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Let's say I have 10yrs ZCB with a yield of 3% I hold the bond for one year what will be the price for my bond if I want to sell it ? thank you for the help.

  • That depends on the prevailing interest rates at the time of sale. – saulspatz Jun 04 '19 at 13:41
  • after one year let's say the 10years yield are at 2,90% and the 9years yield is at 2,7% would this help. –  Jun 04 '19 at 13:43
  • I don't understand what you are saying. I thought the $10$-year bond yields $3%$. What is this $2.9%$? I also don't understand the second sentence. The price of the bond (before commissions or other costs of sale) is the present value of the principal in $9$ years, calculated at prevailing interest rates. – saulspatz Jun 04 '19 at 13:46
  • what do you mean by prevailing interest rates ? is it the 9 years yield ? –  Jun 04 '19 at 13:49
  • The prevailing interest rate is the rate at which the market is pricing similar bonds at the moment. I have already said I don't understand what you mean the "$9$ years yield." If it is the rate used to price $9$-year zero-coupon bonds of similar creditworthiness one year after the purchase of the original bond, then yes it it is. That's a lot to read into the phrase "$9$ years yield" though. – saulspatz Jun 04 '19 at 13:53
  • Sorry, I'll be more clear about it : after one year let's say the 10 years yield of ZCB is 2,90% and the 9 years yield Zero coupon bond is 2,7%, If I want to sell the ZC Bond I bought at 3% yield after one year, my bond will it be worth 100/(1+2,7%)^9 ? –  Jun 04 '19 at 14:04
  • Yes, that's right. – saulspatz Jun 04 '19 at 14:05
  • Thank you for the help :) –  Jun 04 '19 at 14:10
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1 Answers1

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The price is whatever the market will pay for it. If the value at maturity is $1000$, the original price $P$ should have had $P\cdot 1.03^{10}=1000$ or $P \approx 744.04$. After one year at $3\%$ it would nominally be worth $1.03$ times as much or $766.42$. If interest rates have risen in the meantime, say to $4\%$ the new value $V$ would have $V\cdot 1.04^9=1000$ for $V\approx 702.59$. If interest rates have fallen it will be worth more.

Ross Millikan
  • 374,822
  • 4% are the yield of 9 years bond right ? –  Jun 04 '19 at 14:10
  • That is right. We derive the price by assuming the prevailing interest rate, just as I did for the original price of the bond. Of course, the market may believe that interest rates will rise further and not be willing to pay even this much. – Ross Millikan Jun 04 '19 at 14:11
  • Thank you for your help –  Jun 04 '19 at 14:13