q.19 duration garp l1

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david,

I learnt from ur screencast only that zero coupon bond has highest duration
and then order is zero>discount>par>premium.
so as per that logic for question below:

Q.19 A newly issued non-callable, fixed-rate bond with 30-year maturity carries a coupon rate of 5.5% and trades at par. Its duration is 15.33 years and its convexity is 321.03.Which of the following statements about this bond is true?
a) If the bond were to start trading at a discount, its duration would decrease.
b) If the bond were to start trading at a premium, its duration would decrease.
c) If the bond were to start trading at a discount, its duration would not change.
d) If the bond were to remain at par, its duration would increase as the bond aged.

b) If the bond were to start trading at a premium, its duration would decrease. should be the right answer.

Y is it a) i.e If the bond were to start trading at a discount, its duration would decrease.
??I couldnt get.
Please help

 

[David Harper CFA FRM]

Hi snigdha,

That first relationship is correct, but for a given yield as coupon varies; in the case, as price = par, the yield must = coupon, so the yield = 5.5%. Now if yield remains at 5.5%, but we increase coupon, bond becomes premium (price > par) and duration goes lower (per zero>discount>par>premium; intuitive, more cash flow received sooner in the form of higher coupons)

But this question assumes coupon fixed at 5.5% so the variable must be yield: as yield increases, duration decreases. Here, yield higher that 5.5% implies DISCOUNTED bond and lower duration.

... so you are not far off: ceteris paribus, either higher yield or higher coupon imply lower duration.
... so if the question allowed for you to increase the coupon and keep yield @ 5.5%, then you would have answer (b), a premium bond with a lower duration.

David

 

[[email protected]]

WOW... Thanks a lot..!!

 

[sl]

Hi David,

I have a query. This bond is a fixed rate coupon paying bond, if it trades at discount, wouldn't that be a double bonus for the owner, i.e, the owner buys the bond
at a discount and also receives coupon payments? Does that happen in the real world? Or am I missing something?

Thanks
Sundeep

 

[David Harper CFA FRM]

Hi Sundeep,

Yes, it absolutely happens because the issue is "what is the [competitive] market yield for a bond of this risk?" If the coupon is 5.5% but yield is 7.0% (eg) , then the coupon is insufficient and, as the investor, yes, it is a "double bonus" for you to get a 5.5% coupon and a ~1.5% (expected) capital appreciation. Similarly if another bond pays a 10% coupon, it must trade a premium, with an expected capital depreciation (7.0% - 10% = ~3%), to give a competitive yield of 7.0%.
... The issue is the yield (which is an expected, or ex ante, concept), which has two components: coupon income and expected capital appreciation/depreciation.

It's analogous (FWIW) to the post-big bank CDS pricing: there is fixed "coupon" (CDS premium) paid by the protection buyer (100 or 500 bps). But price of risk fluctuates! So, the up-front premium changes to reflect this.

Hope that is helpful, Thanks, David