# Logic behind inverse relationship between bond rate and interest rate

I've been reading that there is an inverse relationship between fixed-rate bonds and interest rate. The explanation behind the reasoning is that as interest rates move, the bond has to compete with new bonds so the price of the bond syncs up the bond's yield with the current interest rate. I found this doc from sec.gov that has a good explanation: https://www.sec.gov/files/ib_interestraterisk.pdf

In Example 2: If Market Interest Rates Increase by One Percent, the face value of the bond is \$1000 but with an increase interest rate of 1% a year later (to 4%), the bond is only worth \$925. The concept makes sense since the yield to maturity of the bond then matches the new interest rate of 4%.

Why would anyone sell the bond at \$925? Aren't they losing both \$75 that they paid originally for the bond AND the interest payments over the next couple of years on the bond? Since people do sell at a lower price, what am I missing here?

• There are lots of reasons why you sell: you #1 need the money. #2 cut losses, #3 think you can make more money in a different investment. – RonJohn Jan 18 at 17:28
• The price you bought the bond for does not matter - just the future payments - see sunk-cost fallacy – mmmmmm Jan 18 at 17:55
• You already lost the \$75, somehow. If the bond's actual value hadn't lost \$75, then people could make a profit by buying the bonds and then just holding them. They can't, which means the value has somehow gone down by \$75. – user253751 Jan 18 at 17:56

Why would anyone sell the bond at \$925?

Why does anyone sell a stock that's gone down? Or bitcoin? Or gold? Because they think the price could go down even more. Or, because they want to cut their losses or move to some other investment, or (make up some other reason).

So you could sell the bond for \$925 (foregoing future interest payments) and buy another bond that has higher interest payments (adding the \$75 that you lost, of course).

The logical fallacy of holding on to an investment because it's gone down in value is called the sunk cost fallacy. The fact that you've lost money is not going to change just by keeping the investment. The only thing that matters is what you think will happen going forward. If you're happy with the fixed payments, then keep the bond. If you can invest is something that has a higher return (with equivalent risk), then sell your investment and buy something else.

Because you're looking at it from the consumer's perspective, not the investor's

Why would anyone sell the bond at \$925? Aren't they losing both \$75 that they paid originally for the bond AND the interest payments over the next couple of years on the bond?

Because they can lend out the money at a higher rate if they sell the bond and then hand out a loan to a qualified buyer. That buyer then goes and buys something now that it would take them years of bond investments to buy, like a house.

Interest rate -> rate of buy now pay later

bond rate -> rate of pay now buy later