Techniques for Valuing MBS
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AIM Statements
Calculate the static cash flow yield of a MBS using bond equivalent yield (BEY) and determine the
associated nominal spread.
Define reinvestment risk.
Describe the steps in valuing a mortgage security using Monte Carlo methodology.
Define and interpret option-adjusted spread (OAS), zero-volatility OAS, and option cost.
Explain how to select the number of interest rate paths in Monte Carlo analysis.
Describe total return analysis, calculate total return, and understand factors present in more
sophisticated models.
Identify limitations of the nominal spread, Z-spread, OAS, and total return measures.
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Bond Equivalent Yield (BEY) and Nominal Spread
The nominal spread is the difference between an MBS static cash flow yield and the treasury
security with the same maturity as the average life of the MBS.
The MBSs have monthly cash flows and treasury securities have semiannual cash flows.
The yield of the treasury security is calculated by doubling the semiannual yield.
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BEY = 2[(1 + im ) − 1]
Where im = monthly mortgage yield
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Problem
The MBS has an average life of 10 years. The MBS has a monthly mortgage yield of 0.45%. If the
10-year treasury bond has a yield of 4.25%, calculate the BEY and nominal spread for this MBS.
In this problem
im = 0.45%
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BEY = 2[(1 + im ) − 1]
BEY = 5.46%
Nominal Spread = BEY – Yield of treasury bond = 1.21%
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Reinvestment Risk
Risk of reinvesting the coupons payments at a lower rate due to the decrease in market rate
market interest rates.
MBSs are more prone to reinvestment risk than bonds.
MBSs have monthly payments which consist of both interest and principal payments.
When the interest rates falls, MBSs payments are subjected to higher prepayment rates.
Bonds have less frequent semiannual payments that consist of interest only.
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Dynamic Valuation
The cash flows for MBSs are dependent upon the path that the interest rate follows and cannot be
valued using the binomial model
The CF from a pass-through security is a function of pre-payment rates and these are affected by
interest rates from the past.
If mortgage rates trend downwards many homeowners will probably refinance their mortgages
and hence the prepayment rates will increase.
If the mortgage rate still keeps falling, the prepayment rates might not fall further. This is known
as refinancing burnout.
This applies to MBS and other types of pass-through security cash flows.
As it is path-dependent, the Monte-Carlo simulation technique is used to value these securities
instead of the binomial model.
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Monte Carlo Methodology
The following four steps are required to value a mortgage backed security using the Monte Carlo
methodology: Step1: Simulate the interest rate path and refinancing path.
Step2: Project cash flows for each interest rate path.
Step3: Calculate the present value of the cash flows for each interest rate path.
Step4: Calculate the theoretical value of the mortgage security.
Theoretica lValue =
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PV [ path (1)] + PV [ path ( 2 )] + ...... + PV [ path ( N )]
N
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Option Adjusted Spread
Option adjusted spread (OAS) is defined as the spread K which when added to all the spot rates of
all the interest rate paths, will make the average present value of the paths equal to the observed
market price plus accrued interest.
MarketValu e =
PV [ path (1)] + PV [ path ( 2 )] + ...... + PV [ path ( N )]
N
OAS is determined with an iterative process.
OAS indicated the potential compensation after adjusting for the prepayment risk.
OAS is superior to nominal spread.
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Zero Volatility Spread (Z-Spread)
Zero volatility is the spread measure that the investor realizes over the entire spot rate the curve,
assuming that the mortgage security is held till maturity.
Z spread is the yield that equates the present value of the MBS cash flows to price of the MBS
discounted at the treasury spot rate plus the spread.
Iterative process is required to calculate the Z-Spread.
Accounts for changes in principal payments ignores the impact of prepayment risk or changing
prepayment rate have on value of MBS.
Option Cost = Z Spread - OAS
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Increasing the number of Rate Paths
Increasing the number of simulated rate paths gives the better estimate of the theoretical value
of MBS.
Mean Standard Error (MSE)
MSE =
Variance of theoretica l values
Number of trials
Smaller MSE indicates the better estimate of the output value from Monte Carlo Simulation.
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Total Return Analysis
The parameters required to calculate the total return for a MBS are as follows: The initial security cost at the time of purchase.
Projected cash flows for the security.
The security's projected horizon value at the horizon date.
PeriodicTo tal Re turn =
Total Horizon Pr oceeds
−1
Total Cost
Annualized Total Re turn = ( PeriodicTo tal Re turn ) *
12
number of month in period
The advantage of using this method is that it allows investors to specify reinvestment returns.
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Problem – Total Return Analysis
Calculate the total periodic return and the annualized total return for a Fannie Mae 5% pass through
security over a 6 – month horizon with the information provided in below: Total Interim Cash Flows = 1,403,900
Total Horizon Value = 8,955,998
Total Cost = 10,049,500
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Factors to Consider for Return Calculation of MBSs
Reinvestment and prepayment assumptions are very important.
Cash flows are path dependent.
Most models adjust for changes in interest rates either immediately, gradually over time or at the
horizon.
Total return models also consider profit and loss, return on equity and financing adjusted returns.
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Limitations for MBS Valuation Measures
Nominal spread does not consider prepayment risk.
Another problem with nominal spread is the difference in timing of cash flows of MBS and
treasury security.
Z-Spread ignores the impact of prepayment risk or changing prepayment rate have on value of
MBS.
OAS has four major limitations:• Modeling risk associated with Monte Carlo simulations
• Required adjustment to interest rate paths.
• Assumption of constant OAS over the in the model.
• The dependency of the underlying prepayment model.
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Limitations for MBS Valuation Measures
Nominal spread, Z-spread, OAS have a common limitation. All these measures assume that the
security is held till maturity.
Total return model output is dependent on the assumptions related to the horizon price and
prepayment rates.
Dynamic rate scenarios are not included in total return model.
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© Pristine FRM – II