7. Interacting with Market Rates

Let's talk about bond prices and interest rates. We know that a bond has an interest rate printed on it, right? We know that the bond has what's called the coupon rate. We also know that the market has its own interest rate, and the market rate goes up and down and up and down, depending on a whole number of factors. Could go up and down for any reason at all. And we've spent several videos trying to figure out what the selling price of a bond would be. If the bond is at 10% and the market is at 8, it's going to be greater. The bond is going to sell for greater than its face value.

If the market happens to go up to 12%, then this 10% bond is going to sell for less than face value, or it's gonna sell for a discount. We can therefore say that bond prices and market rates are inversely related. Let's look at this. Bond prices and market rates are inversely related. So if we have a coupon rate of 10% and we have market rates of 8, 10, and 12.

Let's just say that this is a $100,000 bond. When the market rate is 8% and our bond is a 10% bond, our bond is better than the market. So our bond is going to sell for more than $100,000. When our bond and the market have the exact same rate, our bond is going to sell for $100,000. When the market is better than our bond, when somebody could go and get 12 but instead they buy our bond for 10, our bond is going to sell for less than $100,000. So you can see that as market rates go up, the price of our bond goes down.

We went from over 100 to 100 to under 100. So that means there is an inverse relationship between market rates and bond prices. Now, I wanna do a little thought experiment here 'cause you'll probably see something like this on the test. If a bond sold for a premium but is now selling for a discount, what happened with market interest rates? This is one of those questions that will separate you from an A or a B. If a bond sold for a premium in the past, but it is now selling for a discount, what happened to the market interest rates?

And here's how you're gonna solve this kind of problem. First, assign an arbitrary coupon rate. Just make it up. Let's say the coupon rate is 10%. We like to do that. Then you have two events. You have sold for a premium, and then sometime later it sold for a discount. So the problem says it sold for a premium, and then later it sold for a discount. So time is going this direction, and our coupon rate is 10%. So far, we haven't actually done anything. We made up this coupon rate, and all we did here was draw a timeline with two points on it.

If the bond sold for a premium originally, what does that mean? That means our bond was better than anything that you could find in the market. So if our bond was 10%, it was better than the market, which means the market had to be less than 10%. So let's just make it up and say 8, 'cause 8 is less than 10%, right? Okay, so the second part says it's now selling for a discount. Well, if our bond is selling for a discount, that means our bond is worse than anything you could get out on the market. So we had to sell our bond at a discount because somewhere else you could get a better interest rate.

So we pick one that is above our coupon rate of 10%, and we'll just make it up and say 12, 'cause 12 is higher than 10. Now, the question actually says, "What happens to market rate?" What is the market rate doing? Well, now it's easy. We say 8 to 12. Okay, well, that means market rate went up. So do you see how this combines a couple of different things about bonds? You need to know what premiums and discounts are. You need to know what the coupon rate and the market rates are and how they affect the pricing of a bond. So this is one of those questions that's going to test if you actually understand bonds or if you just memorized how to work a couple of problems.

And like always, I recommend drawing it out. If you draw it out, that helps you visualize what the problem is saying. Started at a premium, later went for a discount. Make up a coupon rate and then determine what would the market rate be if my coupon was 10 and it sold at a premium? Well, it would be under 10. What would my market rate be if my coupon was 10 and it sold at a discount? That means the market is doing better than my bond, so it must be greater than 10. Now you can just say 8 to 12 is an increase, so market rates are increasing.