duration relationship with yield and maturity

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Sujan

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For a bond with long-term maturity AND high yield (upward sloping yield curve*), would the duration be lower or higher?
*Note: This is the Yield to Maturity curve where the yield increases as maturity increases.
 
I think in this case the duration follows maturity - so duration will be higher.
 
Thanks.
But would much appreciate if you can please expand on your answer and explain why would duration follow maturity and ignore the yield (since we know that high yield produces low duration).
Cheers.
 
Duration is price sensitivity to changes in Interest Rates
The first criteria is the bond choose bonds between maturities, if a bond A has longer maturity then then it will higher duration, if the bonds have the same maturities, then it comes down yield, lower the yield, higher the duration…
Remeber,
a) Higher the coupon, lower the duration
b) Longer maturity, higher the duration and vice versa
c) Higher the yield, lower the duration
Hope this helps!
 
Good explanation Varun….
I just use this to remember
Duration = Maturity/Coupon,Yield
 
Thanks Varun.
While I agree with your bullet points on the rules for duration (and where this question stems from) I am not sure that I understand your example.
>>The first criteria is the bond choose bonds between maturities, if a bond A has longer maturity then then it will higher duration, if the bonds have the same maturities, then it comes down yield, lower the yield, higher the duration… <<
To extend your example of two bonds, let’s say that they both have long-term maturities and one has low yield and the other high yield. We know that longer maturities have high duration and we also know that low yields have high duration. So, the bond with the long-term maturity and low yield has high duration, which I am fine with. But, what about the other bond which has long-term maturity AND high yield? Is the duration high or low in this case?
I am not sure whether in your criteria you meant to say that maturities take precedence over yields - and therefore, the latter bond would would have high duration. If this is the case, would appreciate if a reference can be provided to either Schweser or CFAI, as I am not able to find one.
Thanks again.
 
I think it is out of scope of Level 1.
However, I am unsure of the correct reasoning as well or whether one exists. My gut feeling is that we need to the actual data to compute the duration and compare in this case.
Anyway, good question pointed out. Anyone able to shed some light?
 
See by when seeing duartion of bonds…it is always Bond A vs a Bond B
A bond alone cannot tell much abt the duartion….
We always compare bonds and tell that this bond has higher price volatility than Bond B and so on….
So coming to the question, “”“For a bond with long-term maturity AND high yield (upward sloping yield curve*), would the duration be lower or higher?”“””
I would give an answer as YES, it has higher duartion since it has a long maturity, but LESSER duration compared to a bond with a similar maturity and lower yield…..
There are plenty of questions on the same in the Qbank…
Was scratching my head while solving it….
Hope this helps…!!!!
Can the senior guys rus1bus/beatthecfa confirm the same?
 
Thanks guys.
The scenario definitely exists, i.e. upward sloping yield curve (on the yield-maturity graph)
rus1bus/beatthecfa, can we please get a consensus on how the duration should pan out.
Anyone who’s across this - would certainly appreciate your help as well.
Thanks
 
Sujan, I agree with Revenant.
For the exam, you just need to know that Duration increases with Maturity and decreases with Yield. I think you already know this and are not looking for explanation on this.
Now, to your question: What happens to duration, when BOTH Maturity and Yield Increase.
My answer to this is: You cannot predict it, unless you calculate it. And in the exam, they should not ask this, as both these factors have conflicting effect on the result to be able to predict with any surity.
 
Thanks rus1bus - glad that it is not part of Level 1. That helps to park this aside for the time being. I just wonder though what the calculation involves.
Empirical evidence shows that this scenario is live and well. Have a look at the recent yield curve for US treasuries. They are all upward sloping with long maturity AND high yield:
http://www.treasury.gov/offices/domestic-finance/debt-management/interes...
Cheers
 
If I am not wrong, the yields of US Treasuries were downward sloping during the Gulf war…..The reason was that the govt borrowed heavily so short term yields rised beacuse of 2 reasons::
1) the short term outlook of the US economy looked bad (higher yield)
2) Investors believed in the long term, US economy looked good
Thanks!
 
Yes Varun, you are correct.
Also, Short Term rates are influenced by Fed’s fund rate. Meaning Fed’s monetary policy can determine short term interest rates. But, Fed cannot influence Long Term rates. Long Term rates are determined by investor’s outlook of that economy and conditions.
Even in these times, Fed is borrowing heavily by selling Treasuries thru open market operations, to finance huge govt deficit, but still short term interest rates are low because of Fed’s near zero Fund Rate.
 
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