PRMIA Exam 8006 Topic 10 Question 57 Discussion

Mortgage backed securities carry prepayment risk as borrowers tend to prepay mortgages when rates fall, and substitute it with newer cheaper mortgages. This creates the issue of 'negative convexity' for mortgages, ie, they lose value when rates rise, but do not gain in value when rates fall.

Prepayment risk can be offset by instruments that also carry negative convexity. A swaption is an option to borrow in the future at an agreed rate, which may be fixed or floating. An option to borrow in the future paying floating and receiving fixed guards against losses when rates fall, as the option can be exercised for a profit when rates are declining and the mortgage portfolio is being prepaid. A callable bond is very similar to an MBS in that the issuer can call it back when rates fall. Thus a long position in an MBS can be offset by a short position in a callable bond. Thus I and III are valid choices.

A cap allows exchanging fixed for floating when interest rates rise above an agreed rate. A long cap position allows borrowing at a fixed rate in exchange for floating, and a short cap implies receiving fixed and paying floating when rates go above the strike rate. Prepayment risk arises from falling interest rates, therefore a short cap will not protect against such a risk as falling interest rates would mean that no payments would be exchanged. Thus II does not help hedge against the risk in question.

A long position in a fixed for floating swap would require paying fixed and receiving floating when rates are falling. This would just make the problem from prepayments worse as the position would pay fixed and receive a falling rate. Thus IV is not an appropriate way to hedge prepayment risk.