Investment Horizon and Yield Curve

[archived_user]

Per CFAI book
“If the trader does not believe that the yield curve will change its level and shape over an investment horizon, then buying bonds with a maturity longer than the investment horizon would provide a total return greater than the return on a maturity-matching strategy”
Can someone show a this mathematically?
Thanks

 

[archived_user]

This is true for a normal (i.e., upward sloping) yield curve, but not for a flat or inverted yield curve.
You’ll learn more if you do the work than if I do, but I’ll guide you through it.
Suppose that the (annual-pay) par curve, in part, looks like this:

• 1-year par rate: 1%
• 2-year par rate: 2%
• 3-year par rate: 3%

You have a 1-year investment horizon. Consider these two investment approaches:

• Buy a 1-year annual-pay par bond and hold it to maturity
• Buy a 3-year annual-pay par bond, hold it for one year, then sell it

Your job: assuming that the yield curve doesn’t change in the next year, calculate the holding period return for each bond.

 

[archived_user]

I think I can prove it with some general expressions, but are you sure you wanna go that route????

 

[archived_user]

The answers, by the way, are, 1.0000% for the 1-year bond and 4.9416% for the 3-year bond. (And, for whatever it’s worth, it’s 2.9901% for the 2-year bond.)