Question

The current yield curve for default-free zero-coupon bonds is as follows: Maturity (Years) Yтм (4) s.50 1 6.5 7.5 3 005345 a. What are the impliled 1-year forward rates? (Do not round Intermediate calculations. Round your answers to 2 decimal places.) Maturity Forward Rate 2 уваrs % % 3 years b. Assume that the pure expectations hypothesis of the term structure is correct. If market expectations are accurate, what will be the yield to maturity on 1-year zero-coupon bonds next year? O Shift upward O Shift downward c. Assume that the nure evnectatione h at n 00

Answer 1

(a) We can use the expectation theory to answer the question. According to this theory, the interest rate on long-term bond is the geometric average of the interest rate on short-term bonds. Applying this theory, we have:

Maturity - 2 years

(1+2-year bond yield)²=(1+1-year bond yield)∗(1+1-year forward in one year)

(1+6.5%)²=(1+5.5%)∗(1+1-year forward in one year)

1-year forward in one year = 7.51%

Applying the theory again, we have:

Maturity 3 years

(1+3-year bond yield)³=(1+2-year bond yield)²∗(1+1-year forward in two years)

(1+7.5%)³=(1+6.5%)²∗(1+1-year forward in two years)

1-year forward in two years = 9.53%

(b) Shift Upward

According to expectation theory future short term interest rates can be forecasted with the help of long term interest rates. It is also known as Pure Expectations Theory.
This theory suggests that an investor will earn same amount of interest if invests his money in one-year bond in current year and then in another one-year bond next year as compared to investing in a single two-year bond in the current year.

The single reason due to which long-term yields are higher than the short-term yields which may result in Yield curve being upward, the investor wants to economic growth and based on their forecasted inflation they prefer long term securities over short term securities.
Therefore yield curve of YTM on a 1-year zero coupon bond will shift upward if pure expectation hypothesis is correct.