CFA CFA Level 1 Fixed income ( Two spot rates and the Implied forward rates)

# Fixed income ( Two spot rates and the Implied forward rates)

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• 11

Can someone pls tell me how to solve for the relationship between the two spot rates and the implied forward rate in the official CFA text page 443 equation 14?? Am stocked!!. Thanks 🙁

• 4

The formulae is not actually right….. I cld not key in the other factors. I hope you can make sense out of this. Thanks

• 2

Hi @Tgirl – would you mind detailing the question itself here to share with the community? Not all of us have up to date text books, especially the charterholders 🙂

• 2

“Implied forward rates (also known as forward yields) are calculated from spot rates. An implied forward rate is a break-even reinvestment rate. It links the return on an investment in a shorter-term zero-coupon bond to the return on an investment in a longer-term zero-coupon bond. Suppose that the shorter-term bond matures in A periods and the longer-term bond matures in B periods. The yields-to-maturity per period on these bonds are denoted zA and zB. The first is an A-period zero-coupon bond trading in the cash market. The second is a B-period zero-coupon cash market bond. The implied forward rate between period A and period B is denoted IFRA,B–A. It is a forward rate on a security that starts in period A and ends in period B. Its tenor is B – A periods.
Equation 14 is a general formula for the relationship between the two spot rates and the implied forward rate.
A B−A B (1+zA) ×(1+IFRA,B−A) =(1+zB)

Suppose that the yields-to-maturity on three-year and four-year zero-coupon bonds are 3.65% and 4.18%, respectively, stated on a semiannual bond basis. An analyst would like to know the “3y1y” implied forward rate, which is the implied one-year forward yield three years into the future. Therefore, A = 6 (periods), B = 8 (periods), B – A = 2 (periods), z6 = 0.0365/2 (per period), and z8 = 0.0418/2 (per period).

Institute, CFA. CFA Institute Level I 2014 Volume 5 Equity and Fixed Income. John Wiley & Sons P&T, 2013-07-12. VitalBook file.

The citation provided is a guideline. Please check each citation for accuracy before use.
(Institute 433)