# 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?

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.

Close.

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.