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What is Bond Yield Curve?


Bond is a debt instrument which an issuer issues to raise capital from public and pay interest to bond holder for fixed period of time. 
Yield Curve: It is curve on graph which shows different interest rate against different time period or maturities time.
Types of Yield Curve: There are three main types of yield curve.
Normal Yield Curve: This curve shows upward movements of interest rate with increase in time period. It indicates the inflation period will happen in future. If the long term debt instruments shows high yield in comparison to short term debt instruments then it is known as Normal Yield Curve.


Inverted Yield Curve: This curve shows downward movements of interest rate with increase in time period. It indicates that there will be recession period will be occurred in near future. When the short term securities show high yield in comparison to long term securities yield then this curve is formed.


Flat Yield Curve or Hump Yield Curve: It is a curve which does not show any ups and downs in a curve. As the name tells it is a straight or flat curve on a graph. This curve formed when long term and short term investments shows no difference in interest rate.


Bond Yield Curve: The curve shows different interest rate of bond or yield on different maturity period of a bond. The graph shows clear picture of different interest rate offered on bonds according to their maturity time.

Yield to Maturity (YTM): If the bond is active till the maturity date then the total return earn by bondholder by issuer is known as yield to maturity.        
Formula of Yield to maturity:
Yield to Maturity (YTM) = (C + (F – P) / N) / (F + P / 2)
Where,
C = Coupon rate in Rupees
F = Face value
P = Current price/ market price
N = number of years
Example: Mr. Sharma has purchased 10 year bond @ of 7% on Rs. 1000 face value. The current market price is Rs. 1160. Find out the yield on maturity.
Solution:
Yield to Maturity (YTM) = (C + (F – P / n)) / (F + P / 2)
= (70 + (1, 000 – 1, 160 / 10)) / (1, 000 + 1, 160) / 2)
= 54 / 1080
= 0.05 or 5%

Example: A bond has 5 maturity periods with different coupon rate. The face value of the bond is Rs. 1, 000 and the current price is Rs.980. Find out the yield to maturity with the help of given information and also draw yield curve.

Time period
Coupon rate
2 year
4%
5 year
5.8%
8 year
6%
15 year
6.5%
20 year
8.2%

Solution:

Time period
Coupon rate
Yield to maturity
= (C + (F – P/ n)) / (F + P / 2)
2 year
4%
= 40 + (1, 000 – 980 / 2)) / (1, 000 +980 / 2)
= 50 / 990
= 5.05%
5 year
5.8%
= 58 + (1, 000 – 980 / 5)) / (1, 000 +980 / 2)
=62 / 990
= 6.26%
8 year
6%
60 + (1, 000 – 980 / 8)) / (1, 000 +980 / 2)
= 62.5 / 990
= 6.31%
15 year
6.5%
= 65 + (1, 000 – 980 / 15)) / (1, 000 +980 / 2)
= 66.33 / 990
= 6.70%
20 year
8.2%
= 82 + (1, 000 – 980 / 20)) / (1, 000 +980 / 2)
= 83 / 990
= 8.38%


In above graph the curve move in upward direction which states that it is positive curve and invested money in a long term bond gives higher yield on maturity.

Example: Prepare yield curve with the help of following information:
Time period
Yield to maturity
4 year
6.3%
6 year
5.8%
8 year
5.6%
10 year
5.2%

Solution:

In above graph curve moves in downward direction which shows negative curve and there will be recession in near future. Invested money in a long term funds is not a good idea.



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