Which of the following bonds bears the greatest price impact if its yield declines by one percent? A bond with: A) 30-year maturity and selling at 100. B) 10-year maturity and selling at 100. C) 10-year maturity and selling at 70. D) 30-year maturity and selling at 70.
d. longer maturity + lower coupon (as indicated by selling at a discount) = higher duration
Thanks dspapo … But thing I don’t understand is what Coupon rate has to do with bond selling at discount or premium Say, a bond with coupon=8% and YTM = 10% —> selling at discount another bond with coupon =8% and YTM=7% ----> Selling at premium The fact that bond is selling at discount or premium is solely based on YTM and has nothing to do with coupon payments baffles me. Can you please explain how did you get to lower coupon for discount bonds ?? Many thanks !
D The question wants us to find the bond with highest duration. Maturity up = Duration up Yield down = Duration up Comparing two bonds with same maturity, the lower price (selling at deep discount) means higher yield. Vice versa. So we know that higher price = lower yield = higher duration. thunderanalyst, your interpretation about discount and premium is correct. However, in this question, all we need to know is the one with “relatively” higher duration. For any YTM, the $70 bond still has higher yield than $100 bond. Hope this helps.
“Comparing two bonds with same maturity, the lower price (selling at deep discount) means higher yield” No it doesn’t. It probably means that the higher price one has a higher coupon rate and it could mean any number of other things.
Thanks Joey and Heha. I am still confused, why a bond selling at discount will have a higher coupon rate compared to similar bond trading at premium.
I don’t think the coupon rate is the determining factor, but the price of the bond, and the YTM. Could you have a bond selling for $800 with coupon of $80 (i.e. current yield of 10%), and yet have another bond selling for $1000 with coupon of $90 (i.e. current yield of 9%)? both having same maturities. I’m not helping here, only adding to the confusion a little more 
lol thunder. joey just said the opposite. a bond selling at a discount will have a lower coupon than a similar bond trading at a premium. let’s say the market interest rate is 8%. this is the rate that new bonds are issued at in the market. now you have 2 bondholders who each got his bond a year ago. guy A got his bond with a 9% coupon and guy B got his with a 7% coupon. So guy A receives $90 a year on his bond and guy B gets $70 a year on his bond. These are the coupon payments. what do you think is worth more all else the same? of course guy A’s bond is worth more. relative to what you could get in the market today (an 8%, or $80 coupon), guy A’s $90 coupon is worth more. Thus, an investor will pay more than par value for guy A’s bond. Similarly, guy B’s bond is worth less so his is selling at a discount. thus, higher coupon (relative to market interest rates) bonds sell at a premium, and lower coupon (relative to market rates) bonds sell at a discount…
Good example, topher. But do you need to say “relative to market interest rates”?
you don’t necessarily need that phrase but I added it to clarify. you could also say that a higher coupon bond, relative to a lower coupon bond, will be selling at a premium relative to the lower coupon bond. but the lower coupon bond may be selling at a premium to par which makes both bonds premium bonds… lol i hope i’m not confusing too much here.
I get it now. Thanks Topher, things look much better now. "lol thunder. joey just said the opposite. " – I was typing in office, and my boss is always hovering over me
yeah i notice that when i post on this board in the office, which is 90% of my posts, my thoughts aren’t nearly as clear.
So the higher the coupon the less interest rate sensitivity? That seems counter-intuitive to me. Could someone provide an explanation
Yes. Higher coupon = lower duration. There are two identical zero coupon bonds, with 1% and 10% yield. Let’s say market interest rate is going up for 1%. For 1% bond, the change is -100% (from 1% to 0%) For 10% bond , the change is -10% (from 10% to 9%) The calculation is not precise but this is my intuition. Joey, my bad. “Comparing two bonds with same maturity, the lower price (selling at deep discount) means higher yield” It should be two identical bonds with different price.
Dreary Wrote: ------------------------------------------------------- > I don’t think the coupon rate is the determining > factor, but the price of the bond, and the YTM. > > Could you have a bond selling for $800 with coupon > of $80 (i.e. current yield of 10%), and yet have > another bond selling for $1000 with coupon of $90 > (i.e. current yield of 9%)? both having same > maturities. I’m not helping here, only adding to > the confusion a little more Of course. The most obvious reason is credit quality, but also liquidity, optionality, seniority, collateralization, taxation, country of origin, and 30 other reasons.
heha168 Wrote: ------------------------------------------------------- > Yes. Higher coupon = lower duration. > There are two identical zero coupon bonds, with 1% > and 10% yield. > Let’s say market interest rate is going up for > 1%. > For 1% bond, the change is -100% (from 1% to 0%) > For 10% bond , the change is -10% (from 10% to > 9%) > The calculation is not precise but this is my > intuition. > > > Joey, my bad. “Comparing two bonds with same > maturity, the lower price (selling at deep > discount) means higher yield” It should be two > identical bonds with different price. Can somebody clarify this? When the bond is selling at discount, implies high yield and less volatility. How is yield related to Duration in this context and in general. Thanks S
higher yield = lower duration
The only way this question is valid is if each bond has the same coupon rate and they are simply just different scenarios for one particular bond. Duration is a function of both price and the coupon rate, and because discounting has a larger effect in later years as opposed to earlier years, a par bond will have higher duration. In simple terms, if the coupon is the same for both bonds, and one is priced at a discount (higher YTM) and one is priced at par, discounting will be less impactful for the bond at a discount, and the investor will be able to recover his/her money in less time (M Duration was first thought of and expressed in yrs). Do the math…a 30yr 10% coupon bond when the YTM is 10% will be priced at 100. A 1% decline in YTM will cause this bond to go to ~$110. This is a duration of 10. A 30yr 10% discount bond priced at $70 will have a YTM of roughly 14.4%. If the YTM declines by 1% to 13.4%, the bon price increases to ~$75. This is a duration of 7. Don’t get confused with the higher YTM. As long as the bonds have the same coupon and same maturity, the par bond will have a higher duration due to the larger effect of discounting in the later years. Remember, a good way to think about duration is: how long it takes me to recover my initial investment (in present value terms). The correct answer should be A if both bonds have the same coupon rate.
The bigger issue isn’t Macauley duration, it’s credit or whatever else is causing one bond to be priced at 100 and a bond with identical coupon and matuirty to be selling at 70. That 14.4% 30-yr bond may have almost no interest rate sensitivity and be trading close to equity.
Exactly. Which is why for the question you need to think of it as one bond with the same coupon, but just under different scenarios. When it is selling at a discount it will have a lower duration relative to when it is trading at par.