One year ago i invested 300,000 in three bonds. the bonds are 3,5 and 10 year respectively withyields of 4.6%, 5% and 5.3%. interest rates have gone up since the bonds were bought.i need to get rid of some of these bonds. which one should i sell? i don't want the answer ... my question is: do i need to know the coupons to do this calculation? is it true that i can only calculatethe coupon if the quoted yields are at purchase date?

100000 was invested in each bond, by the way - ie. i know the purchase price.

Why would you like to calculate the coupon? Is it a math exercise? Coupon is part of the contract agreed.However, purchase date is at issuance?The key is the relation with par. Was it a discount, or premium? There is the relation between the prevailing rate and the one in the coupon.

Here is my take. If future interest rates are expected to go down, sell the bond with the highest sensitivity. If rates will go up, then sell bond with lowest sensitivity.Lower the coupon, higher the sensitivityLonger the maturity, higher the sensitivity

The coupon isn't stated but i think the effect of the coupon is far outweighed by the price volatility in the longer term to maturity, isn't it?If interest rates rise, prices go down - for longer term bonds prices go down *more* everything else being equal - don't they?

QuoteOriginally posted by: brownie74The coupon isn't stated but i think the effect of the coupon is far outweighed by the price volatility in the longer term to maturity, isn't it?If interest rates rise, prices go down - for longer term bonds prices go down *more* everything else being equal - don't they?I am not sure which factor is dominant. (Coupon v/s maturity). But you can create an excel sheet (with both coupon and maturity different for the two bonds) and then change the interest rates and then calculate the price difference magnitude. I have an excel sheet which does this precisely. I can mail it to you, if you wish to have a look at it.

QuoteOriginally posted by: brownie74The coupon isn't stated but i think the effect of the coupon is far outweighed by the price volatility in the longer term to maturity, isn't it?If interest rates rise, prices go down - for longer term bonds prices go down *more* everything else being equal - don't they?u need to know duration and convexity. maturity isn't enough. u can come up with weird schedule where duration of 5y bond will be greater than of 10y

I don't think you need to know the coupon rate if the yields you list are the yields to maturity (r). Assuming that and assuming there is no default risk, you know for sure the FV of the bond at maturity = 100,000 (1+r)^T, where T = 3, 5 or 10. Today the value of the bond is 100,000 (1+r)^T / (1+R)^{T-1}, where R is the market rate. Now, let's say R jumped yesterday to R' = R + dR. Your loss is 100,000 (1+r)^T [ 1/ (1+R)^{T-1} - 1 / (1+R')^{T-1} ] which is approximately 100,000 (T-1) dR [ (1+r)/(1+R)]^T. To quantify this you need to know whether dR is independent of T.However, you already lost money, your bond is already giving the adjusted market rate if you think about it. You should really act on what you expect the rate to do in the future, not on what happened yesterday.

QuoteOriginally posted by: fizikI don't think you need to know the coupon rate if the yields you list are the yields to maturity (r). Assuming that and assuming there is no default risk, you know for sure the FV of the bond at maturity = 100,000 (1+r)^Twhy do u think it's a zero?

the longer the term to maturity, the more cash flows you have to discount to work out PV - since interest rate is rising, the discounting is worse for long term bonds. short term to maturity will have less cash flows to discount by this increasing yield - so the impact is lesswithout knowing the coupons, you cannot say for sure if the impact of the coupons will be big enough to outweigh the term to maturity. however, this is unlikely i would have thought (?). if it was the case that the short term bond had a huge coupon and the long term one a low coupon - why would you initially buy into that given the risk is higher for long term bonds?apologies for my "childish" reasoning!

brownie74,how was the question originally formulated? Why do you need to get rid of a bond, to do what? Reinvesting the money back in bonds makes no sense as I view it, you will only be worse off if you want the same expiration. Do you have any expectations of the future, will the rates continue to rise, stop, or will they drop?

Quotewhy do u think it's a zero?I do not think that the coupon rate is zero. I assume that the coupons can be reinvested at the original rate, which is a flawed but standard assumption when simple bond questions are asked. brownie74 asked a question which is not simple. The honest answer to it is "it depends", and it depends on many things...

QuoteOriginally posted by: fizikQuotewhy do u think it's a zero?I do not think that the coupon rate is zero. I assume that the coupons can be reinvested at the original rateeven in that case the formula FV*(1+r)^T is only for zeros.

Quoteeven in that case the formula is only for zeros.Any arguments, like, at all?Here is a simple example. You buy a bond at par = $100 and it pays an yearly coupon c ( > 0, mind you!). What is the effective rate r and how is it related to the FV assuming that you reinvest all the coupons at the same rate r?

QuoteOriginally posted by: fizikQuoteeven in that case the formula is only for zeros.Any arguments, like, at all?Here is a simple example. You buy a bond at par = $100 and it pays an yearly coupon c ( > 0, mind you!). What is the effective rate r and how is it related to the FV assuming that you reinvest all the coupons at the same rate r?effective rate is simply YTM of your coupons, FV and current value of a bond. u r making a strong assumption that reinvest at the same rate. that's not what he wants, because he mentioned specifically that rates went up.anyways, if u fix the reinvestment rates, then that's your effective rate, by definition. u dont need effectove rate at all, it's like par bond in this case. u need effective rate when yields r not the same as coupons, i.e. cashflow's discounted at different rate than its stated interest.