Explain why bond prices and interest rates are negatively related. What is the role of the coupon rate and term to maturity in this relationship?

Bond prices and interest rates have an inverse relationship due to the fixed nature of the payments a bond makes. Here's a step-by-step explanation:

1. When you buy a bond, you are essentially lending money to the issuer of the bond. In return, the issuer promises to make regular interest payments to you at a fixed rate (the coupon rate) for a fixed period (the term to maturity), and then to return the principal amount you lent (the face value of the bond) at the end of that period.

2. If market interest rates rise after you've bought the bond, new bonds being issued will offer higher coupon rates to attract buyers. This makes your bond less attractive, because its coupon rate is now lower than the market rate. To sell your bond, you would have to offer it at a discount to make up for its lower coupon rate. So, the price of your bond falls.

3. Conversely, if market interest rates fall, your bond becomes more attractive because its coupon rate is now higher than the market rate. You could sell your bond at a premium. So, the price of your bond rises.

4. The longer the term to maturity of the bond, the greater the price will change in response to a given change in market interest rates. This is because the buyer of the bond is locking in the coupon rate for a longer period, and therefore taking on more risk that market rates will change.

So, the coupon rate and term to maturity of a bond both play a role in determining how its price will react to changes in market interest rates. The higher the coupon rate and the longer the term to maturity, the more valuable the bond is and the higher its price will be, all else being equal. But if market interest rates change, the price of the bond will move in the opposite direction to keep its yield in line with market rates.