why does an amortizing security have more reinvestment risk than a nonamortizing security, all else being equal? is it just because you are getting principal back over time, and any time you get more money back sooner, that increases reinvestment risk?

Yes, let say we have 2 securities (A & B): A is amortizing & B is not & they are both 5yr in maturity. THe one that is amortizing security is much more expose to reinvestment risk because it has a more stream of cash flows compare to security B. And this cash flows of security A will have the tendency of being reinvested in a much more lower interest rate as the mkt interest rate decline. To clarify further: Security type Maturity #CFs A amortizing 5yrs 60 (a portion of interest & principal per month) B option free bond 5yrs 11 (10 C. payments 1 principal at maturity) ANALYSIS: If the interest of A & B is 10% & if the mkt interest fell to 8% in year 3 (beginning) and it will stay that way until yr. 5. Now security A is in the bad condition because all the remaining 36CFs will have to reinvest to a much more lower interest as compare to security B who also subject to reinvestment risk & have to reinvest only its remaining 7 CFs. Hope it will help.

Oooops, its suppose to look like a table in the above… ok, it must be: “To clarify further: Security / type / Maturity / #CFs A / amortizing / 5yrs / 60 (a portion of interest & principal per month) B / option free bond / 5yrs / 11 (10 C. payments 1 principal at maturity)”

I like the asnwer ‘yes’ more.

I’ll second Joey’s post and ask a related question. Is it accurate to state that despite the an amortizing loan’s level payment schedule from origination to maturity, reinvestment risk actually increases as the loan becomes seasoned and the scheduled payments begin consisting more of principal pay-down rather than interest? Or would this only be true of amortizing loans with embedded prepayment options, such as residential mortgages, for which curtailment increases as these loans become seasoned? Thanks in advance.

Forget about amortizing loans for a second. In a coupon bond is there more, less, or same reinvestment risk in the fiirst coupon payment than the last?

JoeyDVivre Wrote: ------------------------------------------------------- > Forget about amortizing loans for a second. In a > coupon bond is there more, less, or same > reinvestment risk in the fiirst coupon payment > than the last? At first I thought, the same…but with the added interest rate risk (because of time), I suppose reinvestment risk would increase with time as well. That being said, first coupon would have less reinvestment risk. ???

Okay, so let’s not worry about the principal/interest portion of a coupon payment (because, regardless, it all has to be reinvested) and focus on the timing of payments instead. Do the last coupon payments face higher reinvestment risk than the first, due to their receipt in the distant future, which allows much more time and uncertainty w/r/t/ interest rate fluctuations?

I’m not sure what the answer is, because I think it’s how you define reinvestment rate risk. It seems to me that you could argue that the last coupon payment has no reinvestment rate risk because you measure reinvestment rate risk to the maturity of the bond (I don’t really like that definition much). The chances that interest rates drop a lot is certainly greater for the last coupon than the first so maybe that makes it higher. But the first one has to be invested for longer so maybe that makes it greater. Hmmm…

we can look at one pure-discount bond with maturity 1 year. Supposedly it doesn’t have reinvestment risk if the time window is 1 year. Now let’s assume we add another null cash flow at the end of two years. How does it affect the new instrument. YTM is going to be the same, interest rate risk is the same. However, now there is additional reinvestment risk because maybe we won’t be able to reinvest money received at the end of year 1 at the same rate. If we change time horizon from 2 years to three years, reinvestment risk will increase. We can see that reinvesment risk is higher for high YTM, longer period from coupon payment to maturity. From this simple excercise it seems like the last coupon doesn’t have reinvesment risk and it is higher for early coupons. What are your thoughts on that?

Ok that’s interesting…

Martikus, is it accurate to conclude that your example is contingent upon us fixing our maturity at a single point in time? So each coupon payment from the original investment is reinvested such that they all mature on the same final date, which is also the date of the final coupon payment from our original investment? Does anything change if we have multiple maturity dates? So the original investment matures whenever, but we reinvest the first coupon in another security that has a shorter- or longer maturity than the original investment, etc., for each coupon payment… Does what we consider to be interest rate risk only exist during the life of a security (between coupon payments and/or prior to maturity) and suddenly become reinvestment risk upon the payment of each coupon and/or a security’s maturity? Man, so much for seeking refuge in a topic I thought I understood… have I derailed this thread?

My answer: earlier payments have higher risk. Reasoning: earlier payments are invested longer, and the impact of this effect is linear (as one approaches today, working backward from maturity). Later payments see greater rate volatility, but the important point is that this part of the risk doesn’t increase linearly since IR’s are mean reverting. I.e. the risk “cone” isn’t a cone, over time for mean-reverting rates it approaches a cylinder. So for any reasonably distant investment horizon I expect that rate volatility will plateau, but the period of reinvestment will increase without bound. (There’s also that nasty part about st dev growing only with t^0.5, but I’ll leave that as an exercise for the reader.) > Martikus, is it accurate to conclude that your example is contingent upon us fixing our maturity at a single point in time? I think we have to make this simplifying assumption.

Actually for something like CIR it’s a gamma.

hmmm not sure if i agree with some of the above posts… reinvestment risk, as i see it, is the uncertainty at having to reinvest your coupon payment at the YTM… so, an amortising security has more scope for reinvestment risk due to the fact that the principal components can be paid before they are scheduled, and that repayments tend to be made when interest rates are lower. BUT, this doesnt necessarily mean that earlier coupon payments have any more reinvestment risk than later ones, since coupons are paid at discrete points in time. Like, this years coupon does NOT necessarily have more reinvestment risk than next year’s coupon, or the year after’s. the uncertainty with having to reinvest each coupon at the YTM will be the same. for each of tehse coupons, theres just as much likelihood that on the day you recveive the coupon (and subsequently reinvest it at that days going rate) the rate you reinvest it will differ from YTM. thats my understanding of it…

Say what? “Amortizing” and “pre-payable” are different. I like the approach of the guys above who seem to define the reinvestment risk as being the risk taken from investing cash flows from the time received until maturity of the bond. I agree with DarienHacker about IR’s being mean-reverting, I guess, but I think his argument works with something in there that gives me a model and says something like the coupon payments are sufficiently far from the starting point relative to interest rate vol that they have essentially the same uncertainty.

> because I think it’s how you define reinvestment rate risk. I think a reasonable definition is semivariance or VaR of the total return at the (fixed) investment horizon, which I believe we’re assuming is the original bond maturity. Two additional points to consider: + Have we glossed over the exact mechanism of “reinvestment”? For simplicity I was assuming the coupons are reinvested in a new zero maturing on the original maturity date. Answers might change if we e.g. turn coupons into a floating-rate investment. + A reason that earlier coupons might have _lower_ reinvestment risk: if you assume the above mechanics for reinvestment, then the earlier coupons get to enjoy more of a term premium (assuming the typical yield curve is upward sloping). E.g. if original is a 10y bond, then the coupon at t=1 is reinvested at the prevailing 9-year rate; while the coupon at t=9 gets the (on average, lower) 1-year rate.

My opinion is that since reinvestment risk means the risk of being able to invest you money at a similar rate of return that you get for your present investment, the first cupon has less risk because it is more likely that the market conditions will change less in 1 month than in 2 years

It says in the study book that reinvestment risk is higher with longer maturity and lower with short maturity bonds. If you split an amortizing bond into more bonds that would pay interest+principal at maturities of let say 1,2 and 3 years the one that is shorter term is less risky. Therefore you can consider the payments as being individual bonds

florinpop Wrote: ------------------------------------------------------- > My opinion is that since reinvestment risk means the risk of being able to invest you money at a similar rate of return that you get for your present investment, the first cupon has less risk because it is more likely that the market conditions will change less in 1 month than in 2 years You’re ignoring term of reinvestment. The longer the term the greater the (possible) loss. No investor really gives a hoot about what rate they’re investing at, all they care about is how many dinero are in their pocket on the day of reckoning. > It says in the study book that reinvestment risk > is higher with longer maturity and lower with > short maturity bonds. I think they mean ‘investment horizon’. Clearly shorter-tenor bonds have higher reinvestment risk. If your horizon is 10y and you buy a 10y zero, you have no reinvestment risk. Splitting into two 5y zeros would add reinvestment risk. Any acceleration of cash flows increases reinvestment risk. > If you split an amortizing bond into more bonds > that would pay interest+principal at maturities of > let say 1,2 and 3 years the one that is shorter > term is less risky. False, see above. The only way the shorter bond is less risky is if you’re comparing apples (investment horizon=1y) to oranges (3y). > Therefore you can consider the > payments as being individual bonds No idea what this means, or how it answers the current question: Given a bond, are its earlier or later coupons subject to more investment risk? (And I think a reasonable def. of risk is dispersion of portfolio return on horizon date.)