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Investment Horizon and Yield Curve

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

"Using Wiley for my CFA journey was by far the best option… I was able to pass on my first attempt.”– Moe E., Canada

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.

Simplify the complicated side; don't complify the simplicated side.

Financial Exam Help 123: The place to get help for the CFA® exams
http://financialexamhelp123.com/

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

“Mmmmmm, something…” - H. Simpson

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.)

Simplify the complicated side; don't complify the simplicated side.

Financial Exam Help 123: The place to get help for the CFA® exams
http://financialexamhelp123.com/