yield curve

[aditya]

hi david,

i got stuck at this question can u please explain this and also please tell what is spot rate????

what i think is that yields should be more for zero coupon bond then for coupon bearing bond......... am i right???

question:>
Suppose that the yield curve is upward sloping. Which of the following statements
is true?
a. The forward rate yield curve is above the zero-coupon yield curve, which
is above the coupon-bearing bond yield curve.
b. The forward rate yield curve is above the coupon-bearing bond yield
curve, which is above the zero-coupon yield curve.
c. The coupon-bearing bond yield curve is above the zero-coupon yield
curve, which is above the forward rate yield curve.
d. The coupon-bearing bond yield curve is above the forward rate yield
curve, which is above the zero-coupon yield curve

adi

 

[David Harper CFA FRM]

Hi adi,

Yes this is correct: "yields should be more for zero coupon bond then for coupon bearing bond"

Note the zero-coupon yield is (same as) the spot rate.

Consider a simple two year spot rate curve: 1-year spot rate = 1%, 2-year spot rate = 2% (i.e., upward sloping spot curve)

The 1-year forward = LN(EXP(2%*2)/EXP(1%)) = 3%. In order to match a 2-year spot rate of 2% [EXP(2%*2)], you have to roll-over at an even higher forward rate: EXP(1%)*EXP(3%)= EXP(2*2%). The forward curve > spot curve

Now if a 2-year pays coupons, note the yield (YTM) here refers to the single yield that discounts all cash flows (coupon and principle) to equal the bond price (YTM = IRR). The yield of a coupon bond is sort of a weighted average of the spot yields attached to its cash flows. As such, it must be less than its highest spot rate; i.e., upward sloping implies the yield (of a coupon bearing bond) will be "dragged down" by lower interim spot rates. In our example, the 2-year spot is 2%, a coupon bearing bond discounts both the 1% 1-year and the 2% 2-year, so it's yield will be somewhere in between the lowest applicable spot and the highest: 1% < yield < 2% but in any case the coupon-bearing yield will be less than the zero.

So, for an upward slopping curve: coupon-bearing < spot (zero-coupon) < forward

David

 

[aditya]

thanx so much for such a clear and lucid explanation ........... as always


adi