’s estate on June 30, 2018. You have grand plans for that money, but those plans will take shape in about 4 months. In the meanwhile, you want all that money to be safely invested in an interest-bearing instrument. You also want to protect yourself against a possible rate decrease. As a poor student right now, you don’t have a lot of money to buy an expensive hedging instrument such as an option.

So, on June 1 of this year, you decide to use 90-day Eurodollar futures contracts to hedge your inheritance money ($5 million). Each contract is worth $1 million notional. The initial margin for each contract is $3,500 and the maintenance margin is $2,500.

Given the following futures quotes, calculate the implied forward rate, daily P&L, indicate if and when a margin call will be issued, and show the money in your margin account.

Date Quote 2 Jun 2018 98.6681 3 Jun 2018 98.6431 4 Jun 2018 98.6475 5 Jun 2018 98.6756 6 Jun 2018 98.6362 9 Jun 2018 98.5969

10 Jun 2018 98.5675 11 Jun 2018 98.5762 12 Jun 2018 98.6113 13 Jun 2018 98.5706 16 Jun 2018 98.5544 17 Jun 2018 98.5156 18 Jun 2018 98.5200 19 Jun 2018 98.5556 20 Jun 2018 98.5550 23 Jun 2018 98.5494 24 Jun 2018 98.5625 25 Jun 2018 98.5956 26 Jun 2018 98.6412 27 Jun 2018 98.6494 30 Jun 2018 98.6688

QUESTION 12

It is 4 months past June 1, 2018. You are the same lucky student mentioned in Question 11. You got the inheritance, went through with the futures contract and invested the money at LIBOR at the end of the futures expiration.

How much total money do you have now as a result? Remember the convergence property of the futures contract for the last step.

QUESTION 13

The current Federal Funds Rate is 2%. Using the following coefficients for the model that uses the Federal Funds Rate to predict its own value one period ahead, predict the Federal Funds Rate for the next 10 years (iteratively predict one year ahead at a time) and plot the resulting graph.

Alpha: 1.5285% Beta: 0.7611%

QUESTION 14

According to the Expectation Hypothesis under Certainty (Classical Expectation Hypothesis), what will be the spot annual rate for two years maturity, three years from now if the current yield curve is as given in Question 9. Use semiannual compounding to covert discount factors into rates.

Use the following mortgage pool information to answer the following two questions:

Pool size: $500 million

Weighted average coupon of the mortgages in the pool (WAC) = 5%

Weighted average maturity of the mortgage in the pool (WAM) = 15 years

Discount rate to create spot discount factors: 3% quoted in continuous compounding

Spot curve is assumed to be flat.

QUESTION 15

Calculate the price of a pass-through with a pass-through coupon of 4.5% under the base assumption of a 150% constant PSA.

Calculate the effective duration and convexity of this pass-through for a 1% rate change under the assumption that a 1% decline in the spot rates will cause the PSA to go up to 250% and a 1% increase in spot rate will push the PSA down to 100%.

QUESTION 16

Break the mortgage pool described above into 5 tranches of $100 million each with sequential payment of principal.

Each tranche gets 4% (not 4.5%) interest on its principal until it is completely paid off. Clearly show in your spreadsheet the price of each tranche, the month and year it starts getting the principal back and the month and year it gets completely paid off.

Because the tranches are equal in size, there is no particular sequence you need to follow (you can call any tranche “Tranche A”).