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A bond that sells at par value must have a duration that equals the time to...

A bond that sells at par value must have a duration that equals the time to maturity.

True

False

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Answer #1

This is ​false. ​A bond that sells at par value would have its coupon rate equal to its yield to maturity (YTM). Its duration may or may not be equal to its time to maturity.

Consider a bond - $1000 par value, 10% Coupon rate and 10% YTM, time to maturity 5 years

Market price = $100 x PVIFA (10% ,5) + $1000 x PVIF (10%, 5) = $1000

Therefore, it sells at pay.

Now, Duration is computed as follows -

where, y = ytm, c = coupon rate, t = time to maturity

years

Therefore, duration is less than its time to maturity.

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