This question illustrates the upward sloping yield under the pure expectations theory. Consider the followings:The current yield for 1-year bond is 7.5% p.a., compounded annually.The current yield for 2-year bond is 8.7% p.a., compounded annually.The current yield for 3-year bond is 10.5% p.a., compounded annually.Based on the information above, what is the 1-year forward rate between year 2 and year 3?9.91%14.19%12.03%None of the above.
Question
This question illustrates the upward sloping yield under the pure expectations theory. Consider the followings:The current yield for 1-year bond is 7.5% p.a., compounded annually.The current yield for 2-year bond is 8.7% p.a., compounded annually.The current yield for 3-year bond is 10.5% p.a., compounded annually.Based on the information above, what is the 1-year forward rate between year 2 and year 3?9.91%14.19%12.03%None of the above.
Solution 1
The pure expectations theory suggests that the yield of a longer-term bond should be the geometric mean of the yields of shorter-term bonds.
In this case, we are asked to find the 1-year forward rate between year 2 and year 3. This is the rate that is implied by the current yields of the 2-year and 3-year bonds.
The formula to calculate the 1-year forward rate is:
(1 + yield of 3-year bond)^3 / (1 + yield of 2-year bond)^2 - 1
Step 1: Convert the yields to decimal form The yield of the 2-year bond is 8.7% p.a., or 0.087 in decimal form. The yield of the 3-year bond is 10.5% p.a., or 0.105 in decimal form.
Step 2: Substitute the yields into the formula The 1-year forward rate is (1 + 0.105)^3 / (1 + 0.087)^2 - 1.
Step 3: Calculate the 1-year forward rate The 1-year forward rate is (1.105)^3 / (1.087)^2 - 1 = 0.1491, or 14.91%.
Therefore, the 1-year forward rate between year 2 and year 3 is 14.91%. The closest answer is B. 14.19%, but this is not exactly correct. So, the answer is D. None of the above.
Solution 2
The pure expectations theory suggests that the yield of a longer-term bond should be the geometric mean of the yields of shorter-term bonds.
In this case, we are asked to find the 1-year forward rate between year 2 and year 3. This is the rate that is implied by the current yields of the 2-year and 3-year bonds.
The formula to calculate the 1-year forward rate is:
(1 + y3)^3 = (1 + y2)^2 * (1 + f)
where: y3 is the yield of the 3-year bond, y2 is the yield of the 2-year bond, and f is the 1-year forward rate between year 2 and year 3.
Substituting the given yields into the formula, we get:
(1 + 0.105)^3 = (1 + 0.087)^2 * (1 + f)
Solving for f, we get:
f = ((1 + 0.105)^3 / (1 + 0.087)^2) - 1 = 0.1403 or 14.03%
Therefore, the 1-year forward rate between year 2 and year 3 is 14.03%. The closest answer is B. 14.19%.
Similar Questions
Suppose the current yield on 1-year bonds is 5% and the current yield on 2-year bonds is 4%. By approximation, calculate the expected yield on a 1-year bond in a year’s time. What does this information tell us about the slope of the yield curve and the financial market’s opinion about the direction of monetary policy?
If the expected path of 1-year interest rates over the next four years is 5 percent, 4 percent,2 percent, and 1 percent, then the expectations theory predicts that today's interest rate on thefour-year bond isA) 1 percent.B) 2 percent.C) 3 percent.D) 4 percent
The forward rate is:1 pointThe expected rate (yield) on a bond several months or years from now.The (inflation-adjusted) rate on a bond.Equal to the yield to maturity of the bond.Equal to the nominal rate of the bond.
11) If bonds with different maturities are perfect substitutes, then the ________ on these bonds must be equal.A) expected returnB) surprise returnC) surplus returnD) excess return12) If the expected path of one-year interest rates over the next five years is 4 percent, 5 percent, 7 percent, 8 percent, and 6 percent, then the expectations theory predicts that today's interest rate on the five-year bond isA) 4 percent.B) 5 percent.C) 6 percent.D) 7 percent.13) If the expected path of 1-year interest rates over the next four years is 5 percent, 4 percent, 2 percent, and 1 percent, then the expectations theory predicts that today's interest rate on the four-year bond isA) 1 percent.B) 2 percent.C) 3 percent.D) 4 percent.14) If the expected path of 1-year interest rates over the next five years is 1 percent, 2 percent, 3 percent, 4 percent, and 5 percent, the expectations theory predicts that the bond with the highest interest rate today is the one with a maturity ofA) two years.B) three years.C) four years.D) five years.15) If the expected path of 1-year interest rates over the next five years is 2 percent, 4 percent, 1 percent, 4 percent, and 3 percent, the expectations theory predicts that the bond with the lowest interest rate today is the one with a maturity ofA) one year.B) two years.C) three years.D) four years.16) Over the next three years, the expected path of 1-year interest rates is 4, 1, and 1 percent. The expectations theory of the term structure predicts that the current interest rate on 3-year bond isA) 1 percent.B) 2 percent.C) 3 percent.D) 4 percent.17) According to the expectations theory of the term structureA) the interest rate on long-term bonds will exceed the average of short-term interest rates that people expect to occur over the life of the long-term bonds, because of their preference for short-term securities.B) interest rates on bonds of different maturities move together over time.C) buyers of bonds prefer short-term to long-term bonds.D) buyers require an additional incentive to hold long-term bonds.18) According to the expectations theory of the term structureA) when the yield curve is steeply upward sloping, short-term interest rates are expected to remain relatively stable in the future.B) when the yield curve is downward sloping, short-term interest rates are expected to remain relatively stable in the future.C) investors have strong preferences for short-term relative to long-term bonds, explaining why yield curves typically slope upward.D) yield curves should be equally likely to slope downward as slope upward.19) According to the segmented markets theory of the term structureA) bonds of one maturity are close substitutes for bonds of other maturities, therefore, interest rates on bonds of different maturities move together over time.B) the interest rate for each maturity bond is determined by supply and demand for that maturity bond.C) investors' strong preferences for short-term relative to long-term bonds explains why yield curves typically slope downward.D) because of the positive term premium, the yield curve will not be observed to be downward-sloping.20) According to the segmented markets theory of the term structureA) the interest rate on long-term bonds will equal an average of short-term interest rates that people expect to occur over the life of the long-term bonds.B) buyers of bonds do not prefer bonds of one maturity over another.C) interest rates on bonds of different maturities do not move together over time.D
Assume the current yield curve shows that the spot rates for six months, one year, and one and a half years are 1%, 1.1% and 1.3%, respectively, all quoted as semi-annually compounded APRs. What is the price of a $1000 par, 4.75% coupon bond maturing in one and a half years (the next coupon is exactly six months from now)?
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