Recall that purchasing a bond is like giving a fixed-interest loan to a company or government. The price of bonds is determined by a variety of factors, including how likely the borrower is to pay you back (i.e. the credit rating), how long you will earn interest on the bond before it is paid back (i.e. time to maturity), how much interest the bond will earn (i.e. the coupon), the amount that will be paid back at maturity (the face value), and any other market forces at play at any given moment. But, all else being equal, interest rates, play the key role in shaping bond prices.

If you had to choose between two similar bonds with different interest rates, you’d take the bond with the higher interest rate, of course.   Take for example, a 10 year bond with a face value of $1,000.

At 5% interest, it will earn you $50 per year.

$1,000 x 0.05 = $50

At 10% interest, it will earn you $100 per year.

$1,000 x 0.10 = $100

Why would anyone buy the bond with the lower interest rate?

People selling bonds try to make them attractive to buyers.  On the secondary market where bonds are re-sold, a seller who is not the original issuer of the bond cannot change the interest rate, maturity date, or the face value of the bond – these things are set only by the issuing institution.  But a re-seller can change the price they are asking for the bond, which may make it worthwhile to a buyer.

To compare the “worthwhileness” of two bond, it’s useful compare their current yields, which is a way of evaluating the return on investment.

current yield = coupon / spot price

In the example above, the 10 year $1,000 bond at 10% has a $100 coupon (the amount paid in interest each year).  This means the current yield (return on investment) is $100 / $1,000, or 10%.

The 5% bond has a current yield of $50 / $1,000, or 5%, which makes it obviously a worse investment.

But if the seller of the 5% bond offers it for only $500 (half its original price), that puts the yield of the 5% bond at $50/$500, or 10%.  This makes it just as good an investment as the 10% bond.

So by dropping the price of the bond, the seller is able to compensate for a less attractive interest rate.

Conversely, a seller who has a bond with a very high interest rate compared to the competition will sell the bond at a higher price than its face value.  Take the example where a seller has a 10 year $1,000 bond at 10%.  Imagine that all the other bonds on the market are only offering 5%.  The yield that the competition are offering is $50 / $1,000 = 5%.  The seller of the 10% bond can offer to sell her bond for $2,000, and she will still be offering an attractive 5% yield, which is in tune with the competition.

yield = $100 / $2,000 = 0.05

She is set to make a $1,000 profit.

And thus interest rates and bond prices are inversely correlated.

QED