Immunization target rate, YTM and yield curve

[solarpower03]

Hi all,
Can someone explain the relationship here. This is in book 4, page 29.
Many thanks
Solar

 

[tzu]

YTM assumes flat yield curve i.e., all the cash flows are reinvested at YTM.
Immunization target rate is the total return on bond i.e., coupon + reinvestment return + capital gain/loss, arising from the horizon price rise/fall.
If the yield curve is upward sloping, the reinvestment rate (return) will be higher, but the horizon price will be lower because of rising interest rates. Fall in Price would be more than the increase in return from higher reinvestment rate
Therefore, when the yield curve is upward sloping, Immunization target rate -total return will be lower than YTM because of stronger price effect(decrease).
Hope this helps.

 

[solarpower03]

tzu Wrote:
——————————————————-
> YTM assumes flat yield curve i.e., all the cash
> flows are reinvested at YTM.
>
> Immunization target rate is the total return on
> bond i.e., coupon + reinvestment return + capital
> gain/loss, arising from the horizon price
> rise/fall.
>
> If the yield curve is upward sloping, the
> reinvestment rate (return) will be higher, but the
> horizon price will be lower because of rising
> interest rates. Fall in Price would be more than
> the increase in return from higher reinvestment
> rate
>
> Therefore, when the yield curve is upward sloping,
> Immunization target rate -total return will be
> lower than YTM because of stronger price
> effect(decrease).
>
> Hope this helps.
Thank you. However, the book says that when the yield curve is upward sloping, then the immunization target return will be less than the YTM because of ‘lower reinvestment return’ (Page 29 book 4- para 4), however you are attributing this to price effect rather than high reinvestment effect.
Many thanks for your suggestion,
Solar

 

[tzu]

The book says that when the yield curve is upward sloping, then the immunization target return will be less than the YTM because of ‘lower reinvestment return’ (Page 29 book 4- para 4), however you are attributing this to price effect rather than high reinvestment effect.
Hi Solar,
The explanation given in the book is a bit confusing and I may be wrong in my interpretation which is based on my understanding of los on total return analysis. I understand the logic given in the text book that the total return would be different from YTM given interest rate forecasts and changes in interest rates. But I was not satisfied with the explanation of YTM being higher than the total return when yield curve is upward sloping. The assumption of price effect being stronger that the reinvestment rate is making sense and helps me to understand this concept but as I mentioned earlier it may not be a good assumption..

 

[manstey]

This is the way I understand it..
The yield curve is upward sloping so in the early years of the bonds life, interest rates are low (lower then YTM). Coupon payments will be reinvested at this lower rate and thus have lower reinvestment return at horizon. Lower reinvestment return results in lower total return (immunization target rate of return). Therefore, the immunization target return is less than the YTM because of ‘lower reinvestment return.’

 

[me.tega]

Manstey got the explanation correctly. Only difference is that the interest rates are high in the early years of the bonds life. When the yield curve is upward sloping and you are at the extreme end of the yield curve, say 20 years, you reinvest coupons at the high rates. As time goes by and portfolio is at 5 years, you reinvest at lower rates compared to initial 20 years (remember yield curve is upward sloping) since you now have a 5 year horizon.
The initial YTM of 20 years is now higher than the rates at which you can reinvest and that leads to a lower immunization rate, with an upward sloping yield curve. It is the other way round for a downward sloping yield curve…

 

[tzu]

Thanks M.tega, your explanation makes sense, but why are you not considering price change which would be caused by increase in interest rates with an upaward slopping yield curve. AM I missing something?

 

[me.tega]

There is a statement in the curriculum that was stressed as the foundation of immunization… I will paraphrase.
When you immunize a portfolio, it is a kind of hedge such that when interest rates fall, the upward price movement of the bonds are counteracted by lower reinvestment rates and when interest rates rise, the downward price movement of the bonds are offset by the higher reinvestment rates. By doing this you are sure of getting your immunized rate, or very close to it.