# Duration/YTM

Hey guys, can’t figure out this question from book 5 (2006 version fyi) - any ideas? Assume the yeild curve for zero-coup T-bills is as follows: The three numbers used are Modified Duration, Current YTM, Forecast YTM in order: A ( 2, 4.96%, 4.5%) B (5, 4.8%, 5.0%) C (10, 4.95%, 5.0%) D (15, 5.14%, 5%) E (20, 5.1%, 5%) F (25, 4.99%, 5%) G (30, 5.05%, 5%). A. If interest rates decline as previously showed in the forecasted curve, what security would mazimize captial gain? Choices: A-G? Can someone please explain how to solve this?

probably G because it has longest time to maturity (highest modified duration) and pretty high YTM -> highest discount -> highest capital gain. The yield curve surprises me a little though.

Just cause I do not fully understand this material yet, may I ask why the yield curve surprises you?

You can read more about yield curve here: http://en.wikipedia.org/wiki/Yield_curve a normal yield curve would have higher yield for higher maturities as A through D but in the example yield then it goes down and then up again. I was just a little surprised that they didn’t use a normal yield curve in the example. You will read more about yields in Fixed income section. There are three theories covered: pure expectation, liquidity preference and market segmentation.

The asnwer seems to be D though by multiplying the durations time delta interest rate. G seems to be the second best best choice. And yeah, it’s a pretty odd yield curve.

you are right, Joey.

Where does this question say anything about the maturities? How can you make any assumptions about the yield curve? All I see is Modified Durations increasing, which may or may not be indicative of longer maturities.

duration of a pure discount bond is roughly equal to its time to maturity http://en.wikipedia.org/wiki/Bond_duration

wyantjs Wrote: ------------------------------------------------------- > Where does this question say anything about the > maturities? How can you make any assumptions > about the yield curve? All I see is Modified > Durations increasing, which may or may not be > indicative of longer maturities. And even with coupon bonds you should think that big durations = long maturities.

So the consensus is D?

-De * (Change in Rate) * 100 ==> Change in Price per basis point. So do that for each case. D gives you the biggest #. Change in Rate includes the sign (+ or -). So the final figure would either be a + or a -ve number. CP

JoeyDVivre Wrote: ------------------------------------------------------- > wyantjs Wrote: > -------------------------------------------------- > ----- > > Where does this question say anything about the > > maturities? How can you make any assumptions > > about the yield curve? All I see is Modified > > Durations increasing, which may or may not be > > indicative of longer maturities. > > > And even with coupon bonds you should think that > big durations = long maturities. I don’t disagree with that. I was just making the point that we don’t know for sure, and really testing the water to make sure that I wasn’t missing something.