Can somebody please help me understand this statement in the curriculum?
“In general, for an upward-sloping yield curve, the immunization target rate of return will be less than the yield to maturity because of the lower reinvestment return. Conversely, a negative or downward-sloping yield curve will result in an immunization target rate of return greater than the yield to maturity beacuse of the higher reinvestment return.”
Isn’t this supposed to be the opposite?
for an upward-sloping yield curve, the immunization target rate of return will be less than the yield to maturity because of the HIGHER reinvestment return??
This threw me off initially as well, but you need to think in terms of the immunization strategy as a whole. When the yield curve is upward sloping, your immunization coupons are lower because you “locked in” in a fixed rate. So while everything else along the curve is yielding higher coupons, your portfolio is not because it is immunized.
“In general, for an upward-sloping yield curve, the immunization target rate of return will be less than the yield to maturity because of the lower reinvestment return.”
Here they are talking about the lower reinvestment return from your immunized intruments. It threw you off because you were probably, like me, thinking in terms of the yield to maturity of generic (non-immunized) instruments.
Okay mate, you have got me puzzled. Correct me if I am wrong,
At time T,
Lets say I have bought par bonds maturing in 5 years and immunized them to yield X% in 5 years (liability date) when yield curve is flat
during the interim T to T+5,
the yield curve has become upward-sloping. My 2 components of YTM, “locked-in” coupon income and the par bonds’ change in price, stay the same. But the reinvestment income, I have been receiving is gonna be higher (coz of higher interest rates). So overall the YTM (now) is higher than the previous YTM (flat), and the immunized target rate of return (needed) is lower than YTM (flat) coz of (I can get by with) lower reinvestment return (or in other words higher available reinvestment income)
Does that make sense? Or am I completely off base?
What they’re saying is that if the yield curve slopes upward, then I’ll be reinvesting my coupons at lower rates than the YTM on my bonds; hence, my realized yield will be lower than the YTM. My target yield has to be my realized yield: I need to get what I need to get.
For example, if I need to earn (target yield) 5%, I need a realized yield of 5%, so I’ll need a YTM on my bonds of higher than 5%.
Similarly, if the yield curve slopes downward, my reinvestment rate will be higher than the YTM on my bonds, so my realized yield (my target yield) will be higher than the YTM. If I need to earn (target yield) 5%, I need a realized return of 5%, so my bonds’ YTM will be less than 5%.
In addition, you can’t switch to a higher yield just because the slope of the yield curve has increased. Otherwise you’re no longer immunized. Remember you decided to target X%, so you must stick to X%. By reinvesting the coupons at a higher rate, for e.g., your portfolio will no longer immunized. So while everyone else is reinvesting at >X%, you’re still forced to reinvest at X% since that’s what you decided to do via immunization.
Same concept holds when the yield curve is downward sloping. You will be targeting X% while everyone else is earning
In summary, your portfolio is “immune” to market movements.
this got me too during the exams but the way I thought of it and remembered it is as follows (very simplified I guess):
Assuming you need to hit a target return of 10% over an immunization period of 10 years.
You purchase a 10 year bond with a YTM of 10%. Now recall that the YTM is the yield you get assuming that coupons are reinvested in at that same rate. (i.e. if your YTM is 10%, your coupons are assumed to be reinvested at 10% as well)
Then, assume for simplicity sake that the yield curve is uniformly upward sloping (i.e. 1 year - 1%, 2 year - 2%, 3 year - 3% etc) and never changes.
Now, obviously, your coupons are NOT going to be reinvested at 10%. Your year 1 coupons will be reinvested at the prevailing rate for a 9Y maturity bond (assuming you reinvest coupons in a bond). For an upward sloping yield curve, the YTM on your new 9Y bond would be 9% which is lower than the YTM than your original 10Y bond of 10%.
This will apply for each year onwards. i.e. Year 2 coupons invested in 8Y (8%) bond. Year 3 coupons invested in 7Y (7%) bond.
Hence, your realized return at the end of the entire period will be less than the 10% YTM on the 10 year bond you initially purchased as you never get the 10% on your reinvested coupons as assumed by YTM.
So to get 10% realized return you would actually need a YTM higher than 10% on the initial bond used to immunize the portfolio.
I do hope that I am correct. Perhaps S2000 can confirm if my take on things is correct. If it is, I think it would be an easier way to remember it.
Wouldn’t the year 1 coupons be reinvested in a longer maturity, not necessarily the 1 year yield? Wouldn’t they go into something with around 9-years till maturity?
Guess I’m just not entirely clear why, if the YC is upward sloping, you receive lower reinvestment income…aren’t you reinvesting at higher rates than before so your realized return is higher than the original YTM, not lower?
Thanks CPK, as always. That makes sense, guess I was thinking we were only talking about reinvestment returns…it does say,“because of the lower reinvestment return”. If we’re talking about total return, then yes, I’m with you…they would be lower with an upward sloping YC.
I made that mistake in phrasing my reply. Yes, the year 1 coupons would be invested with 9 years to maturity. All else equal, the YTM for a 9Y bond at that point would be lower than your original 10Y YTM bond.
Before you abuse me, i admit this is an old post, but i had the same question. I have also gone through the site a couple time and i admit there is no consensus on the explanation. However my take is:
If the yield curve is upward sloping, the reinvestment income is higher and therefore one can do with a lower target immunisation rate to match the YTM bond. The oppsite is true for a downward sloping yield curve.