Higher Coupon = Lower Duration

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Justin Case

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Can someone please help me clarify something…
I understand that a higher coupon bond provides for a lower duration as per the Macaulay/Modified definition (lower time to payment), but my confusion stems from the Price-Yield Curve perspective.
If I have a high paying coupon bond, then I can assume that it’s priced at a Premium to Par (meaning that It would be at the top left hand-side of the Price-Yield curve). If I’m in this section, then a Change in Price/Change in Yield should result in a higher number, i.e. a high Duration given that this is a forumla for Duration. In that case, wouldn’t a High paying Coupon=High Duration?
I know this is wrong, but I was wondering if someone could help me out with where I’m off with my point of view??
Thanks!
 
Justin Case wrote:Can someone please help me clarify something…
I understand that a higher coupon bond provides for a lower duration as per the Macaulay/Modified definition (lower time to payment), but my confusion stems from the Price-Yield Curve perspective.
If I have a high paying coupon bond, then I can assume that it’s priced at a Premium to Par (meaning that It would be at the top left hand-side of the Price-Yield curve).
Click to expand...
No, you can’t. If you have three bonds A, B, and C, paying, respectively, 3%, 4%, and 5% coupons, all of which have a 6% YTM, then none of them is priced at a premium, but bond C pays a higher coupon than bonds A and B, and B pays a higher coupon than A.
Justin Case wrote:If I’m in this section, then a Change in Price/Change in Yield should result in a higher number, i.e. a high Duration given that this is a forumla for Duration. In that case, wouldn’t a High paying Coupon=High Duration?
Click to expand...
A higher number compared to what? Compared to the numbers further to the left on the curve? That’s true, but that only shows how YTM affects duration. Here, you have to compare three curves: the price/yield curve for bond A, the price yield curve for bond B, and the price/yield curve for bond C. And you cannot compare them simply by looking at the slope of the price/yield curve, because (modified/effective) duration doesn’t measure that slope (which is the dollar price change); (modified/effective) duration measures the percentage price change, so you have to take that slope and divide it by the bond’s price.
If you draw the price/yield curves for bonds A, B, and C, the slopes will look similar for any given yield, but bond B will have a higher price than bond A, and bond C will have a higher price than bond B. Thus, for a higher coupon you’re dividing that slope by a higher price, giving a lower percentage change.
Justin Case wrote:I know this is wrong, but I was wondering if someone could help me out with where I’m off with my point of view??
Click to expand...
I hope that this helped a bit.
Justin Case wrote:Thanks!
Click to expand...
My pleasure.
 
Magic gives a good explanation of this. I would suggest plotting the curves out in excel and adjusting the parameters to see what happens to the Price Yield curve.
Each bond has its own P-Y curve. Effectively, when you’re talking about duration, you’re looking at matching the price and yield of both bonds (because you normalize them by calculating the % changes). So think about this problem in the context of not where each bond plots on the P-Y curve but what the 2 curves look like at the point they cross, when the P and Y of each bond are equal. The bond with the higher coupon will have a lower slope thus it has a lower duration.
To think about this conceptually, if you have 2 bonds, both with equal prices and yield, and one has a higher coupon, then necessarily, it must also have a lower FV or lower time to maturity,
If it has a lower FV, this will obviously decrease the duration.
If it has a lower time to maturity, this will also decrease the duration.
This can be complicated if we adjust both parameters at the same time but be assured that the decrease due to one will more than offset the increase due to the other.
 
Justin Case wrote:
Can someone please help me clarify something…
I understand that a higher coupon bond provides for a lower duration as per the Macaulay/Modified definition (lower time to payment), but my confusion stems from the Price-Yield Curve perspective.
If I have a high paying coupon bond, then I can assume that it’s priced at a Premium to Par (meaning that It would be at the top left hand-side of the Price-Yield curve). If I’m in this section, then a Change in Price/Change in Yield should result in a higher number, i.e. a high Duration given that this is a forumla for Duration. In that case, wouldn’t a High paying Coupon=High Duration?
I know this is wrong, but I was wondering if someone could help me out with where I’m off with my point of view??
Thanks!
Click to expand...
No if you have a higher coupon paying bond that means you are getting more money back than others in real terms, For example - YTM is 5% and coupon is 10% for X and 6% for bond Y, So if YTM change to 6%.
Here bond Y will variate more than X, Because Bond X is already getting 10% and reinvesting it on 5% but Bond Y is only getting 6% and reinvesting it on 5%.
The percentage change is greater for bond Y that is why they have a greater impact.
 
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