When yield falls, the price of bond will rise at lower rate or Higher rate or same rate ? What is the reason for your answer ? If possible please provide example.
Greetings friend! To use simple numbers:
Current yield = (annual coupon amount)/(bond price)
and
Bond price = (annual coupon amount)/(current yield)
So if current yield is 10%, it means the coupon is $100 and the bond price is $1000 for example.
If yield then decreases by 10% (from 10% to 9% in this case), it means that the bond price = ($100)/(0.09) = $1,111.11
The bond price has therefore increased by 11.1% when the bond yield decreased by 10%.
Cheers!
Draw a graph in Excel. It should be pretty easy and will give you a lot more insight than a few words from any of us.
Thank you Greybeard and S2000magician for your replies.
My pleasure.
I hope that you drew a graph and that it helped.
I understood why the relationship between YTM rate movement and Bond price movement is not linear. I do not know how to draw the graph in excel to depict this relationship.
Can you please tell me why for finding the bond price we discount the coupon interest amount to present value using market interest rate ?
Thanks
If someone wants to sell a bond that has a 10% coupon, but the market can easily buy bonds with otherwise similar characteristics bearing a 12% coupon or yield, the 10% coupon bonds would need to be priced at some discount otherwise folks wouldn’t want to buy them.
Thank you.
From the example you have given, it is clear that the rate of decrease in market rate and rate of appreciation in price of bond are not always same.
I am unable to understand why it is so. What exactly is happening mathematically that is making the rates unequal.
Would it be possible to explain this as simply as possible?
I will defer to S2000magician and other math experts for the best explanation.
In my simplistic non-expert view, this is a feature of math where the numerator and denominator are changing at different magnitudes (rates of change) when the answer of the fraction stays constant. When you change either the numerator or the denominator by some percent of change, keeping the final answer constant, the remaining denominator/numerator that you’re solving for will change at a different rate of change generally. You can play around with numbers on your calculator for example.
For instance on a not entirely related note, but it helps me in my thinking about it, if your porfolio generates a negative 50% return (it dropped 50% in value), then to get back to where you were originally before it dropped there, you would need a 100% gain in the current (lower) portfolio not a 50% gain.
Thank you
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