# Inverse relationship between asset prices and interest rates

### Bond Yields and the Price of Bonds | Economics Help An explanation of the inverse relationship between bond yields and the price So a cut in interest rates is likely to increase the price of bonds. You have just learned how the interest rate is a payment for postponing the use The relationship given by Equation 6 makes perfect sense. This explains why the prices of government (and corporate) bonds tend to vary inversely with the. Consider, the simplest Gordon model of asset prices in which future dividends If the interest rate were to fall to 9%, the asset price would rise to (\$/. 09). That's the inverse of what they've been doing since , or . The one- to -one relationship between bond yields and the PE is a good.

Actually, the math is much simpler on this because you don't have to do it for all of the different coupons. You just have to look at the final payment. There is no coupon. So if I were to draw a payout diagram, it would just look like this.

## The Relationship Between Bonds and Interest Rates

This is one year. This is two years. Now let's say on day one, interest rates for a company like company A, this is company A's bonds, so this is starting off, so day one, day one. The way to think about it is let's P in this I'm going to do a little bit of math now, but hopefully it won't be too bad.

Let's say P is the price that someone is willing to pay for a bond. Let me just be very clear here. If you do the math here, you get P times 1. So what is this number right here? Let's get a calculator out. Let's get the calculator out. If we have 1, divided by 1.

• Relationship between bond prices and interest rates

Now, what happens if the interest rate goes up, let's say, the very next day? And I'm not going to be very specific.

### The Relationship Between Bonds and Interest Rates- Wells Fargo Funds

I'm going to assume it's always two years out. It's one day less, but that's not going to change the math dramatically. Let's say it's the very next second that interest rates were to go up.

Let's say second one, so it doesn't affect our math in any dramatic way. Let's say interest rates go up. So now all of a sudden, so interest, people expect more. We'll use the same formula. We bring out the calculator. We bring out the calculator, and I think you have a sense we have a larger number now in the denominator, so the price is going to go down. Let's actually calculate the math. So now, the price has gone down.

Now, just to finish up the argument, what happens if interest rates go down? What is someone willing to pay for this zero-coupon bond? The price is, if you compound it two years by 1. You get the calculator out again. The price went down. When interest rates went down, the price went up. I think it makes sense. The more you expect, the higher return you expect, the less you're willing to pay for that bond. Consider, for example a consol, which is a bond paying fixed nominal interest every year for ever with no repayment of the principal.

The present value of such a bond is determined by Equation 6 where R is the fixed annual interest or coupon yield and r is the rate of interest on other assets of similar risk. When the interest rate rises, the price of the bond, which is the present value of the coupon yield, goes down.

Plug any number for R you choose into Equation 6 and you will see that a rise in the interest rate from 5 percent to 10 percent, for example, will reduce the value of the bond by half.

## Bond Yields and the Price of Bonds

Another type of bond is one that pays coupon interest per year of some amount R for a fixed number of years, after which the principal is also paid back. The value of a bond of this type is given by 7. It is easy to see that the market value of this bond will also fall when the rate of interest rises because the denominator of every term to the right of the equal sign increases.

Finally, there are bonds like treasury bills issued by the Treasury Branch of the Government that pay no coupon interest at allthe purchaser of treasury bills buys only the right to receive a fixed amount at some future date, usually 1 or 3 months hence. If we let this fixed amount be T, then the market value of the bill will be simply 8. The buyer pays sufficiently less than a dollar for each dollar to be received at maturity to yield an interest rate equal to the rate prevailing for other securities of similar risk.

As the market interest rate rises, the amount investors will pay to purchase the fixed future amountthat is, the value of the billwill fall. When the interest rate rises the penalty for consuming now rather than in the future increases, so the fixed future receipts of principal and coupon interest are worth less today. If one wants to consume the future earnings from the security now, one will have to pay more for that privilege.

You should now understand a number of things about the rate of interest. First, you should understand that it is a payment for postponing consumption. It is not the price of money, but rather, the price of postponing the use of money.

Second, you should understand that the interest rate will be positive in the economy because capital, broadly defined to include knowledge, technology and human capital as well as physical capital is productivethat is, produces income.

Third, you should understand that it makes no sense to add together or compare dollar amounts to be paid or received at different points of time without discounting them.