Treasury Yield Curve

[JAbdo9644]

Hi Everyone,

Say for example, that the 5 year par yield to maturity as per the treasury par yield curve is 6%.

Does that mean that ALL treasury bonds that now have 5 years to maturity (regardless of what their original tenor was) must trade at a YTM of 6%?

If it so happens that one such bond offers a coupon rate of less than 6%, then it'll be a priced below par to compensate for the lower coupon. Similarly if it offers a coupon rate of higher than 6%, it'll be priced above par to make it a fair deal as well.

Essentially, if the 5 year par YTM is 6%, then I should price ALL outstanding treasury bonds that now have 5 years remaining in their life at a YTM of 6% regardless of what their coupon rates are?

Is that correct?

Thanks Everyone !!
Jamal

 

[David Harper CFA FRM]

Hi @JAbdo9644 Can I slightly edit your question to this:

Say for example, that the 5 year par yield to maturity as per the treasury par yield curve is 6%.
Does that mean that ALL treasury bonds that now have 5 years to maturity (regardless of what their original tenor was) must trade at a YTM of 6%?

I do that to distinguish between "par yield" and "yield to maturity"; aka, "yield".

The answer is, No. The 5-year par yield is a function of the zero-rate curve (vector) including all zero rates (including the 5-year zero rate). What's cool to me about the par yield is that it makes no direct reference to bond prices (they indirectly contribute by revealing the zero rates). So, in your example, a 6.0% 5-year par yield summarizes information about the 5-year discount function (i.e., set of discount factors). That's also how I would think about the par yield: it is a single number that summarizes the discount function. If you follow me here, then you are likely near to understanding why par yields are swap rates.

Given the 5-year par yield (and therefore, this 5-year discount function), the yield-to-maturity of various 5-year bonds will vary with their coupon rates! This is true even if we assume those bond are priced exactly according to the discount function; realistically, technical factors would cause prices to vary (aka, trade cheap or rich). So, to me, the answer is a double no.

Here's one of my videos on par yield https://forum.bionicturtle.com/threads/t3-13-par-yields-are-swap-rates.22426/

 

[JAbdo9644]

Thanks so much for the kind reply Prof. David !

So in practice, the correct approach would be to unwind or extract the spot (zero) curve FROM the given par curve, and then use this extracted zero curve to price any bond with 5 yrs remaining to maturity, no matter what the coupon is. In effect I'd be discounting each coming payment using its corresponding zero rate. And I got all these zero rates via bootstrapping the par curve. Would that be a correct to go about it?

If the answer is yes, wouldn't that make the treasury par curve that's published daily of limited use if its taken as it is? If we don't do the work ourselves and extract the zero curve from it, what information does it really give us? Also, why wouldn't the treasury dept. just publish the zero curve instead straight away?

Thanks a lot in advance Prof. David, your interesting discussions tempt us to ask questions

Jamal