Hedging Mortgage Securities

Mortgage is annuity!

Mortgage has negative convexity!

If use positive convexity derivative to hedge mortgage, one will incur big loss when the yield reduces!

Risks:

1. Interest rate risk: Parallel shift
2. Spread risk : over treasury, relative value to T-bond reduces as widen
3. Prepayment risk: shorting call option
4. Volatility risk: more volatile, higher call value
5. Model risk: e.g. wrong assume of prepayment model, ignore technological and institutional innovations

If spread risk is not hedge, can be use to capture extra return (e.g. increase exposure when spread risk is high)

Yield Curve Risk: Twist of Yield Curve

For a non-callable bond with bullet payment, only a particular key rate duration is important.

But for a mortgage security, all key rates are important.

Principals only strips (PO) has negative duration (move in tandem with interest rate) for short maturities and then positive. Interest-only strips (IO) are opposite.

This is because when long term interest rate decreases, prepayment risk increases, PO receives more cash flow but IO receives less.

To hedge Mortgage Security, one can construct a two-bond hedge and solve the linear equations. The manager needs to:

1. Incorporate reasonable possible yield curve shift
2. Includes reliable assumption in MC for interest rate
3. Know the security price change
4. Use average price change method