Question

Suppose the zero rate for a 1-year investment is 0.062, the zero rate for a 2-year investment is 0.072, and the zero rate for a 3-year investment is 0.082 (all rates are continuously compounded). What is the forward rate for the 3^rd year?

Answer 1

ForwatdRate for 3rd Year = [ [ (1 + YTM 3 ) ^ 3 / ( 1 + YTM 2 ) ^ 2 ] ^ ( 1 / 1 ) ] - 1
= [ [ ( 1 + 0.082 ) ^ 3 / ( 1 + 0.072 ) ^ 2 ] ^ ( 1 / 1 ) ] - 1
= [ [ ( 1.082 ) ^ 3 / ( 1.072 ) ^ 2 ] ^ ( 1 / 1 ) ] - 1
= [ [ 1.2667 / 1.1492 ] ^ ( 1 / 1 ) ] - 1
= [ [ 1.1023 ] ^ ( 1 / 1 ) ] - 1
= [ 1.1023 ] - 1
= 0.1023
= I.e 10.23 %

YTM3 - Zero Rate for 3 Year Investment

YTM2 - Zero Rate for 2 Year Investment