Investment Horizon and Yield Curve

CFA Level II
#1

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

#2

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.

#3

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

#4

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.)