Question

Assume that as of today, the annualized interest rate for a seven-year bond is 10 percent, while the annualized interest rate for a three-year bond is 7 percent. Use only this information to estimate the annualized interest rate for a four-year bond expected in three years. Use the geometric average method.

Answer 1

As per geometric mean return formula the holding period return is the total return over multiple periods. Hence seven-year investment rate comprises of three-year investment rate and future extended four-year rate of return.

(1+r7)7 = (1+r3)3 x (1+r4)4

(1+ 0.1)7 = [(1+ 0.07)3 x (1+r4)4]

(1.1)7 = [(1.07)3 x (1+r4)4]

1.9487171 = 1.225043 x (1+r4)4

1.9487171/ 1.225043 = (1+r4)4

(1+r4)4 = 1.5907336313909

1+r4 = 4 √1.5907336313909

        = 1.12305070745382

r4 = 1.12305070745382 – 1 = 0. 12305070745382 or 12.31 %

Annualized interest rate for a four-year bond expected in three years is 12.31 %