FinQuiz smart summary, study session 10, reading 26

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2013, Study Session # 10, Reading # 26

“HEDGING MORTGAGE SECURITIES
TO CAPTURE RELATIVE VALUE”
PV = Present Value
I.R = Interest Rates
MBS = Mortgage Backed Securities
MP = Market Price

1. INTRODUCTION
MBS outperform similar I.R risk govt. securities due to higher spread offered.

CF = Cash Flows
Y.C = Yield Curve
PC = Positive Convexity
NC = Negative Convexity
PO = Principal Only
IO = Interest Only

2. THE PROBLEM
Yield on mortgage security is CF yield (I.R that makes PV of CF equal to
MP).
MBS exhibit both positive convexity (a given change in I.R, gain > loss) &
negative convexity (vice versa from P.C).
Home owner’s prepayment option is main reason for MBS NC.
Value of mortgage security = value of a treasury security-value of
prepayment option.
When I.R , value of MBS falls less than treasury value due to in
prepayment option.

Positive / Negative Convexity & Duration Changes

When I.R

Positively convex security
Duration
steeper)

(become

When I.R

Negatively convex security
Duration
flatter)

(become

Positively convex security
Duration
flatter)

(become

MBS are considered market directional investments when I.R .
For proper management ⇒ separate mortgage valuation decision from
portfolio I.R risk management
Without proper hedging (duration of mortgage securities) portfolio’s
duration drift adversely from its target duration (shorter than desired

when IR & vice versa).

3. MORTGAGE SECURITIES RISKS
Yield on MBs = yield on equal I.R risk treasury + spread
Spread = option cost (for bearing prepayment risk) + OAS (for other risks).

A. Spread Risk
Portfolio manager does not seek to hedge spread risk instead capture OAS
by allocation when spreads are wide & vice versa.
Monte Carlo approach is used to calculate OAS.
Historical OAS comparisons are of limited use (dependent on prepayment
model).
Spread risk (OAS may change) is managed by investing heavily in MBS
when initial OAS is large.

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Negatively convex security
Duration
steeper)

(become


2013, Study Session # 10, Reading # 26

B. Interest Rate Risk
Can be hedged directly by selling a package of treasury notes or treasury
note futures.
After hedging for I.R risk, a manager can earn the treasury bill rate plus

OAS reduced by the value of prepayment option.
Yield Curve Risk

Exposure of a portfolio or security to a nonparallel ∆ in Y.C shape.
Key rate duration is one approach to quantify Y.C risk.
Value of option free single bullet bond is less sensitive to shape of Y.C
while portfolio of option free bullet bonds are much more sensitive to
shape of Y.C.
Mortgage security is amortizing so more sensitive to shape of Y.C.
Po strips have high positive while IO strips have high negative duration.

C. Prepayment Risk
Because of prepayment option duration of MBS varies in an undesirable
way (extending as rates rise & vice versa).
Managing NC bears cost {options or dynamically hedge (futures)}.
Buy futures ⇒ lengthen duration when I.R & vice versa.

D. Volatility Risk
Prepayment option becomes more valuable when I.R volatility .
OAS widens when volatility & vice versa.
Use dynamic hedging when implied volatility > future realized volatility &
buy options for hedging when implied volatility < future realized volatility.

E. Model Risk
Risk related to prepayment model.
To check model error sensitivity for securities hurt by:
Faster than expected prepayments⇒ prepayment rate assumed by model.
Slower than expected prepayments⇒ prepayment rate assumed by model.
Prepayment models should consider impact of technological improvements
Model risk can’t be hedged explicitly but can be managed by keeping portfolio’s

exposure to it in line with broad based bond market indices.

4. HOW INTEREST RATES CHANGE OVER TIME
Exposure to potential Y.C shifts can be measured through
Key rate duration.
Investigating how Y.C has changed historically.

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2013, Study Session # 10, Reading # 26

5. HEDGING METHODOLOGY
To properly hedge I.R risk associated with MBS, following should be
considered.
Y.C changes over time.
Effect of Y.C change on prepayment option.

A. Interest rate Sensitivity Measure
Measure a security’s or a portfolio’s % price change in response a shift in
Y.C assuming OAS is constant.
Two treasury notes (2 year 10-year) can hedge all I.R risk in mortgage
security (two bond hedge).

B. Computing the Two-Bond Hedge
Step 1
For an assumed shift in level of Y.C calculate price of MBS & 2 year & 10 year treasury note.
Step 2

calculate price ∆ for all three securities (2 price changes for each security).
Step 3
calculate avg. price change.
Step 4-6
For an assumed twist in Y.C repeat steps 1-3
Step 7-8
Compute ∆ in value of two-bond hedge for a ∆ in level & twist of Y.C as

Hଶ × ሺ2 − Hprice୐ ሻ + Hଵ଴ × ሺ10 − Hprice୐ ሻ
Hଶ × ሺ2 − Hprice୘ ሻ + Hଵ଴ × ሺ10 − Hprice୘ ሻ
Step 9
Determine set of equations that equates the ∆ in value of two bond hedge to ∆ in price of mortgage
security.

Level:Hଶ × ሺ2 − Hprice୐ ሻ + Hଵ଴ × ሺ10 − Hprice୐ ሻ = −MBSprice୐
Twist:Hଶ × ሺ2 − Hprice୘ ሻ + Hଵ଴ × ሺ10 − Hprice୘ ሻ = −MBSprice୘
Step 10
Solve the equations in step 9 for values of H2 & H10

C. Illustrations of the Two-Bond Hedge

D. Underlying Assumptions
Y.C shifts are reasonable.
Prepayment model works well.
Assumptions underlying Monte Carlo model are realized.
Avg. price ∆ for small ∆ in I.R is good approximation of MBS price∆.

6. HEDGE CUSPY-COUPON MORTGAGE SECURITIES
Some mortgage securities (cuspy coupon) are very sensitive to small
I.R movements (more negative convexity than current coupon

mortgages).
Solution ⇒ add I.R option to two bond hedge to offset some or all
cuspy coupon N.C.

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