Question

You note the following yield curve in The Wall Street Journal. According to the unbiased expectations theory, what is the one-year forward rate for the period beginning two years from today, 3f1? (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16)) Maturity Yield One day 1.58 % One year 2.10 Two years 2.34 Three years 2.45

Answer 1

2.58%

Step-by-step explanation:

Mathematically, the relationship between the different interest rates using the equation is shown below:

(1+S2)^2=(1+S1)^1*(1+2y1y)

The spot rate in year 2 is the same as the spot rate in year 1 multiplied by the 1-year forward rate beginning in year 2.

S2=2-year rate =2.34%

S1=1-year rate =2.10%

2y1y=one-year interest rate 2 years from now=the unknown

(1+2.34%)^2=(1+2.10%)^1*(1+2y1y)

(1+2y1y)=(1+2.34%)^2/(1+2.10%)^1

2y1y)=(((1+2.34%)^2/(1+2.10%)^1)-1

2y1y=1.025805642-1

2y1y= 2.58%

The formula shows that borrowing or lending for 2 years at 2.34% is the same as borrowing or lending at 2.10% in year and 2.58% forward rate in year 2