Why do interest rate changes affect the price of longer term bonds more?

Hello,





I understand the concept that higher interest rates mean lower bond prices and vice versa.





However, what I don't understand is why an interest rate decrease causes the price of long-term bonds to rise at a higher percentage than the rise of short-term bond prices.





Likewise, if interest rates go up, why would the long-term bond prices do down at a higher percentage than short-term bond prices.





Would appreciate anyone's help.





Thanks!|||The current price of a bond is determine by computing its present value using the current interest rate of similar bonds rather than the interest rate at which it was issued. The present value of a bond is the sum of the present value of a future amount (the face value of the bond) and the present value of an annuity (the bond's coupon payments). As the term to maturity increases, the effect of interest rate changes becomes greater. As the present value formulas are exponential functions, the effect increases with time at an increasing rate. The proper term for this effect is interest rate sensitivity.





This should become apparent if you do some sample present value (PV) computations in a spread sheet. You can do it in two steps: PV of a future amount and PV of an annuity.|||The assumption would be that the long term bond would be more valuable because it has more years of the higher interest rate.


i.e. If a 25 year bond is 10% coupon priced at 100 and interest rates are 10%


Now interest rates go down to 5%


In theory your bond and the short bonds should go to 200


But you can see that you have secured 10% for the next 25 years against the current rate of 5%


Of course rates could shoot back to 10% the next day but unlikely.


It wouldn't be the case if rates looked historically low. If rates were 2% you wouldn't want to lock in with a 25 year bond.





I always remember buying an undated PIB (Coventry BB) with a 10.5% coupon at about 拢101% about 10 years ago. It is still paying 10.5% and its price is now about 拢180%|||Interest rate changes affect long term bonds less than short term bonds. However, If interest rates fall then the price of long term bonds rise...the bonds are then said to be trading at a premium. If rates rise the price of bonds fall..the bonds are said to be trading at a discount.|||Look at zero coupon bonds, first. The value of a zero coupon bond is:





P(y) = 100/(1+y/2)^N = 100*(1+y/2)^(-N)





where P(y) is the price, y is the yield and N is the number of half-year periods until you get your cash flow. How much does the price change for a small change in yield? If you know Calculus, you know that you can take the derivative of the Price function %26amp; that will tell you the rate of change.





The derivative of the price function is:





P'(y) = -50*N*(1+y/2)^(N-1) = P(y)*(N/2)/(1+y/2)





Note that bigger values of N will have a greater effect on the change in price.





OK -- that is the math.





Not here is something that might explain the intuition. Suppose you have a million dollars and you put it in the bank today at 5% interest. How much is it worth tomorrow? Just a little over a million, right? How much is it worth in five years? (1MM*1.05^5).





Now -- suppose interest rates go up to 6%. How much is it worth tomorrow? Not much more than when rates were worth 5%. But how much will it be worth in five years? A lot more -- because you are getting more than $10K extra in interest every year.|||you can buy and sell the bonds.so people who buy them will pay what the current interest in the world is...not the interest rate when someone else bought the bond........maybe a couple of years ago...........|||It is based on current situation and futurre expectation.


The deposits, bonds, commercials papers are various competitive avenues for investments and speculations suitable for different categories . Money manages, long and short term investors all go in different directions