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MBS Spreads

MBS Spreads. Simple Static Spread. Three Steps Estimate yield to maturity of the MBS BEY basis allowing for the delay Find the yield to maturity of the Treasury security with similar duration 10-year frequently used Swap yields can be substituted for Treasury

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MBS Spreads

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  1. MBS Spreads

  2. Simple Static Spread • Three Steps • Estimate yield to maturity of the MBS • BEY basis allowing for the delay • Find the yield to maturity of the Treasury security with similar duration • 10-year frequently used • Swap yields can be substituted for Treasury • Compare the current spread to some benchmark • Recent history

  3. First Step • Estimate the MBS yield to maturity using a tool like Bloomberg QY or the MBS spreadsheet • Inputs • Description of collateral pool • WAM • WAC • Servicing • Price you have to pay • Prepayment Speed • Based on • Historical speeds • Model predicted speeds • Predicted scenario

  4. Second Step • Find the yield to maturity of Treasury with similar duration • An estimate of the duration of the MBS is a by-product of estimating the yield to maturity • Faster prepay speeds– shorter duration • No prepay– duration ~ 9-10 years • Treasury durations are easy to obtain • 10 year Treasury~~ 7-8 year duration • 5 year Treasury~~ 4-4.5 year duration • 7 year Treasury ~~ 6 year duration • While 7-year Treasury may provide best match, five & ten year securities may be more actively traded

  5. Third Step • In our example, we estimated a Yield of 5.62% (BEY) based on the 7.1% recent CPR (D=5.75) • Spread to five year Treasury: 92bp (5.62-4.70) • Duration of five year 4.5 years • Spread to ten year Treasury: 89bp (5.62-4.73) • Duration of 10 year 8.0 years • But the real question is: IS THAT ENOUGH? • One answer is to look at history • Bloomberg facilitates comparing the yields on any two securities • Generally use “generic” TBA MBS yields • Based on issuer, coupon & seasoning • Plot and summarize the difference in yields

  6. Pros Simple to calculate Cons “Static”– assumes nothing changes Ignores current Yield Curve shape Ignores rate “volatility” Volatility affects option values Ignores relationship between future rates and prepay speeds Static Spreads– Pros Cons Let’s Tackle the Yield Curve shape issue first

  7. Z-Spread • Because our MBS has cash flows spread over the next thirty years, comparing its yield to any single fixed maturity is questionable • Preferable to devise a measure of “spread over the curve”

  8. Yield Curve Shape Can Bias Static Spread • Consider an upwardly sloped Treasury “spot” curve • GE is offering the following security for a price of $178.84 • Yield to maturity 7.79%. Is this enough?

  9. Is 7.79% Enough? • Average Life of GE security is 1.5 years • Duration is 1.48 years ~~ 1.5 years • Interpolating the spot curve to find Treasury at 1.5 years: 7% • Static Spread is 79 basis points. Say you calculate the historical average spread and find it is fifty bp. Does this mean that current price is a “bargain”? Not necessarily

  10. Is 7.79% Enough? • What spread over the curve gives us a price of 178.84? • Recall early problems where we priced securities by discounting cash flows at time t with the spot rate at time t. • Now we simply add a “spread” to the formula • Need to solve this equation for s • S=50 bp

  11. Now consider a different yield curve shape • Consider an downward-sloped Treasury “spot” curve • GE is offering the same security but now with a price of $185.47 • Yield to maturity 5.18%. This is only 18 bp over the interpolated spot curve at 1.5 years. Is this a “bad” deal?

  12. Z spread is independent of yield curve shape • Solve for the “spread over the curve” here: • So the spread over the curve here is the same as in the upwardly sloped yield curve

  13. Calculating Z-Spread for MBS • What do we need? • Treasury spot yield curve • Monthly for 360 months • Projection of Cash Flows • Already have this in MBS spreadsheet • Price • Standard input to MBS spreadsheet • Trial and Error search on computer to find “s”

  14. Modified MBS Spreadsheet • Input normal factors needed to project cash flows • Collateral description • Price • Speed • Use new tab to input Treasury curve from current market • For example, from IYC page on Bloomberg • Use Goal seek to solve for Z-spread • Note that this is less accurate than Bloomberg’s calculation of Z-spread because we only input a few points along the yield curve and used linear interpolation to fit the rest. Bloomberg uses many more points and more sophisticated methods to fill in the missing points • Working with the same 5% FNMA MBS, and the yield curve in the handout, we find a Z-spread of 85 bp • Bloomberg reports 87 bp (see page 21 of handout) • Recall that the “static spread was around 90 bp. In general, when yield curve is upward sloping, Z-spread < static spread.

  15. Other Answers to “Is it Enough?” • Recall the “Cons” to Static Spreads • “Static”– assumes nothing changes • Ignores Current Yield curve shape • Ignores rate “volatility” • Ignores relationship between future rates and prepay speeds • Z-Spread deals with the yield curve problem, but we need more tools to deal with the others OAS & Scenario Analysis

  16. Option Adjusted Spread (OAS) • Mortgages are fixed income securities with imbedded options • Call Option gives borrower the right to prepay • Default option gives borrower the right to stop paying • For agency MBS, the direct default risk is minimized by the guarantee • Converts default risk into essentially random cash flow risk • Purely random risks are not “priced” • The major challenge is to determine whether you are being paid enough for writing the call option • Recall that much of the time, a call option expires unexercised • Ex-post cost is zero • However, when it is “in-the-money” it can cost the writer a great deal • Key to valuing the call option is figuring out the “expected present value” of the costs when it is exercised

  17. OAS • OAS is essentially an extension of the concept of a Z-spread • Modified to move from static analysis to consider multiple scenarios or future paths of interest rates • Z-spread was basically a “static” concept of spread since it was based on today’s yield curve with no consideration of the uncertain future interest rates. • Even when we talked about the “scenarios” suggested by the VALL forecasts, what we were really doing was simply shifting rates once and for all and adjusting the forecasted prepay speed. • Conceptually, we were making our best guess about the future and generating the best guess of cash flows • Resulted in a single estimate of yield

  18. OAS • Basic Idea • Generate a number of interest rate scenarios • Each scenario is a random path of short term spot rates over time • Ratet for t=1,…,360 • Each path must be consistent with today’s yield curve • Forward rates implied by today’s yield curve form a base • For each scenario, generate the cash flows from the MBS • Entails predicting mortgage prepayment speeds consistent over time with that scenario • CPRt=f(Δrates, econ variablest, personal characterisiticst) • Make a guess at an OAS • Solve for Price=PV of future cash flows for each scenario • Discount at 1/(1+ratet+OAS)t • Calculate average price over all scenarios for the OAS • Repeat steps 3 & 4 until average price equals actual price

  19. Using the OAS Tab • Takes the “scenarios” from the VALL Bloomberg page • Simplifies things since we can use the projected prepayment for each scenario and don’t need to build our own model • Note that I started with a base yield curve and then simply shifted that curve up or down and then projected monthly rates as in the Z-spread tab • For each scenario, I ran the MBS spreadsheet and then cut and pasted the cash flows (based on the projected speed) into the OAS tab as values • Then, I guess a single OAS and for each of the nine scenarios, I calculate a “price” • Price is calculated as the PV of future cash flows where each PV is discounted by the yield curve plus the assumed OAS • The treasury base changes in each scenario, but the OAS “add-on” is fixed • Then I calculated a “weighted” average price • Weights reflect subjective probability

  20. OAS Spread • For the MBS that is coded into the spreadsheet, • The market data is from late October 2004 • The MBS static spread over the 7 year Treasury was about 125 bp • the static Z-spread based on the yield curve in the base scenario was just under 120 bp • The estimated OAS spread was just under 50 bp • Found using goal seek to set the weighted average equal to the observed price • Bloomberg QY for this security reported an OAS of about 70 bp but was based on more complex scenarios and allowed for rates and the yield curve to vary over time, which in turn makes prepay speeds vary over time • In general, OAS should be less than the Z-spread • Borrowers exercise the call option in their own self interest • Taking the option effect into account (which the static Z-spread does not) reduces the spread or what is deemed to be the “excess” return.

  21. Scenario Analysis • In stock investing, theory tells us that the return we earn is equal to the IRR that equates the PV of all future dividends with the purchase price • But more commonly, people estimate a “holding period return”

  22. Scenario Analysis • Reasons for looking at a finite holding period and not “forever”: • More confident projecting cash flows (dividends or prepay speeds) over a short horizon • More confident in how market will value the firm (or the MBS) in the near term • For example, if we can project earnings and P/E ratios, we can estimate future values of S • For an MBS, we need to know spreads over Treasury • Same principles lead us to value commercial real estate based on a short term projection of NOI over a finite number of years and an estimated sale price (based on a “going out” cap rate)

  23. Scenario Analysis • Consider an Investment in a 7-year Treasury bond • 6% Coupon • Price to yield 6% (i.e., par) • Duration is about 6 years • Close to the duration of the base case MBS duration Three possible scenarios for the state of the world one year from now: Rates rise 100 bp Rates stay constant Rates fall 100 bp

  24. Scenario Analysis -Bond Example • Assume we plan to purchase this bond, hold it for one year and sell it at the end of a year • Interest payments are known for certain • $3 every six months (per $100 of principal) • Sales price at end of year uncertain • Selling a 6-year, 6% bond • Three scenarios give us three different prices • Roughly speaking, the holding period return varies +/- 5% for a 1% change in market rates

  25. Scenario Analysis • Next, let’s look at what happens to the yield on the 5% MBS purchased at a price of 96-03 that we have previously studied • Collateral • WAC: 5.624 • WAM: 28 y 4 mo • Servicing .624% • Prepay speed 157% PSA • Based on VALL median projection of lifetime prepay speed for no change in rates • MBS duration: 5.7 years • Mortgage yield (no delay) 5.69% • 96 bp over 10 yr T • Now look to the right of the input section of the MBS tab

  26. MBS Inputs for Scenario Analysis Example

  27. MBS Base Case Scenario • Table shows • Monthly cash flows to the investor based on projected MBS cash flows • Balance of Pool left to be sold after twelve months • In the “Rates Do Not Change” Scenario • Need to estimate price at which this 5% MBS could be sold • WAC best guess is about 5.624% • WAM: best guess is 27.33 years • Prepay speed: best guess– 157% • Spread over Treasuries (roughly 100 bp)

  28. Scenario Analysis MBS Base Case • Results • Price of MBS one year ahead is 95.99 ~ 96 even • Slightly less more than 96-03 because of the shorter maturity and the fact that the seasoning ramp is over • Proceeds from selling $90,395,412.37 at a price of 95.99 generates $86,767992.43 • IRR for 1 year holding period is 5.51% • Slightly less than the 5.69% ytm because we used a 1.00% spread not 96 bp to determine the future selling price. If we used 96 bp spread, the price is 96.2 or slightly higher than 96.09 because of the shorter time to maturity effect on discount bonds • Nevertheless, for the MBS in the no change scenario, we have essentially the same story as in the bond example • YTM is close to holding period return if rates do not change

  29. MBS: Rates Fall 100 bp • Next, as with Treasury example, consider the rates fall 100 bp case for the MBS • Need to adjust the prepay speed for both the first 12 months of cash flows and also for selling the remainder of the MBS • Use the VALL report to estimate prepay speeds increase to 360% PSA • Enter this prepay speed to generate new cash flows and new balance of MBS available for sale • New duration of MBS is 3.29 years • New projected yield is 6.22% (no delay) because the higher speed accelerates the recapture of the discount • But that is the yield impact if the MBS is held to maturity. Let’s now look at the holding period return

  30. Resulting Holding Period Cash Flows and IRR Inputs for down 100 bp scenario Only change is prepay speed increased to 360 PSA speed

  31. MBS: Falling Rates • From a Holding Period Return perspective, the increased speed has two negative implications • Although MBS prices have risen because of the decline in rates, we have less to sell at the higher price • $79.870 million now versus $90.395 in base case • Because the duration of the remaining MBS we have to sell is shorter, the price rise for a 1% shift in required yield is less than it would have been if the duration were unchanged. • New price calculated at 100.88 versus a price that would have been 101.56 if PSA speed did not change from 157% when rates fell • However, the overall result is still favorable and the results show a 1 year holding period return of 10.25% • Up 4.74% from base case

  32. MBS: Rates Rise 100 bp • Finally, consider the rates rise 100 bp case for the MBS • Need to adjust the prepay speed for both the first 12 months of cash flows and also for selling the remainder of the MBS • Use the VALL report to estimate prepay speeds slow to 126% PSA • Enter this prepay speed to generate new cash flows and new balance of MBS available for sale • New duration of MBS is 6.35 years • New projected yield is 5.62% (no delay) because the slower speed hurts the ytm for securities bought at a discount • BUT, it gets worse!

  33. MBS: Rising Rates • Now the slower speed means that we have more to sell and what we are selling at a higher yield has a longer duration and hence a bigger price decline • Remaining Principal for sale: • $92.0 million now versus $90.395 in base case • Price of MBS at resale one year from now:. • New price calculated at 89.98 versus 95.99 in the base case and $90.95 if speed did not change from 157 to 126PSA • In this case, the overall result is hurt on all fronts. The 1 year holding period return is a 1 year holding period return of -.54% • Down 6% from base case

  34. Down: Less improvement in price, big decline in balance Up :More decline in price plus increase in balance Moral: Mortgage do worse when things go bad & do less well when things go well Main reason for this asymmetric behavior is the imbedded call option. “Negative Convexity”

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