Page 60 - FINAL CFA SLIDES DECEMBER 2018 DAY 14

LOS 52.h: Define forward rates and calculate
spot rates from forward rates, forward rates Session Unit 14:
from spot rates, and the price of a bond 52. Introduction To Fixed Income Valuation
using forward rates., p.54
The Relationship Between Short-Term Forward Rates and Spot Rates

• Geometrically, borrowing for 3 years at the 3-year spot rate, should be same as borrowing for

one-year periods in 3 successive years:

• (1 + S ) = (1 + S )(1 + 1y1y)(1 + 2y1y). Thus,
3
3
1
S = [(1 + S )(1 + 1y1y)(1 + 2y1y)] 1/3 – 1, which is the geometric mean return!
1
3
tanties
Example: Computing spot rates from forward rates: If the current 1-year spot rate is 2%, the
1-year forward rate one year from today (1y1y) is 3%, and the 1-year forward rate two years
from today (2y1y) is 4%, what is the 3-year spot rate?

st
nd
A $ compounded at 2.997% for 3 years = A $ that compounds at 2% 1 year, 3% 2 year and 4% 4 th
year!