2015 Fixed Income 3C Higher coupon rate = shorter duration?

Who can explain this to me?

2 year annual coupon of 100% on $1,000 par.

Year 1 = $1000

Year 2 = $2000

2 year zero coupon on $3,000 par

Year 1 = $0

Year 2 = $3000

Which has a shorter duration?

Think about Macaulay duration.

Here’s what I got:

1st one: Duration = (1000/3000)*1+(2000/3000)*2= 1.67

2nd one: Duration= 0*1 + (3000/3000)*2 =2

Thank you both and pls correct me if I’m wrong.

For that same question my answer was wrong because I didnt talk about duration. but this is what I said for trade 2 having positive value. Let me know if you agree with my answer.

since you are buying a 3 year non-callable with 5% coupon and selling a 3 year zero coupon, and there is a upward parrallel shift in the yield curve forcasted. I said because interest rates are increasing the non-callable coupon paying bond will outperform the zero coupon bond because the coupon payments will be reinvested at a higher interest rate, there for it will have positive value on the portfolio.

The answer talks about duration, but is my answer still correct?


You take the PV of the each divided by the PV.

1st one:

Y1= 1000/(1+100%) = 500

Y2= 2000/(1+100%)^2 = 500

Duration = 0.5*1+0.5*2 = 1.5 years

2nd one (assume same interest rate):

PV today= 750

PV (Y2) = 3000/(1+100%)^2 = 750

Duration = 1*0 + 2*(750/750) = 2 years.

Vanilla zero bonds have the same duration as their maturity.

Are you assuming YTM = coupon rate?

I think that definately makes sense. Higher coupon will be reinvested at higher expected rate vs 0 coupon. However CFAI doesn’t list it as an answer. Will an answer like that be counted?

You wrote that much for an answer? Seems a lot to me.

Well, no, i didnt write all that but to me my answer makes sense but they didnt talk about reinvesting at a higher rate. I said that the trade would add positive value so I gave my self one point out of 3 but since I didnt talk about duration I didnt give my self the extra 2 points

This is exactly what i said, I’d like to get your thoughts

Circled positive “because rates are increasing the coupon paying bond will outperform the zero coupon bond because coupons can be reinvested at a higher interest rate, which will increase return”

think about it logically, the larger and sooner the cashflows, the shorter the duration.

Yea, I get that I am just trying to figure out how many points i would have gotten for that question considering my answer makes sense.