Hi everyone,
I was hoping if someone could help me understand this concept. It says in the CFAI reading that:
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Why is the reinvestment return lower in upward sloping curve? Shouldn’t it be the opposite as the coupons that are being received now get reinvested at a higher rate?
This has been discussed many times here; the search function may help locate the other threads.
In fact, the coupons are reinvested at a _ lower _ rate, not a higher rate.
Suppose that the yield curve is:
To make things simple, imagine that the yield curve doesn’t change for the next 3 years.
If you own a 3-year bond, your YTM is 3%, but your actual yield will be lower. A coupon you receive today will be invested at 3%, but the coupons received next year and the year after that will be invested at, respectively, 2% and 1%.
This is the most common question I find candidates asking in Fixed Income, it is located in Volume 4, Study Session 10, Reading 20- Fixed Income Portfolio Mgt, Section 4 Bluebox 9, page 36 question 2…whew!
The best answer is found in the candidate curriculum itself, turn back to page 33 and read section 4.1.1.3
If you don’t want to look there think of it this way…the immunization target rate of return is determined by the actuary based based on their analysis of what discount rate they used for the liability stream (think future pension benefit obligations). Recall this discount rate is always nominal. Lets say for grins it is 4%.
The immunization target rate of return (liability discount rate - 4%) will ALWAYS be different from the bond portfolio (fixed income portfolio) yield to maturity unless the term structure is flat. Remember as time passes (maturity decays) the bond return changes as the bond portfolio moves along the yield curve. It can also be different if the yield curve is upward sloping after the discount rate for the liability stream was determined.
Now the bond manager seeks a portfolio of high credit quality (Treasury), non-callable bonds to immunize the liability stream . Lets say she finds current Treasuries at 4% BUT the yield curve is upward sloping. As we know for an upward sloping yield curve the yield to maturity (YTM - requires a flat curve) will be very different from the flat discount rate used by the actuary.
Here is the kicker…for an upward sloping curve distant coupons paid every six months will be reinvested at higher yields, since the yield curve is upward sloping. Or according to the textbook…“for an upward sloping yield curve, the immunization target will be less than the yield to maturity because of the lower reinvestment rate” (his next part is added for clarification) The immunization target rate assumed the coupons are reinvested at 4% but the bond portfolio return with an upward sloping curve and coupons received will be reinvested at higher rates due to the yield curves upward sloping nature.
I hope that helped…whew!
Marc LeFebvre, CFA
so on the contrary, if your yield curve is downward sloping, that means the later your investment is your reinvestment rate is higher, so in the end you can actually achieve higher total return that YTM target? say my first coupon can get 1%, second coupon can get 2% and third coupon 3%? is that how i should think about this?
In a word: _ Bingo _!