Rolldown return

[kenneth0505]

I do not understand this statement, Can anyone help? Thanks a lot

It is true that if the yield curve is upward (downward) sloping, the rolldown return will be higher (lower) than the start-of-period YTM because the bond will decline in remaining term to maturity over the horizon period and be priced at a lower (higher) YTM at the end of that period.

[VWJETTY]

Yes. A reminder you can only use roll down return if the stable is up-ward sloping and stable.

[S2000magician]

@VWJETTY

Yes. A reminder you can only use roll down return if the _ stable _ is up-ward sloping and stable.

What about the barn? Or the paddock?

[VWJETTY]

@S2000magician

@VWJETTY

Yes. A reminder you can only use roll down return if the _ stable _ is up-ward sloping and stable.

What about the barn? Or the paddock?

(sigh) I know why I failed last year now haha.

[firefirehelphelp]

I am confused about this point too. Can someone help out please?

[S2000magician]

All they’re saying is that if the yield curve slopes upward, shorter-term forward rates are lower than longer-term forward rates. If the yield curve doesn’t change, then in the future you’ll be discounting by lower forward rates than in the past (because the time to each cash flow will be shorter), so the price will be higher than the original yield curve suggested. A higher price translates into a higher yield.

[S2000magician]

I just posted a simple example here: https://www.analystforum.com/forums/cfa-forums/cfa-level-ii-forum/91364057

[firefirehelphelp]

@S2000magician

This assumes that the yield curve doesn’t change.

Here’s a simple example; suppose these spot rates:

• 1-year: 3%
• 2-year: 5%

The implied 1-year forward rate starting 1 year from today is 7.0388% (= (1.05² / 1.03) − 1). A 2-year, annual-pay bond paying a coupon of 6.0% will have a price of $1,019.70 (= $60 / 1.03 + $1,060 / 1.05²) and a YTM of 4.9412% (because $60 / 1.049412 + $1,060 / 1.049412² = $1,019.70).

If the yield curve is unchanged one year from today, then the bond will have a price of $1,029.13 (= $1,060 / 1.03). Your 1-year return will be ($1,029.13 + $60 − $1,019.70) / $1,019.70 = 6.8081%.

Why?

Because the value of the bond is being discounted at 3% (the current 1-year spot rate) rather than 4.9412% (the original YTM).

If the current 1-year spot rate were 4.9412%, then your 1-year return would be 4.9412%. I’ll leave it to you to verify that.

Hi S2000magician,

Thanks for trying to explain. I am quoting the example you gave so that it is easier to refer. I am still confused. Could you please help me out with the following queries:

(1) In the example you gave, what is the rolldown return? Would it be 6.8081%?

(2) The statement made in the OP said “the rolldown return will be higher (lower) than the start-of-period YTM because the bond will decline in remaining term to maturity”. This is different from your example, where the bond value actually increases from $1,019.70 to $1,089.13 ($1,029.13 + $60). What am I misunderstanding?

Thank you once again.

[S2000magician]

@firefirehelphelp

(1) In the example you gave, what is the rolldown return? Would it be 6.8081%?

Yes.

@firefirehelphelp

(2) The statement made in the OP said “the rolldown return will be higher (lower) than the start-of-period YTM because the bond will decline in remaining term to maturity”. This is different from your example, where the bond value actually increases from $1,019.70 to $1,089.13 ($1,029.13 + $60). What am I misunderstanding?

Actually, in my example the bond value increased from $1,019.70 to $1,029.13 ; the $60 is the coupon payment, which is no longer part of the value of the bond.

Depending on the steepness of the yield curve (and whether the bond is selling at a premium or a discount), the bond price may increase or decrease during the holding period. (Why the OP said that it will decline, uncategorically, I don’t understand.) What’s important is that the new YTM is lower than the original YTM (because the yield curve slopes upward and hasn’t changed), so the new bond price is higher than the original YTM suggested it would be.

@firefirehelphelp

Thank you once again.

My pleasure.

[firefirehelphelp]

@S2000magician

Depending on the steepness of the yield curve (and whether the bond is selling at a premium or a discount), the bond price may increase or decrease during the holding period. (Why the OP said that it will decline, uncategorically, I don’t understand.) What’s important is that the new YTM is lower than the original YTM (because the yield curve slopes upward and hasn’t changed), so the new bond price is higher than the original YTM suggested it would be.

Hi S2000magician,

Isn’t your new YTM higher than your original YTM?

Original YTM = 4.9412%

New YTM = 6.8081%.

Thank you for your help.

[S2000magician]

@firefirehelphelp

@S2000magician

Depending on the steepness of the yield curve (and whether the bond is selling at a premium or a discount), the bond price may increase or decrease during the holding period. (Why the OP said that it will decline, uncategorically, I don’t understand.) What’s important is that the new YTM is lower than the original YTM (because the yield curve slopes upward and hasn’t changed), so the new bond price is higher than the original YTM suggested it would be.

Hi S2000magician,

Isn’t your new YTM higher than your original YTM?

Original YTM = 4.9412%

New YTM = 6.8081%.

Thank you for your help.

No.

Original YTM = 4.9412%.

Realized yield = 6.8081%.

New YTM = 3.0000%.

[Michael_V]

"

firefirehelphelp wrote:

(1) In the example you gave, what is the rolldown return? Would it be 6.8081%?

Yes."

Hi S2000,

Isn’t this 6.8081% return the full rolling yield opposed to the roll down return? From the text, the roll down return is a component of this 6.8081%; ((end price - bgn price)/bgn price). Including the coupon payment would make this the “rolling yield” according to the text. The “rolldown return” being only the price component of total return. Not sure if this is just semantics, for the test I imagine it is an important distinction.

[CaliforniaDreaming]

Hah. A magician of finest jest…