We can estimate the manager’s projected return on the 3-year bond using duration and the projected yield changes. The manager predicts the then-2-year bond to trade at a yield 10bp lower than the implied forward rate (+60bp versus +70bp). That differential multiplied by the projected ending duration is a better relative price return: 0.10 × 1.93 = +0.19%. Add the return of today’s 1-year bond , and that is the manager’s approximate projected return of 1.69% ≈ 0.19 + 1.50.
My question
(1) To arrive at the 1.69%, why do we add 1.50%? Shouldn’t we be adding the coupon rate for the then-2-year bond of 1.91%?
(2) Also, if there is a good source of information that explains the learning points from this LOS, please do share it.
the context is that the manager only has a time horizon of 1 year and given the data, we’re expected to devise a strategy that produces the best return for 1 year of holding period.
for the 3-year bond and assuming that the manager’s forecast is correct:
the 3-year bond price after 1 year of holding should equal to: PMT=2.23 FV=100 i=2.51% n=2 which is equal to 99.46
subtract 99.46 from 100 which is our cost basis at year 0 which gives us a return of -0.5396 (negative due to price decrease 1 year from now)
but you receive a 2.23 dollar coupon from your holding and so your return for holding the 3-year bond for 1 year is 2.23 - 0.5396 or equal to 1.6904
now, what I just explained is the way in the CFAI curriculum. Schweser introduced another method, which is to calculate the bps differential between forward implied yield and the manager’s forecast (in this case 10 bps or 0.1), multiplied by projected Modified Duration of the bond after 1 year of holding (for 3 year bond, this is 1.93) and add it to the 1-year bond holding period return which is 1.5%.
