# difference between YTM and return on bonds

Hello,

In a mock question, we are asked to say if the global full life return on a bond will be equal, higher or lower than the YTM, if the spot curve stay the same during the full life of the bond.

The answer is :

[question removed by moderator]

What i do not understand is that YTM is computed from the spot curve (actually it is a ”complex” mean of the spot curve that accounts for __lower__ and__ higher__ rate on the spot curve), so if the spot curve did not change, shoudn’t it be the same to reinvest at the different forwards or at the unique YTM ?

Shoudn’t YTM of the bond be equal to the global return if the spot curve DO NOT MOVE ?

Thanks a lot !

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Apparently the spot curve slopes upward; the answer says that, but your question didn’t.

Their answer is wrong.

Consider this par curve;

The corresponding spot curve is:

You buy a 1½-year bond paying a 2.76% coupon, so you pay $1,000. Let’s see what happens to your cash flows over the next 1½ years, and what your investment is worth in 1½ years. We’re assuming that the par rates (and, therefore, the spot) rates don’t change during that time.

^{2}= $14.13.^{2}= $13.94.At the end of 18 months, your investment is worth $14.13 + $13.94 + $13.80 + $1,000 = $1,041.87. Your semiannual effective return is ($1,041.87 / $1,000)

^{1/3}− 1 = 0.0138 = 1.38%. Your annual return is 2 × 1.38% = 2.76%, which is exactly the YTM.Simplify the complicated side; don't complify the simplicated side.

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Hi S2000magician,

I’m a little bit confused here.

From your response, “Six months from today you get a coupon payment of $13.80 (= $1,000 × 2.76% × ½). As there is one year left until the bond matures, you can reinvest that coupon at the 1-year spot rate of 2.4024%.”, six months later, you get the coupon payment, but why are we using reinvestment rate of 2.4024%, which is 1-year spot rate? Shouldn’t it be 1 year forward rate after 6 months?

Regards,

Brockman

I cannot be held responsible for anything I wrote over 2½ years ago.

However, this one time I think that I’m correct: we’re told that the spot curve doesn’t change during the life of the bond, so 6 months from now the 1-year spot rate will be the same as it is today: 2.4024%.

Simplify the complicated side; don't complify the simplicated side.

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