Bond Theorems
Posted by Prashant Shah on October 6, 2010
For better understanding of bonds learning bond theorems thoroughly is a must. Here is the list of bond theorems

Price and interest rates move inversely

A decrease in interest rates raises bond prices by more than a corresponding increase in rates lowers the price

Price volatility is inversely related to coupon

Price volatility is directly related to maturity

Price volatility increases at a diminishing rate as maturity increases
Lets understand the theorems with illustrations:
Theorem1 : Price and interest rates move inversely
Lets assume 3 year 10% coupon paying bond for illustration
When YTM = 10%  Price = 100 
When YTM = 11%  Price = 97.55 
When YTM = 9%  Price = 102.53 
Hence it can be concluded that as yield increase price of the bond decline and viceversa.
Theorem2 : A decrease in interest rates raises bond prices by more than a corresponding increase in rates lowers price
Lets assume 3 year 10% coupon paying bond for illustration
When YTM = 10%  Price = 100  
When YTM = 11%  Price = 97.55  Change in price = 2.45% 
When YTM = 9%  Price = 102.53  Change in price = +2.53% 
This the most important theorem of bond which says that price movement of bond with change is interest rate either side is not equal. Price of the bond increases more than it declines when equal change in interest rate is given. In above illustration you can clearly see that when yield declines by 1% price increases by 2.53% while in case of increase in yield by 1%, price decline is 2.45%. As price curve of the bond is convex, you gain more than you lose.
Theorem3 : Price volatility is inversely related to coupon
Lets assume 3 year 10% coupon paying bond and 3 year 11% coupon paying bond for illustration.
3 year 10% coupon paying bond
When YTM = 10%  Price = 100  
When YTM = 11%  Price = 97.55  Change in price = 2.45% 
When YTM = 9%  Price = 102.53  Change in price = +2.53% 
3 year 11% coupon paying bond
When YTM = 10%  Price = 102.48  
When YTM = 11%  Price = 100  Change in price = 2.42% 
When YTM = 9%  Price = 105.06  Change in price = +2.52% 
Lets assume current YTM is 10% and then it increases to 11% and declines to 9%. You can clearly see in the above tables that price movement of the 11% coupon bond is lower than 10% coupon bond. It can be concluded that higher coupon bonds are less volatile than smaller coupon bonds.
To be continued…
Rizwan Mohd said
Introduction was an aowsem undastand very easyly to the student of MBA investment management subject very easy to understand
Manish said
Dear prashant sir practically why higher coupon bonds are less volatile than smaller coupon bonds though i saw this in the above theorems but still i want to know more abt it? and one thing i want to know from you that longer maturity bond tend to be more volatile than shorter duration bond but i think we can earn more by taking the advantage of price volatilty bcoz in the long term when interest rate increases price decreases but at the same time coupon payments are re invested at higher rates on the other hand if interest rates falls price increases which we can sell it in the secondary market by adding premium to it.
am i right? and anything more which would u like to add in it?
Lokesh Kash said
Where can I find continued part?
Prashant Shah said
Dear Lokesh,
Thanks for the interest. I publish the remaining part as early as possible.
Regards,
Prashant V Shah
Supraja Geetha sri said
Hii sir ,can u provide me a case studies also on bond pricing theorems .
Prashant Shah said
Hello.
Please let me know for which curriculum you want it?
Regards.