# Which bond should I pick if both have the same YTM, tenor, credit risk? One has a higher coupon rate than the other.

#### Ixeua

##### New Member
Suppose I am presented 2 bonds

 YTM Coupon A 5% 6% B 5% 4%

Given that both bonds have the same YTM, tenor, credit risk would either bond be better than another?

A couple of things come to mind. In particular that the Macaulay duration (how fast an investor gets their money back) of bond A is shorter than that of bond B. Would there be any scenarios when B would be a better pick?

#### lushukai

##### Well-Known Member
Subscriber
Hi @Ixeua ,

I guess another necessary assumption would be that both bonds would be the same price? In that case, the principal of bond A is less than bond B (that you receive back at the end of the bond tenor).

My experience tells me that when interest rates are decreasing, bond B would be a better choice as the duration of bond B is greater than bond A, which causes the price of bond B to increase greater than bond A. This makes it a better hedge in a bond-equity portfolio.

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
HI @lushukai I don't think they can be the same price: For A, y<c such that p>100. For B, y>c such that p<100. I'm not sure that price per se is an issue: I think the (most common) unstated assumption, for comparison purposes, is that you have the same (eg) $1,000 or$10,000 to invest in either. So, you just end up buying different face amounts given the same value.

The textbook answer is that Bond A offers higher re-investment risk: slightly more coupon income to reinvest along the way (which is related to its lower duration, as there is a trade-off between re-investment and rate/duration risk).

The other thought I had is that Bond A is a premium-priced bond (i.e., y<c --> p>100) and, pulling to par, experiences a small capital loss. So there is a slight tax difference, I think. But it's not a really well-worded question, actually. I hope that's interesting!

#### Ixeua

##### New Member
Hi Thanks! Could you go into detail into the hedging part? A lot of books I read don't include strategies on bond hedging so I am interested on how bond hedging strategies work.

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
@Ixeua what is the question's source (where did you see/find it)?

#### Ixeua

##### New Member
Hi @Ixeua ,

I guess another necessary assumption would be that both bonds would be the same price? In that case, the principal of bond A is less than bond B (that you receive back at the end of the bond tenor).

My experience tells me that when interest rates are decreasing, bond B would be a better choice as the duration of bond B is greater than bond A, which causes the price of bond B to increase greater than bond A. This makes it a better hedge in a bond-equity portfolio.

Hi @David Harper CFA FRM. The hedging bit was in reply to @lushukai 's answer here.

If you are asking about the original question, that was purely theoretical. Not from any particular source.

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Thanks @Ixeua appreciated, just wondered if the original question had a source. I realize your f/up was in reply to Lu Shu's answer. I think he just means that a hedge might prefer the hedge position to be more sensitive (i.e., higher duration) to interest rates. I don't have time to go into that huge topic. Our Tuckman text covers it quite in depth with many examples. Thanks,

#### Ixeua

##### New Member
Thanks @Ixeua appreciated, just wondered if the original question had a source. I realize your f/up was in reply to Lu Shu's answer. I think he just means that a hedge might prefer the hedge position to be more sensitive (i.e., higher duration) to interest rates. I don't have time to go into that huge topic. Our Tuckman text covers it quite in depth with many examples. Thanks,
I am new here. Could you direct me to that? I would really appreciate it.

Staff member
Subscriber

#### lushukai

##### Well-Known Member
Subscriber
HI @lushukai I don't think they can be the same price: For A, y<c such that p>100. For B, y>c such that p<100. I'm not sure that price per se is an issue: I think the (most common) unstated assumption, for comparison purposes, is that you have the same (eg) $1,000 or$10,000 to invest in either. So, you just end up buying different face amounts given the same value.

The textbook answer is that Bond A offers higher re-investment risk: slightly more coupon income to reinvest along the way (which is related to its lower duration, as there is a trade-off between re-investment and rate/duration risk).

The other thought I had is that Bond A is a premium-priced bond (i.e., y<c --> p>100) and, pulling to par, experiences a small capital loss. So there is a slight tax difference, I think. But it's not a really well-worded question, actually. I hope that's interesting!
Thank you David! I should definitely know this (especially on the bond premium/discount portion + pulling to par) ... it is part of my full-time job as well