It says for an upward yield curve, the immuniz target rate of return will be less than the yield to maturity bcoz of the lower reinvestment return. And the opposite for a downward curve
How come? I thought when the yield is upward, ie interest rate increase, then the portfolio value decrease is offset by a higher reinvestment income. So why do they say the reinvestment return is low?
Pls what am i missing here?
They say the YTM will be less than the target return because of reinvestment risk.
Remember, the YTM is not the true yield you will get when you hold your portfolio at maturity. The YTM number assume that you manage to reinvestment the coupons at the YTM, which never happens in reality.
The YTM is only an approximation. So you shouldn’t focus on it to immunize the portfolio.
In the curriculum it is said that the immuniz target rate will be less than YTM for an upward yield curve. That is what I dont get, since in that case, we should get more when reinvesting at higher interest rate. So why are they talking about lower reinvestment Return?
I think when you reinvest your coupons your doing so on shorter maturity than your current bond, therefore at a lower rate than your YTM, so the yield you get decrease also.
On the other hand, if the yield curve is downward, you reinvest your coupons at shorter maturity, therefore at a higher rate than your current YTM, so your target rate will end up being higher than your YTM.
hi guys, i have a sperate question here - what is the YTM here - is that the YTM of the portfolio asset or the liability?I assume it is the YTM of the liability?
My understanding to this topic is that when the yield curve is upward, the reinvestment income from the shorter-end on yield curve would lock in the low reinvestment rate for the rest of the term. So, lower reinvestment return received.
I admit it is confusing to me… 
This is for your assets.
If the yield curve slopes upward and, for simplicity, doesn’t change, then as you get coupon payments you’ll be reinvesting them for maturities shorter than the original, and those reinvestments will be at lower rates than the original (because of the upward-sloping yield curve). Therefore, your realized yield will be less than your original YTM.
Here’s an easy example: you buy a 2-year, $1,000,000 par annual pay bond, paying a 6% coupon. The 1-year par rate is 3% and the 2-year par rate is 6%; thus, you spend $1,000,000 for this bond.
After 1 year you get a coupon of $60,000 that you reinvest for 1 year at 3%. One year later it’s worth $61,800. After 2 years you get $1,060,000, so your entire portfolio is worth $1,121,800. You’ve earned 5.9151%.
Thanks Magician! I am a bit clear now. Guess in your example, 6% is the YTM and 5.19% is the immunization rate?
Just have a quick side question - what is the YTM here - the YTM of the portfolio or the YTM of the liability or basically the same thing? Appreciate your response as I am a bit confused
You’re correct: YTM = 6%, immunization rate is 5.91%.
YTM applies to assets. Not to liabilities so much.
S2000, somewhere in the curriculum it is written that in order to immunize a target yield/target value of a portfolio we need:
a portfolio of the same duration as the investment horizon
PV of CF = PV of liaibilities
My question is what discount rate do we use to compute the PV of CF? Isn’t the PV of CF of a fixed income equal to the market value of the portfolio? If so, is the discount rate that we use the YTM?
Yes to both.
You take money from someone, that’s the PV of the liability. You put that money in an asset, that’s the PV of the asset, and you start off with zero surplus. Depending on the yields you picked for the assets, (and the risks that follow), determine how the surplus changes as time passes.
It also says that you discount liabilities at the Internal Rate of Return, so I am guessing the Immunization Rate of 5,91% is the internal rate of return of the liabilities?
It also says that you discount liabilities at the Internal Rate of Return, so I am guessing the Immunization Rate of 5,91% is the internal rate of return of the liabilities?
I would tend to agree because thats the discount rate to calc PVL. Anyone has second thoughts here?
I need to mark here to recap later
Hi s2000
Why isn’t the assumption here that the coupon gets re-invested at the 1-year forward rate in 1-year i.e. ((1+6%)^2)/((1+3%)^1)-1 = c.9%.
Is that what you mean by assuming the yield curve doesn’t change?