Why Do Bond Yields Rise When Market Rate Interest Goes Up, Also What Does This Have to Do With the Coupon?

Interest rates go up —> Bond prices fall
Interest rates go down —> Bond prices rise

As long as the bond's issuer remains stable, the bond gives the investor a guarantee that the issuer will make the interest (or coupon) payments at certain intervals and will then pay back the original sum of money lent (the principal) at a specified date (the maturity date). It is because of this that most investors assume high-quality bonds have no risk.

The problem occurs if you wish to sell your bond before it matures, on the secondary market. If interest rates have risen since you bought your bond, newly issued bonds will be sold with higher coupon payments than what your bond pays. As a result, no other investor will buy your bond at the par price. They can, instead, purchase a newly issued bond at par price, but one that pays higher interest. So, in order to make your bond competitive, you would have to sell it at a discount. The discount necessary would be the price at which your old bond yields the same interest to the new investor as the newly issued bonds would. Remember that bonds are only issued and redeemed at par. What happens in between is based on free market forces.

Here’s an example. Let's say that you bought a 10-year Treasury bond on the day of its issue, at $1000 par. It was issued with a 5% coupon rate, meaning that it pays $50 per year in interest. A year later, you decide to sell. So you decide to sell your bond on the secondary market to get your money back. But the Fed has raised interest rates. Now, 10-year Treasury bonds are being issued with a 7% coupon rate. These new bonds are sold at $1000 par and pay $70 per year in interest. You cannot simply sell your bond at its par price of $1000 because no rational person would buy it from you at that price. They would buy the new bonds instead. In order to sell your bond, you would have to lower its price to around $714. Your bond still pays $50 per year in interest, as is stipulated in the bond's contract. But now, the new owner buys it for $714 and receives $50 per year in interest, which calculates to a 7% interest rate (50 divided by 714 = 0.07), the same as newly-issued Treasuries.

The actual coupon payment has not changed. Rather, the ratio of that coupon payment to the price has changed. In a secondary market where people can choose to sell their bonds before maturity, prices of outstanding bonds will fluctuate based on prevailing interest rates. This is because current interest rates influence newly-issued bond coupon rates, which compete with outstanding bonds. The outstanding bonds still pay the same coupons and are redeemed at the same par amount on the maturity date, but their selling prices will fluctuate while outstanding.

As things look now, the Fed is not going to be lowering interest rates any time soon. If anything, investors are worried about the Fed raising interest rates some more. So, the best way to get face value for your specific bond is to hold it until it's maturity date.

Of course, if you are referring to a savings bond, then none of the above applies, because you cannot sell savings bonds on the secondary market.
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