Reading 50 - Valuing Mortgage-Backed and Asset Backed Securities

Question 1

What is the cash flow yield

Answer 1

Is the discount rate the makes the price of a mortgage-backed security (MBS) or asset-backed security (ABS) equal to the PV of its cash flows.

Question 2

What are the steps to computing the cash flow yield?

Answer 2

• Estimate the future monthly cash flows
• Calculate the monthly rate of return that makes the PV of these future cash flows equal to the security’s current market price.

** The monthly cash flow yield is usually converted to a bond-equivalent basis for comparison to yield to maturity

BEY = 2 [(1+monthly cash flow yield)⁶ -1]

Question 3

The cash flow yield has two major deficiencies… When we use cash flow yield as our estimate of the bond’s expected return, we have to assume these 2 things…..

Answer 3

1. That the cash flows will be reinvested at the cash flow yield prevailing when the MBS/ABS is priced (aka reinvestment risk)
2. The MBS/ABS will be held until the last loan in the pool is paid off. If the security is sold prior to maturity, uncertainty is introduced regarding terminal cash flows (aka price risk)

Question 4

What is the nominal spread?

Answer 4

The difference between the cash flow yield on an MBS and the YTM on a Treasury security with a maturity equal to the average life of the MBS.

Question 5

What is a limitation of using nominal spread to analyze MBS?

Answer 5

We don’t know how much of the nominal spread reflects the significant prepayment risk associated with MBS.

Question 6

What is the Zero-volatility spread?

Answer 6

Used to measure the relative value for a MBS or ABS.

Is the spread that must be added to each Treasury spot rate that will cause the discounted value of the cash flows for an MBS or ABS to equal its price, assuming the security is held till maturity.

Question 7

What is the key limitation to using the Z-spread (Zero-Volatility Spread)?

Answer 7

That it only considers one path of interest rates, the current Treasury spot rate curve.

Question 8

What are the 5 steps in the valuation of an MBS using the Monte Carlo simulation model?

Answer 8

1. Simulate interest rate paths (ex 1,000 different paths) and cash flows using assumptions concerns benchmarks rates, rate volatility, refinancing spreads, and prepayment rates
2. Calculate the PV of the cash flows along each of the 1,000 interest rate paths
3. Calculate the theoretical value of the MBS as the average of the present values along each path.
4. Calculate the OAS as the spread that makes the theoretical values equal to the market price
5. Calculate the option cost as the zero-volatility spread minus the OAS.

Question 9

Describe path dependecy in passthrough securities…

Answer 9

Relevant CF to be discounted is either call or theoretical price (less)

• CF from MBS are dependent on the path that interest rates follow which is against a major assumption of the binomial model (cant be used)
• CF for passthrough securities are a function of prepayment rates and prepayment rates in any given month are affected by past interest rates

Question 10

What are the two sources of path dependecy in passthrough securities?

Answer 10

1. If mortgage rates trend downwards, prepayment rates will increase at the beginning of trend as homeowners refinance their mortgages.
   - Prepayment will slow as the trend continues because most of the homeowners that can refinance, will already have done it (prepayment burnout)
   
   2. Cash flows that a particular CMO tranche receives in any one month depends on outstanding principal balances in other tranches which is dependent on prepayment history and interest rate path.

Question 11

How is the Option-Adjusted spread calculated using a Monte Carlo simulation model?

Answer 11

• Same process as the OAS from the binomial model
• We want to determine the spread the makes the MBS value equal to its current market price.
• OAS is the spread we have to add to every spot rate along every interest rate path
• Is the MBS spread after we take into account optionality of cash flows
• Is the dollar difference between price and theoretical value of spread

Question 12

How can the implied cost of the embedded option be expressed?

Answer 12

=zero volatility spread - option adjusted spread

-Option cost is derived from OAS

Question 13

How should the OAS be interpretted?

Answer 13

• Measures the average spread over treasury spot rates, not the comparable treasury yield
• Want OAS to be large which indicates a larger risk adjusted spread which leads to lower relative price
• Can interpret OAS for an MBS as the additional compensation for credit, liquidity and modeling risk after the cost of the option has been removed

Question 14

What is modeling risk in regards to OAS??

Answer 14

• Uncertainty from assumptions in the complicated monte carlo model framework
• The model is very sensitive to the interest rate volatility assumption and the prepayment assumption
• Interpretation of OAS depends on the security credit risk, liquidity risk, and modeling risk relative to the benchmark.

Question 15

Does the OAS using a Treasury benchmark reflect , credit risk, liquidity risk modeling risk for a Ginne Mae passthrough

???

Need to answer for each of the 3 risks!!

Answer 15

• CredIt risk - No
• Liquidity risk - Yes
• Modeling risk - Yes

Question 16

Does the OAS using a Treasury benchmark reflect , credit risk, liquidity risk modeling risk for a Ginne Mae CMOs ???

Need to answer for each of the 3 risks!!

Answer 16

• Credit risk - No
• Liquidity risk - Yes, support tranches have more than PAC I
• Modeling risk -Yes, CMOs have more than passthorughts. CMO support tranches have more than PAC I

Question 17

Does the OAS using a Treasury benchmark reflect , credit risk, liquidity risk modeling risk for Freddie Mac/Fannie Mae passthroughs ???

Need to answer for each of the 3 risks!!

Answer 17

• Credit Risk - Yes, but small
• Liquidity Risk - Yes
• Modeling Risk - Yes

Question 18

Does the OAS using a Treasury benchmark reflect , credit risk, liquidity risk modeling risk for Freddie Mac/Fannie Mae CMOs ???

Need to answer for each of the 3 risks!!

Answer 18

• Credit Risk : Yes, but small
• Liquidity Risk : Yes, CMO support tranches have more than PAC I
• Modeling Risk : Yes, CMOs have more than PAC I

Question 19

Does the OAS using a Treasury benchmark reflect , credit risk, liquidity risk modeling risk for Non-agency MBS and real estate ABS ???

Need to answer for each of the 3 risks!!

Answer 19

• Credit Risk - Yes
• Lquidity Risk - Yes, more than agency issues
• Modeling Risk - Yes

Question 20

What does the term representative paths refers to regarding Monte Carlo model simulations?

Answer 20

• As number of paths generated by monte carlo model increases, better the estimate is
• Reduced set of paths employed through computational procedures that
• Theoretical value is then weighted average of PV of each rep path weighted by path rates
• Get the theoretical value and find the one that equals the Market price which is the OAS bps

Question 21

How are Cheap or Rich securities determined when using option-adjusted spread analysis?

Answer 21

• Compare OAS and option costs of various tranches
• Securities with longer effective durations have larger oas and option costs because of the higher interest rate exposure.
• Cheap = high OAS relative to required OAS and low option costs
• Rich = Low OAS relative to required OAS and high option costs
• Cheap are typically undervalued and want to buy them

Question 22

What are two things to note regarding absolute valuation using option-adjusted spread analysis?

Answer 22

1. Tranches trading at a premium will see gains when prepayment rates decrease
2. Increases in assumed interest rate volatility increases the option cost and reduces the value of MBS
   - Gains in value are more pronounced for tranches with higher effective duration

Question 23

What are the reasons why effective durations reported by various dealers and vendors may differ?

Answer 23

1. Differences in changes in y - if it is an incremental change and the change is too large, the effects of convexity mess with the estimates
2. Prepayment models differ among dealers
3. OAS is a product of the monte carlo simulation model. Differences in the inputs to the model will affect the measurment of OAS
4. Differences in the spread between 1 month rate and financing rate. Different assumptions about this relationship will get different results

Question 24

What is the formula we can use to estimate the % price in a bond for a given change in yield?

Answer 24

% change in bond price ~ duration effect + convexity effect

Question 25

When analyzing interest rates with effective duration and convexity what are the main points you need to know?

Answer 25

• Interest rate risk - risk that price of fixed income security will change as yield changes
• Larger the duration the greater the interest rate risk
• Duration only gives estimates of actual change in the price of a bond for small changes in yields
• Convexity adjustment gives a more precise estimate for larger changes in yield.
• Greater the convexity, lower the interest rate risk

Question 26

What is Cash flow duration?

Answer 26

• Version of effective duration that allows for CF to change as interest rates change
• Uses a static valuation procedure to determine the prices

Question 27

What are the steps to calculate Cash Flow Duration?

Answer 27

1. Make a prepayment rate assumption and use it to estimate cash flows
2. Compute CF yield based on the market price and CF estimates
3. Increase CF yield by the change in y and with the use of a prepayment model, recomputes prepayment rates (usually lower than original rates)
4. Recompute the CF using the prepayment rates generated and discount these at the higher cash flow yield
5. Decrease CF yield by change in price and with the use of a prepayment model, regenerate prepayment rates (normally greater than the original rates)
6. Recompute cash flows using prepayment rates just calculated and discount these at the lower CF yield

Question 28

What is the major criticism of cash flow duration?

Answer 28

• Based on unrealistic assumption that new MBS prepayment rate is constant over entire life.
• Effective duration computed using the Monte carlo simulation is much better than CF duration for MBS

Question 29

What is Coupon Curve duration?

Answer 29

• Based on relationship between coupon rates and prices for similar MBS.
• Look at a coupon curve and use the different percents and prices in the duration equations

Question 30

What are the advantages and limitations of Coupon curve duration

Answer 30

• *Advantages**
• Easy to apply
• Uses market prices that should reflect market expectations
• *Limitations**
• Only applicable to generic MBS.
• Not readily applicable for CMO structures and other mortgage backed derivatives

Question 31

What is Empirical Duration?

Answer 31

• Is determined using regression analysis of historical relationship between security prices and yields

Question 32

What are some of the adavantages and disadvantages of empirical duration?

Answer 32

Advantages

• few assumptions
• Requirement parameters are easy to estimate with reg analysis.
• Time Series data for treasury prices and yields are readily available

Disadvantages

• Time series price data on mortgage securities may be difficult to obtain
• embedded options can distort the results
• Volatility of spreads over treasuries can distort price reaction to interest rate changes

Question 33

When should the nominal spread be used to evaluate a specific fixed income security?

Answer 33

• Spread between CF yield and the yield on treasury securities with same maturity and average life
• Spread at one point on treasury curve
• Should never be used for MBS and ABS because it masks the fact that some of the spread is compensation for accepting prepayment risk

Question 34

When should a zero-volatility spread be used to evaluate a specific fixed income security?

Answer 34

• Spread over entire Treasury spot rate curve if MBS is held until maturity.
• Suitable for assessing the value of option free bonds
• Shouldn’t be used with bonds that have prepayment options because it doesn’t reflect possibility that CF may change as interest rates change

Question 35

When should a option-adjusted spread (OAS) be used to evaluate a speicifc fixed income security?

Answer 35

• Assess the value of fixed income securities that have embedded options that make it possible for cf to change as interest rates change
• Amounts of cfs that are not interest rate path dependent should use binomial model but if it is dependent, use the Monte Carlo

Question 36

Given the following information, which bond has the greater interest rate risk and what is the change in price if rates increase by 50 basis points?

                      Par          Mkt Price       PVBP per $1,000

Bond A 2,000,000 1,987,500 0.885

Bond B 7,000,000 8,588,250 1.025

Answer 36

PVBP (price value of a basis point) is the absolute value of the change in bond value for a 1 basis point change in yield.
Change in price = -PVBP × change in basis point x par in thousands
Bond A = -0.885 × 50 × 2,000 = -88,500
Bond B = -1.025 × 50 × 7,000 = -358,750

Question 37

Given the following information, which bond has the greater interest rate risk and what is the change in price if rates increase by 50 basis points?

                         _Duration_                  _Convexity_

Bond A 4.5 45.8
Bond B 7.8 125.0

Answer 37

Bond B has the greater interest rate risk since the change in price is larger than bond A.
Change in price = (-D × change in bp × 100) + (C × change in bp² × 100)
Bond A = (-4.5 × 0.005 × 100) + (45.8 × 0.005² × 100) = -2.25 + 0.1145 = -2.14%
Bond B = (-7.8 × 0.005 × 100) + (125 × 0.005² × 100) = -3.9 + 0.3125 = -3.59%