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# P1.T4.907. The coupon effect and carry roll-down scenarios (Tuckman Ch.3)

#### Nicole Seaman

##### Director of FRM Operations
Staff member
Subscriber
Learning objectives: Define the coupon effect and explain the relationship between coupon rate, YTM, and bond prices. Explain the decomposition of P&L for a bond into separate factors including carry roll-down, rate change, and spread change effects. Identify the most common assumptions in carry roll-down scenarios, including realized forwards, unchanged term structure, and unchanged yields.

Questions:

907.1. Assume that the following upward-sloping zero rate (aka, spot rate) curve prevails:

Tuckman introduces the concept of a coupon effect in Chapter 3. Each of the following statements relates to this coupon effect and is necessarily true EXCEPT which statement is false?

a. Given this spot rate curve, the two-year par rate (aka, par yield) must be less than 3.4%
b. Given this spot rate curve, a zero-coupon bond with a two-year maturity must have a yield (yield to maturity) of 3.4%
c. Given this spot rate curve, a coupon-bearing bond with a two-year maturity must have a yield (yield to maturity) that is less than 3.4%
d. Given this spot rate curve, the yields (yields to maturity) of all bonds with two year maturities must be identical due to the Law of One Price

907.2. As shown in the exhibit below in a format similar to Tuckman's table 3.2., the price of a bond as of 5/28/2019 is $113.335. This bond pays a semi-annual 10.0% coupon and has maturity of 1.5 years; that is, it matures on 11/30/2020. Currently, the six month forward rates are 0.60%, 1.00% and 1.50% (see green row). (Bruce Tuckman, Fixed Income Securities, 3rd Edition (Hoboken, NJ: John Wiley & Sons, 2011)) If we make a scenario assumption of UNCHANGED TERM STRUCTURE, which of the following is nearest to the carry roll-down over the next six months? a. -$4.185
b. -$1.090 c. +$3.270
d. +$5.990 907.3. As shown in the exhibit below in a format similar to Tuckman's table 3.2., the price of a bond as of 5/28/2019 is$100.026. This bond pays a semi-annual 5.0% coupon and has maturity of 1.5 years; that is, it matures on 11/30/2020. Currently the six month forward rates are 4.00%, 5.00% and 6.00% (see green row). This is a steep curve indeed, but notice that the bond has much credit risk as the spread is 3.00%. (Bruce Tuckman, Fixed Income Securities, 3rd Edition (Hoboken, NJ: John Wiley & Sons, 2011))

Over the next six months, how will the carry-roll-down (CDR) compare under an assumption of unchanged yields versus an assumption of realized forwards?

a. The CDR loss under unchanged yields will exceed the CDR loss under realized forwards
b. The CDR loss under realized forwards will exceed CDR loss under unchanged yields
c. The CDR loss under realized forwards will be equivalent to the CDR loss under unchanged yields
d. Both approaches will generate CDR gains; that is, the CDR will be a gain under both realized forwards and unchanged yields