Value of mortgage security = value of a treasury security-value of prepayment option.. Positive / Negative Convexity & Duration Changes Negatively convex security Positively convex secur
Trang 1“HEDGING MORTGAGE SECURITIES
TO CAPTURE RELATIVE VALUE”
1 INTRODUCTION MBS outperform similar I.R risk govt securities due to higher spread offered
PV = Present Value
I.R = Interest Rates
MBS = Mortgage Backed Securities
MP = Market Price
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
Negatively convex security Positively convex security Positively convex security Negatively convex security
Duration (become flatter)
Duration (become steeper)
Duration (become steeper)
Duration (become flatter)
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
CF = Cash Flows Y.C = Yield Curve
PC = Positive Convexity
NC = Negative Convexity
PO = Principal Only
IO = Interest Only
Trang 2B 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
Trang 35 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
Hଶ× 2 − H price + Hଵ × 10 − H price
Hଶ× 2 − H price + Hଵ × 10 − H price
Level: Hଶ× 2 − H price + Hଵ × 10 − H price = −MBS price
Twist: Hଶ× 2 − H price + Hଵ × 10 − H price = −MBS price
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
Step 9 Determine set of equations that equates the ∆ in value of two bond hedge to ∆ in price of mortgage security
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