FRM2009.E2.36
Category:FRM2009 -> Full2
Question:
[source: 2009 sample exam II] Your firm’s fixed‐income portfolio has interest‐only CMOs (IO), callable corporate bonds, inverse floaters, noncallable corporate bonds. Your boss wants to know which of the following securities can lose value as yields decline.
a. callable corporate only
b. inverse floater only
c. IO and callable corporate bond
d. IO and noncallable corporate bond
[my adds]
36b. What is unique about the duration of an interest only (IO) strip?
36c. What is unique about the duration of an inverse floater?
36d. How does the price of the callable corporate bond compare to the price of a noncallable corporate bond, for both low and high yields (assume otherwise identical features)?
36e. How and where (in the yield curve) does the call option induce negative convexity?
36f. Does negative convexity imply negative duration?
Answer:
CORRECT: C
The IO decreases in value because a decline in rates implies an increase in mortgage prepayments, which decreases the notional principal upon which the IO pays its interest
INCORRECT: A - While the price of a callable corporate may decline as the call goes in the money, the IO also decreases in value
INCORRECT: B - The IO decreases in value, but so can the callable corporate
INCORRECT: D - The noncallable corporate bond increases in value as yields decline
Reference: Tuckman, Chapter 21
I disagree with this answer. I agree that an IO has negative duration but a callable bond exhibits negative convexity at low yields. As noted below, negative convexity does not imply negative duration. If someone can correct me, please give help? - David
36b. What is unique about the duration of an interest only (IO) strip?
It exhibit negative duration unlike most fixed income instruments.
36c. What is unique about the duration of an inverse floater?
Unlike most instruments, floaters tend to have a duration that is greater than their maturity!
36d. How does the price of the callable corporate bond compare to the price of a noncallable corporate bond, for both low and high yields (assume otherwise identical features)?
price of a non-callable = price of callable + value of embedded option, or
price callable = price non-callable - price of call option
At high yields, the bond price is low and the value of the call option is low: the price of the callable is nearer to the price of the non-callable
At low yields, bond price is high and the value of the call option is low: the price of the callable is significantly lower than the price of the non-callable
In all cases, the price of the callable is less than the price non-callable where the difference equals the value of the call option
36e. How and where (in the yield curve) does the call option induce negative convexity?
At low yields, because the issuer will call the bond and this limits the upside price potential of the bond. Negative convexity exhibits at low yields for the callable bond
(per Tuckman, the prepayment option on the mortgage is the MBS equivalent to a call option)
36f. Does negative convexity imply negative duration?
No! That’s why the sample answer is incorrect.
Negative convexity implies the dollar duration is decelerating instead of accelerating
In a noncallable bond, as the yield decreases the dollar duration (the first derivative) is dropping (i.e., convexity or upward concavity); e.g., 4% to 3% giving dollar duration of, respectively, -600 and -700 would not be unusual.
In a callable bond, the negative convexity means a yield decrease is associated with an increase in dollar duration. However, the dollar duration would still generally be negative! For example, 4% with -600 dollar duration changing to 3% and -500 implies negative convexity (i.e., the first derivative is decelerating).