can anyone tell me why when we have an upward sloping yield curve, we have an immunization rate that is less than the YTM becuase of "lower" reinvestment return, and vice versa if we have a downward curve. If the slope is upward sloping, isn't the expectation higher yields therefore higher reinvestment return? Help would be appreciate. Thanks.
Edited 2 time(s). Last edit at Sunday, February 27, 2011 at 02:04AM by darlia.作者: cityboy 时间: 2011-7-11 19:20
This was discussed until cow come home and nobody really understood why.作者: IAmNeil 时间: 2011-7-11 19:20
The trick is to hold the shape of the yield curve constant through the immunisation period. Let's say the 2year yield is 2%, the 3year yield is 3% and the 5year yield is 5%. If the immunisation period is 5 years, any asset cash flow received at the end of year 2 will be reinvested at 3%, because this is the rate for a 3 year investment.
Because we are not satisfying the assumption under YTM, that all cash flows are reinvested at the YTM, we have to start off with a present value of the asset, that is slightly greater than the present value you would need if all cash flows were reinvested at the YTM. And because your present value is slightly higher, your immunisation rate is lower.作者: dyga 时间: 2011-7-11 19:20
Thank you! That makes sense.作者: Analyze_This 时间: 2011-7-11 19:20
Since the ITRR is determined (at a FIXED %) according to the TARGET VALUE and initial investment (market) value, it seems that the term structure of interest rates (upward-, downward-sloping or flat) is irrelevant.
In Example 5 (CFAI Text Vol 4, P27), the target rate (yield) or the ITRR is a bond equivalent yield of 7.5% {[(13,934,413/9,642,899)^(1/10)] - 1x2} which is resulted from the TARGET VALUE of 13,934,413, initial investment (market) value of 9,642,899 and horizon period of 10. This 7.5% is set (determined) at the outset of the immunization and it will not be changed, whether the term structure is upward-sloping, downward-sloping or flat.
In this example, Target Rate (ITRR) = YTM = 7.5% since the term structure of interest rates is flat. In case of upward- or downward-sloping, different YTM may be required to attain the target value of 13,934,413, but Target Rate (ITRR) is still the same (7.5%). The 7.5% is the TARGET rate (ITRR) at which we can attain the target value of 13,934,413 in 5 years and it shall be a FIXED rate in any case.
Note that the table on P28 is irrelevant to this discussion because it shows various scenarios of PARALLEL SHIFTS from a flat yield curve IMMEDIATELY after investing in the bond.
