Can anyone show me how they arrived to the reinvestment rate of 1.0 for the 2 yr horizon in this problem? I understand everything else but this 1.0 figure is driving me nuts.
In the solution it says “assuming yields rise linearly over the initial two-year period, the higher investment rates will boost cumulative return by approximately 1.0% over 2 years, so that the annual return over 2 years will be approximately -1.09% [=3.25+(-9.68+1.0)/2].”
Part of me is thinking that the coupon in yr 1 is reinvested at 1% and then the coupon reinvested in the next year should be at 2% if the yields are increasing linearly by 1% per year.
I tried to use the logic in the part of the solution regarding the 7 yr horizon to think it through and the added reinvestment rate is 4.0 (after accounting for the 2 yr horizon and additional 3 yr horizon) which I understand as each year’s coupon being reinvested at 2% per year after the 5 yr horizon.
So along that line of thinking, wouldn’t the initial 2 yr horizon in my original question use a reinvestment rate of 3.0 (=1.0 for yr 1 + 2.0 for yr 2)?
The reinvestment rate will be 1% higher in Year 1. So the coupon in Year 1 will be reinvested at the 1% higher rate until Year 2. Therefore the additional return over that 2 years due to higher reinvestment rate is 1%.
Thanks for the response. I guess my question wasn’t really clear . In the prompt it only gave us that the central bank was expected to raise yields by 200 BP’s over the next 2 yrs.
Wouldn’t that mean 1% per year if we’re to assume that the yields rise linearly over the 2 yr period?
Unfortunately the assumption of linear increase was stated in the solution (it should have been stated alongside the question).
But following the assumption of 1% increase per year, the reinvestment rate will be:
1% higher in Year 1 (one year later right when you receive the first coupon)
2% higher in Year 2 (two years later when you receive the second coupon)
For a two-year horizon, there is only one coupon reinvested, which is the first coupon that was received and reinvested at the 1% higher rate. The reinvestment rate that is 2% higher is not relevant for this horizon of 2 years (but will be relevant if the horizon is 3, 4, 5 years, and so on)
. In the prompt it only gave us that the central bank was expected to raise yields by 200 BP’s over the next 2 yrs.