# Fixed Income - Interest Rate risk

Can someone please explain the statement below. This is related to risks associated with Investing in Bonds. When interest rates rise, bond values fall. I am new to finance and am studying Fixed Income for Dec 08 Level 1. Thanks, Preeti

my suggestion to you is to go to the cfai books if you need some basic understanding. that is a really basic concept and the book will explain it.

THis is a VERY critical concept that you need to understand 100% I’ll try to expalin with an example. If I issue a bond for \$1000 and the coupon rate is 7% and the interest rate is 7%, than you’ll pay 1000 for the bond because coupon rate is the same as market. Now lets say I have a \$1,000 bond and the coupon rate is 6% but the market interest rate is 7%. This means if you buy my bond, you’ll make less money in interest than if you were to buy a bond in the open market. Therefore, I would sell my bond to you at a discount to compensate. THe same goes for the opposite, if my coupon rate is higher than the market interest rate, you would be willing to pay more for my bond because you make more in interest. Thus, bond price and interest rates are inversely related. Make sure you understand this. If interest rates go down, bond prices go up and vice versa.

Hi preeti, I’ll attempt to clarify this for you. First of all, understand that there are two interest rates involved here. 1/ Coupon Rate - is the interest which you get on the bond… say \$ 100 bond with a 6 % coupon rate - this means you will get 100 * 6% = \$6 annually. ( Bear in mind, mostly U.S Bonds pay semi-annual interest) 2/ The other one is the interest rate prevailing in the market. Say if you invest in an asset with a similar risk to that of the bond you will receive 8 % So, you’ll be interested in investing in the investment which gives you greater interest. Isn’t it? Thus, in the above scenario, you’ll be willing to invest in the other asset with similar risk which pays 8% instead of the bond which pays you only 6%. in the above case, eventhough the interest is 6% and you earn \$6 per annum, your expectation will be only 8% and you’ll pay for the bond only \$75 for the bond instead of \$100. Work through this - \$6 /75 = 8 % which is equivalent to the market rate. Thus when the market rate is more than the coupon rate offered on bond, you’ll be willing to pay less for the bond, so that you can earn the same amount of interest for a similar risky asset. Hope this helps and not confuses…

Thanks a lot guys! This helps! I just booked for the exam and am still waiting for the CFAI material. Scheweser material is really concise!

when interest rates go up your future cash flows from the bond are discounted at a higher rate, so their future value is worth less

this is the way it finally made intuitive sense to me. i buy a 10 year bond at 5%. a year later i have a 9 year bond paying 5%. 9 year rates have gone up to 6%. why would someone buy my 9 year bond paying 5% at 100 when they can get a 6% bond at 100. the only way i can entice someone to buy my bond at 5% would be to charge them less that 100. therefore interest rates up, prices down

oops my post is supposed to say “so their present value is worth less”

r u frm science background?? r u frm satyam>?? cheers abhi

I think guys are right here in explaining thru figures. However I will try to explain it analytically first and then with formula. As mentioned bond has two interest rates associated with itself - one is Coupon Rate and other is Interest Rate. Lets keep it simplest with Fixed Coupon. Now you have these coupon flows pretty much constant throughout the life of bond, however the market interest rates keep changing. Suppose the market interest rates are higher than the coupon rate, in which case a rational investor would like to earn market interest rate (higher return) and hence he would be interested in paying less for the bond paying less coupon (to experience higher yield). So if Interest Rate further moves north, the bond price will move south. Conversly, if Interest Rate moves down (say lesser than coupon rate) then this bond would be considered better (due to higher coupon payments) and hence investor would be ready to pay higher price, hence price moves up. This logic is very well explained by formula to calculate bond price: Bond Price = (CP1/(1+i) + (CP2/(1+i)^2) + … + (CPn/(1+i)^n) + (FV/(1+i)^n) where i = Interest Rate, CPn = nth Coupon, FV = Maturity Value of bond So when i increases, bond price decreases and vice-versa. I hope this explains better.