Spot and Forward Rate
Spot Rate and Forward Rate
Spot Rate:
It is nothing more than the YTM on bond. It is the rate of interest on bond maturing at any time in the future.
It is also known as geometric average of 1 year forward rates in the future.
Hence, YTM on bonds can be calculated as:
When forward rates are given then; oS1 = oF1 oS2 = [(1+of1)(1+1F2)](1/2) -1 oS3 = [(1+of1)(1+1F2)(1+2F3)](1/3) -1 and so on.
Forward Rates:
It is the interest rate established today , that will be paid on money to be borrowed at some specific date in the future, and to be repaid at a specific but even more distant date in the future.. Forward rate is the interest that links the current spot rate over holding period to the current spot rate over a longer holding period. In particular, it is written as ‘ tFt+n’.
Based on the spot Rates of bonds, we do calculate the forward rates as:
tFt+n = { [(1+oSt+n)t+n/(1+oSt)t]1/n} – 1
Where,
T= time when the bond will be issued.
N= maturity period of the bond.
PROBLEMS
Q.1 Assume 4- year bonds are currently yielding 7 percent and 3 – years bonds are yielding 6 percent. What is the implied yield for 1-year bonds starting 3 years from now ? Show your work.
Q.2 Use the following data:
Bond Maturity, years YTM
W
X
Y
Z 1
2
3
4 8.0%
9.0
10.5
12.0
Calculate the implied 1- year forward rate starting in year 2. Calculate the implied 1-year forward rate starting in year 3. Calculate the implied rate for a 3- year bond starting in year 2.
Q.3 If a 15-year T-bond is yielding YTM =12% and a 5- year T- bond is yielding YTM =8%,what is the expected return on a 10 – year bond starting at the end of Year 5 ?
Bond’s Duration
The formula use to calculate the bonds basic duration is the Macaulay duration, which was created by Fredrick Macaulay in 1938.it, has been commonly used since 1960s. It is also known as Macaulay’s duration. Bond duration is the average amount of time required by the security to receive the interest
Spot Rate:
It is nothing more than the YTM on bond. It is the rate of interest on bond maturing at any time in the future.
It is also known as geometric average of 1 year forward rates in the future.
Hence, YTM on bonds can be calculated as:
When forward rates are given then; oS1 = oF1 oS2 = [(1+of1)(1+1F2)](1/2) -1 oS3 = [(1+of1)(1+1F2)(1+2F3)](1/3) -1 and so on.
Forward Rates:
It is the interest rate established today , that will be paid on money to be borrowed at some specific date in the future, and to be repaid at a specific but even more distant date in the future.. Forward rate is the interest that links the current spot rate over holding period to the current spot rate over a longer holding period. In particular, it is written as ‘ tFt+n’.
Based on the spot Rates of bonds, we do calculate the forward rates as:
tFt+n = { [(1+oSt+n)t+n/(1+oSt)t]1/n} – 1
Where,
T= time when the bond will be issued.
N= maturity period of the bond.
PROBLEMS
Q.1 Assume 4- year bonds are currently yielding 7 percent and 3 – years bonds are yielding 6 percent. What is the implied yield for 1-year bonds starting 3 years from now ? Show your work.
Q.2 Use the following data:
Bond Maturity, years YTM
W
X
Y
Z 1
2
3
4 8.0%
9.0
10.5
12.0
Calculate the implied 1- year forward rate starting in year 2. Calculate the implied 1-year forward rate starting in year 3. Calculate the implied rate for a 3- year bond starting in year 2.
Q.3 If a 15-year T-bond is yielding YTM =12% and a 5- year T- bond is yielding YTM =8%,what is the expected return on a 10 – year bond starting at the end of Year 5 ?
Bond’s Duration
The formula use to calculate the bonds basic duration is the Macaulay duration, which was created by Fredrick Macaulay in 1938.it, has been commonly used since 1960s. It is also known as Macaulay’s duration. Bond duration is the average amount of time required by the security to receive the interest