11 terms

Hedging Mortgage Securities - add a few cards to the card set created by ndeep167

Convexity

Convexity refers to the nonlinear relationship between the value of a fixed-income instrument and its yield.

Define Negative Convexity

the security loses more from a give increase in yield than it gains from a corresponding decrease in yield

how a mortgage security's negative convexity will affect the performance of a hedge.

There is a problem with using a hedging instrument that has positive convexity (indicated below by the prescript pc) to hedge an asset with negative convexity. If the downside risk from a yield increase is hedged exactly, then the portfolio will likely lose value when interest rates decrease.

pc position is short and the nc position is long,

pc position is short and the nc position is long,

What are the risks associated with investing in mortgage securities?

(1) Spread risk

(2) Interest rate risk

(3) Prepayment risk

(4) Volatility risk

(5) Model risk

(2) Interest rate risk

(3) Prepayment risk

(4) Volatility risk

(5) Model risk

Define spread risk

the risk of the mortgage security's yield spread over the corresponding T-bond widening, & thus lowering the value of the mortgage security

Define interest rate risk

the price fluctuation caused by the volatility of the yield on Treasuries with which the yields on mortage securities are highly correlated

Define prepayment risk

the cause of negative convexity, which means the mortgage security loses more from a given increase in yield than it gains from a corresponding decrease in yield

Define volatility risk

associated w/ the embedded prepayment option.

An increase in volatility increases the value of an option. Because the mortgage security is short the option:

An incr. in yield volatility -> increase in option value -> decrease value of mortg. security

An increase in volatility increases the value of an option. Because the mortgage security is short the option:

An incr. in yield volatility -> increase in option value -> decrease value of mortg. security

Defina Model Risk

Model risk can be from naively projecting past patterns of interest rates into the future. Another source is not recognizing the effects of technological and institutional innovations, which make prepayment more convenient to the borrower, thus increasing the risk from that source.

Contrast an individual mortgage security to a Treasury security with respect to the importance of yield-curve risk.

for a single noncallable bond, yield curve risk is not as important because of the comparatively large cash flow at maturity (i.e. principal)

for mortgage securities there is no

bullet payment at the end [i.e., rather than interest·only payments {coupons) with the principal paid at the end, mongage security payments can contain interest, principal, or

both]. A manager has to consider hedging against changes in more than a single key rate.

for mortgage securities there is no

bullet payment at the end [i.e., rather than interest·only payments {coupons) with the principal paid at the end, mongage security payments can contain interest, principal, or

both]. A manager has to consider hedging against changes in more than a single key rate.

compare duration based and interest rate sensitivity approaches for hedging mbs

Duration based removes risk assoc. with increase in rates but - 1. Neg. Convexity - can produce a net loss when rates decrease. 2. not effective with observed patterns of yield curve changes over time and effect of yield curve changes have on propensity to refinance (aka prepayment)

A two-bond hedge can, given certain assumptions, hedge against both a change in interest rates and a twist in the yield curve. This is done by forecasting a given rate and curve twist and the associated average price change for the mortgage security and the two bonds being used to hedge. This gives a two-equation and two-unknown system to determine the positions needed for the two-bond hedge.

A two-bond hedge can, given certain assumptions, hedge against both a change in interest rates and a twist in the yield curve. This is done by forecasting a given rate and curve twist and the associated average price change for the mortgage security and the two bonds being used to hedge. This gives a two-equation and two-unknown system to determine the positions needed for the two-bond hedge.