So I read the actual book and schweser, but I’m still confused. There is this section that says “If portfolio duration is less than liability duration, the portfolio is exposed to reinvestment risk” Ok I get that part because you still have to reinvest. After that, it says “if interest rates are decreasing, the losses from reinvestment income would be greater than the gain in the value of the bonds.” So what happens if interest rates are rising? Is the original portfolio now subject to price risk instead of reinvestment risk? If this is the case, is it safe to make the assumption that it doesn’t matter if portfolio duration is greater than or less than the liability duration to conclude if the portfolio is subject to reinvestment or price risk? And thus price/reinvestment risk depend on the movement of interest rates instead?
can you please point out which book (Schweser or CFAI), and corresponding Page #s?
I believe reinvestment income in the case of falling interest rates will be lower than the price gain at the end of the horizon. Additionally - Reinvestment income gains during rising prices will still be less than the Price Loss the Portfolio undergoes when rates fall.
The two offset each other partially. and the purpose of immunization is to determine that portfolio which is able to completely offset the two effects. And you do that by making sure of an assured rate of return required for your portfolio - which is the amount that the liabilities will go up to at the end of your horizon, and having a “cushion” with which you work.
The two effects Price and Reinvestment risks are always present on the portfolio - hence another necessary condition is to have the Portfolio (Asset) duration to match the Liability Duration (keep the two lock in step) as well.
“If portfolio duration is less than liability duration, the portfolio is exposed to reinvestment risk"
On total return basis : Coupon income+reinvestment income+ change in price
Coupon are fixed, so we are exposed to change in reinvestment income (reinvestment risk) & change in price (price risk)
Portfolio assets duration is less so they r maturing before the liabilties dates. To fund the liabilities thru assets we will have to make an assumption about the reinvestement of these assets which exposes our portfolio to reinvestment risk. Since future reinvestment rates are unknown, the total future value of a bond portfolio’s coupon payments plus reinvested income is uncertain.
“if interest rates are decreasing, the losses from reinvestment income would be greater than the gain in the value of the bonds_.” (this will hold good if duration of assets are less than duration of liabilities ) So reinvestment risk_
If Int rate are increasing, so the gain from reinvestment income would be lower than the losses from the losses in value of bond. When duration of assets are greater than liabilities. (Price risk)
So to immunize you choose classical single period immunization (stands good for a single period & 1 time change in interest rate) . That is your reinvestment risk & price risk should exactly offset each other
Further to add to this, the statement which has been a matter of debate many times on this forum is as follows:
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 because of the higher reinvestment return.
Can you explain why “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 _”. I know it’s given in the text though.
reinvestment return is lower because reinvestments are being done at a shorter duration of the YTM curve than the original investment . If the curve stays the same shape and is upward sloping , the shorter end has a lower YTM than the far end.
So reinvestments fetch lower yield ( and that is assumed to mean lower total return as well )
It makes sense that the total return will be low 'coz prices fall when II/y rates raise. But reinvestment rate will be higher so coupons will be reinvested at a higher rate and hence reinvestment income should be higher, right?
“…because reinvestments are being done at a shorter duration of the YTM curve…” - Sorry, did not understand. When yield curve is upward sloping, reinvestment rate will increase as coupons can be reinvested at a higher rate. Am I missing something? Thanks
Upward sloping does _ not _ mean interest rates are _ rising._ It just means that rates at longer maturities are higher and rates at lower maturities are less .
Do not use words like “rising” and “falling” here .
The text does not allude that rates are rising when it says the curve is upward sloping
Year 1 2 3 4 5
Flat curve (int rate%) 4.5 4.5 4.5 4.5 4.5
Upward (int rate%) 4.5 5 5.5 6 6.5
Down (int rate%) 4.5 4.25 3.75 3.5 3
Now if you invest in Flat curve, you can calculate your immunized target rate of return and compare it with the fixed YTM. If Tgt rate > req YTM, you pursue active management or else not
Now YC changes & become upward sloping.Means interest rate for longer maturities are higher than compared to shorter maturities. Now when you will calculate your reinvestment income it will lower. Since at the time of Yr 1 alhough you are investing at higher interest rate but for a lower time period. Vice versa for downward sloping.
This is the point we are trying to understand. Right?
ok, I think I am getting closer. sorry to ask for more clarification. this needs to be nailed down for me :).
when we say lower reinvstement ret for upward sloping, are we comparing reinv. return for short term(like 1 yr) with longer maturities like 10 yrs in upward sloping curve? perhaps yes. but why r we comparing reinv ret only for 1 yr or any shorter term only?
because the horizon to the maturity of the liability is shrinking.
remember in Lvl I for cash flow calculations and NPV the implicit assumption in the calculation was that the IRR would remain constant .
Well , this is what happens when the IRR ( or in this case YTM ) is not assumed constant. It reduces at each term expiry on the asset side
comparison is for the investment horizon - because that is what we are interested in.
If for the whole period - rates are upward sloping - each period coupon is reinvested at a higher rate. So the Price realized at the end will have a HIGHER loss (due to the rate change) and that loss is offset by Reinvestment income gains. But overall Price trumps reinvestment.
So the YTM at the end will be lower than the YTM you started out with.
the example 5 Pg 27-28 -kind of shows you the entire stream of thought. The one where they calculate the entire stream of cashflows - Interest, Interest on Interest and so on…
target value = value at horizon date under scenario of no change in forward rates
for an upward sloping yield curve, forward rate > spot rate,
also YTM = approx. average of spot + forward rates
e.g. if 1 period rate today is 5%, and 1-period forward rate is 7%,
1.05 x 1.07 = (1+ytm)^2 and ytm = 6% approx = average(5%,7%)
if the forward rate curve remains unchanged (as per definition of target value), then reinvestment at the end of first period will be done at 5% and not at 6%
since reinvestment rate 5% < 6% ytm, the portfolio value at the horizon date will be lower than with reinvestment at YTM
hence target rate of return < YTM
ok. Got it. it’s clear now.
Thanks everybody