Forecasting Return Based on Yield to Maturity

CFA Level III Fixed Income
#1

My questiong is regarding to the CFA level 3 - Volume 2 - Reading 11 - Example 1 - Page 221.
It is said in the example that:
1.The bond portfolio’s YTM is 3.25%, its modified duration is 4.84.
2.Clients invest in a strategy that uses cash flows to maintain a roughly constant maturity and duration profile.
3.YTM are likely to rise by 200bps over the next 2 years.
The example asks you to project approximate returns for this strategy over the horizons of 2, 5 and 7years.

  1. It looks so wierd to me because usually the YTM rises or drops IMMEDIATELY rather than GRADUALLY. As illustrated in the solution of this example, the modified duration is mutiplied by the 200bps YTM change to get the so called Capital Loss 2 years later(time 2). In my opinion, the modified duration at time 2 should be used to calculate the capital loss instead of time 0’s modified duration. Or is it because “strategy uses cash flows to maintain a roughly CONSTANT maturity and DURATION profile”?

  2. the solution also says “assuming yields rise linearly over the initial 2 year period, the higher reinvestment rates will boost the cumulative return by approximately 1.0% over 2 years”. I have no idea how to get the 1.0% cumulative return.

  3. I am struggling with the concept of capital loss and reinvestment impact. from my opinion, the capital loss is resulted from the coupons after the horizon being discounted by the new YTM, and the reinvestment impact is resulted from the coupons before the horizon being reinvested by the new YTM. am I right?

#2

Hello there,
I have the same confusion that you mentioned in Point #2.
Did you figure it out. THanks

#4

I think, its should be 2% instead of 1% of 2 years.
Additional Reinvestment return = integration of (rdt)
but r = t
So, Additional Reinvestment return = integration of (tdt) = 1/2 x (t^2) with limits of t from 0->2
=> Additional Reinvestment return = 1/2 x (2^2 - 0^2) = 2%

#5

We have annual (not continuous) compounding. Hence one can reinvest the first coupon only at the beginning of year 2 and then the additional reinvestment return is equal (0+2)/2 =1% as stated in the solution.

#6

I am not sure if I understand your question 1 & 3 correctly. however, to me,

  1. Firstly there is no rule that YTM should rise and drop immediately or gradually. The 200bps is ‘expected future rise’, now we are projecting the price impact at time 0 on this.
    3.Not just the coupon, principle as well. But yes I think you are broadly correct.