Question

. Spot rates and forward rates:Assume that the current yield curve for zero-coupon bonds (spot rates) is as follows:y1 = 0.5%, y2 = 0.75%, y3 = 1.0%, y4 = 1.25%, y5 = 1.5%a. Plot the spot rates against maturity (yield curve). Is the yield curve upward or downward sloping? Do market participants expect interest rates to increase or decrease in the future? b. What are the implied 1-year forward rates f2, f3, f4, and f5? Are interest rates expected to increase or decrease?Assume that there is no uncertainty about future short rates. This means that future 1 year interest rates will be equal to current forward rates (which you calculated in b.).c. In that situation what will be the spot curve (that is, the yields to maturity on 1, 2, 3, and 4-year zero coupon bonds) in 1 year? d. What is the price of a 5-year coupon bond making annual coupon payments of 2% and a par value of 1000 today? Is the bond trading above or below par? Why?e. What is the price of this bond next year (remember, it is then a 4-year coupon bond)? What is the rate of return on this bond over the next year?

Answer 1

Check the explanation

Step-by-step explanation:

As is observable in the first attached image below, the yield curve is upward sloping. According to the pure expectations hypothesis which states that current short-term interest rates are a reflection of long-term term interest rates, market participants should expect long-term interest rates to rise going forward.

(b) Implied one-year forward rate calculation:

`1+f2 = [(1+y2)^(2)] / (1+y1)`

f2 = 1.0006%

`f3 = [{(1+y3)^(3)} / {(1+y2)^(2)}] - 1`

f3 = 1.502% approximately

`f4 = [{(1+y4)^(4)} / {(1+y3)^(3)}] - 1`

f4 = 2.004% approximately

`f5 =[{(1+y5)^(5)} / {(1+y4)^(4)}] - 1`

f5 = 2.506% approximately.

As implied one-year forward rates are observed to be rising and there is no uncertainty about future spot rates, future interest rates are expected to rise.

(C) Kindly check the second attached image below for the solution to question c

(d) The bond's price would be calculated by summing the Present Values(PVs) of the bond's future cash flows (in the form of annual coupon payments and face value redemption). The discount rate, however, should be the spot rates from the yield curve instead of a single promised yield to maturity.

Let bond price be Pm

Therefore, Pm = 20 / 1.005 + 20 / (1.0075)^(2) + 20 / (1.01)^(3) + 20 / (1.0125)^(4) + 1020 / (1.015)^(5) = $ 1024.872 approximately.

The bond's market value is above its par value, thereby implying that the bond is selling at a premium. This happens whenever the bond's discount rate (or spot interest rates in this case) is below the bond's annual coupon rate.