With the new and excellent Veronesi text, the FRM finally, formally introduces concepts of effective duration and effective convexity. P2 candidates now have three durations: Macaulay, modified and effective. The key (IMO) to grasping "effective" is to realize it is the non-analytical "full revaluation" approach: if you meditate on the formula, you can see how it is just computing the slope (rise/run) based on two points on the price/yield curve (i.e., it computes the slope of secant line which is very near to the tangent line). If you get this, you can confirm that, in the case of a vanilla bond, "effective" duration approximates "modified" duration and has a identical interpretation; but when the bond contains embedded options, the failure of the analytical linear approximation (i.e., mod duration as a function of Mac duration) insists that we must directly (numerically) retrieve an approximation of the slope - David
AIM: Describe the effective duration and effective convexity of standard MBS instruments and the factors that affect them.
Questions:
105.1. The current term structure is flat with a yield of 4.0%. Assuming 100%, the price of $500 million pass-through mortgage-backed security (MBS) is $584.2 million. Assuming a 4.5% yield and 50% PSA, the value of the MBS drops to $573.5 million; assuming a 3.5% yield and 150% PSA, the value of the MBS increases to $591.9 million. What are, respectively, the approximate effective duration and effective convexity of the MBS?
a. 2.7 and -133
b. 3.1 and -205
c. 4.6 and -375
d. 5.8 and -412
105.2. In regard to the effective duration and effective convexity of a pass-through mortgage-backed security (MBS) pool, EACH of the following is true EXCEPT:
a. "Effective" signifies the analytical approximation that is necessary due to variations in prepayment speed; i.e., analytical solutions are not available
b. Due to prepayments, at low yields we expect negative duration
c. Due to prepayments, at low yields, we expect negative convexity
d. As market yields decrease, it is reasonable to increase the PSA assumption; e.g., from 150% PSA to 175% PSA
105.3. Barry the analyst calculated the effective duration of a pass-through MBS as 5.3 years. His effective duration is based on re-pricing the MBS with a yield shock of 50 basis points; i.e., current yield plus and minus 50 bps. However, Barry's manager observes that Barry did not vary the prepayment (PSA) assumption when re-pricing under either the higher/lower yield scenarios. His manager argues that Barry should vary the PSA assumption as he varies the interest rate input. If Barry varies the PSA assumption as instructed by his manager, which of the following is true?
a. The accurate duration will be lower than 5.3 years
b. The accurate duration will be higher than 5.3 years
c. It does not matter, neither duration nor convexity will be impacted
d. Duration is approximately unchanged at 5.3 years but convexity will increase
Answers:
AIM: Describe the effective duration and effective convexity of standard MBS instruments and the factors that affect them.
Questions:
105.1. The current term structure is flat with a yield of 4.0%. Assuming 100%, the price of $500 million pass-through mortgage-backed security (MBS) is $584.2 million. Assuming a 4.5% yield and 50% PSA, the value of the MBS drops to $573.5 million; assuming a 3.5% yield and 150% PSA, the value of the MBS increases to $591.9 million. What are, respectively, the approximate effective duration and effective convexity of the MBS?
a. 2.7 and -133
b. 3.1 and -205
c. 4.6 and -375
d. 5.8 and -412
105.2. In regard to the effective duration and effective convexity of a pass-through mortgage-backed security (MBS) pool, EACH of the following is true EXCEPT:
a. "Effective" signifies the analytical approximation that is necessary due to variations in prepayment speed; i.e., analytical solutions are not available
b. Due to prepayments, at low yields we expect negative duration
c. Due to prepayments, at low yields, we expect negative convexity
d. As market yields decrease, it is reasonable to increase the PSA assumption; e.g., from 150% PSA to 175% PSA
105.3. Barry the analyst calculated the effective duration of a pass-through MBS as 5.3 years. His effective duration is based on re-pricing the MBS with a yield shock of 50 basis points; i.e., current yield plus and minus 50 bps. However, Barry's manager observes that Barry did not vary the prepayment (PSA) assumption when re-pricing under either the higher/lower yield scenarios. His manager argues that Barry should vary the PSA assumption as he varies the interest rate input. If Barry varies the PSA assumption as instructed by his manager, which of the following is true?
a. The accurate duration will be lower than 5.3 years
b. The accurate duration will be higher than 5.3 years
c. It does not matter, neither duration nor convexity will be impacted
d. Duration is approximately unchanged at 5.3 years but convexity will increase
Answers:
