Example says safety net return = 8% and current rate =9%

You know that since the 9% > 8% that you’re still safe. However the question then says the immunization rate jumps to 12%. I see and understand the math but why does the same generality not hold, that is 12% > 8% so still have a safety margin? Says now the portfolio would need to be immunized (meaning triggered at SNR of 8%).

Guess it just seems odd how the rate goes from 9% to 12% thereby earning a higher return yet somehow the rate of return is no longer high enough. Anyone else think that?

Also had couple related but one-off questions if y’all could help me out understand:

1.) unlike contingent immunization, is classical immunization a purely passive strategy?

2.) Seems like price risk shouldn’t be a concern. If you set the maturity date equal to liability due date than you know the price at maturity, it’s only during holding period that value fluctuates…obviously this doesn’t address reinvestment risk though. So is the point being that, what good would matching dates be if reinvestment return changes negatively and you miss your required end value, so that is why you focus more on matching duration?

3.) why is it that it seems that only reinvestment risk, not price risk, is the concern when immunizing against nonparallel shifts?

4.) lastly, is there a general understanding which impacts total bond return more, price change or reinvestment returns?

Thank you for the help. Sorry for the laundry list.

not sure why you would say the first statement that you just did … when the YTM goes up from 8% to 12% on a 8% coupon bond - your bond portfolio (Assets) are going DOWN in value - since the bond just became a discount bond from the Par bond it was.

is true. Classical immunization allows Price risk to be offset by Reinvestment Risk - that is all. In Contingent immunization - there are pieces of active management introduced, conditionally, provided the rate of return that you can earn on your portfolio is higher than your required rate of return (safety net rate of return).

both price risk and reinvestment risk are important. Reinvestment rate is NEGATIVE - only if rates FALL. And if rates fall - your End price at the horizon WILL BE HIGHER. But not achieving your reinvestment level required makes the yield fall below the target yield required.

Matching duration only helps if there are parallel shifts to the yield curve. Considering that non-parallel shifts are more common - you need to match duration (To ensure you have funds to pay off liabilities when due or at least that you are close) and you also need to match convexity (to ensure that the non-parallel shift does not take you way off).

Use an example to determine how much each component of return affects you. Look at the example 9 in the book for various periods of return, various rates of return - to see which affects the bond portfolio more - is it reinvestment or price…

I understand why the price fell. I guess in the example the implication is that now at the higher 12% YTM, the price decrease more than offsets the resulting increase in reinvestment income - and therefore won’t achieve the required teriminal value, thus the portfolio must now be immunized?

Not sure what example 9 you are referring to. I guess the answer to which causes the greatest impact on total return (price change or reinvestment return) would be, it depends…can go either way?

Also, tell me if this is beyond the scope of the readings, but how do they determine the duration of multiple liabilities? If it’s a single payment, they say duraction = time to maturity (similar to a zero). Are we just supposed to take what is given?

If it is a guaranteed instrument - 2 parts of the equation Coupons future value and the value of the investment at the end of the time horizon are fixed. Only Reinvestment Income makes the change.

Yes. Look at how they do the Immunization for General Cash flows - Have a zero for the Principal Payment MINUS the Coupon on the first bond (which is a zero) at the first liability date … and so on.

CPK, once you have computed the total horizon value and you know the PV price, why can’t you just do a TVM calculation with n=1? Will this not also give you the horizon effective total return, as opposed to finding the semiannual return ( n=2 ) first then Finding EAY? Doesn’t the FV capture the full annual compounding to allow you to compute EAY directly, that is with n=1.

ive tried it and it gives the same answer albeit with very very minor rounding error.