What is the relationship between interest rates and bond prices?

How do bonds work?

Bonds are a debt-based investment where an individual loans money to a government or corporation. They do so on the condition that the borrower will pay the money back when the bond reaches its date of maturity (expiry), plus any coupon payments that are due.

A bond’s coupon is the periodic return that an investor will receive for loaning the value of the bond to the borrower (a government or corporation). For example, a bond with a £1000 value and a 5% interest rate will have cash flows (coupons) of £50 a year until it reaches it maturity. If the bond’s maturity was ten years, then the trader would receive £500 in total from the coupon payments, as well as their initial £1000 investment back once the bond reaches its maturity.

Because a bond’s coupon is fixed, demand for the bond – and its price – will shift as the interest rates available elsewhere increase or decrease.

Bonds and interest rates: an inverse relationship

All else being equal, if new bonds are issued with a higher interest rate than those currently on the market, the price of existing bonds will decline as demand for those bonds falls. Equally, if new bonds are issued with a lower interest rate than bonds currently on the market, the price of existing bonds will increase in line with demand.

The degree to which a bond’s price will change given any shift in interest rates is calculated by assessing the present value of the bond’s future cash flows. This is because traders use a method known as discounted cash flow to value a bond according to the future returns that they could expect.

Under the discounted cash flow (DCF) method, the theory goes that an investor with an expectation of a 5% annual return would be indifferent in receiving £47.62 today or £50 a year from now. As illustrated in the table below, a bond’s price is based on the sum of all of its discounted cash flows – each future payment the investor expects to receive.

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Discounted cash flow for a 5% bond with a 10-year maturity

The discounted cash flow figures were calculated by dividing the coupon payments (£50) by the frequency of the payment (one year) plus the interest rate (0.05). So, for the table above, we would divide £50 by 1.05 to the power of one, which gives us the DCF for the first year.

To calculate the second year, we would divide 50 by 1.05 to the power of two; for the third year, we would do the same to the power of three and so on. The amount that must be discounted for the tenth year is £1050 because that is the year in which the bond reaches its maturity, and the lender will be repaid the initial value of the bond plus the coupon payment for that year.

The reason bond prices adjust is because investors will discount the future cash flows by different amounts, based on the returns they could receive elsewhere. To properly explain the inverse relationship between bond prices and interest rates, let’s look at some examples.

What happens to bond prices when interest rates rise?

If a trader currently held a bond with a 5% interest rate, but a new bond was issued with a 10% interest rate, they would have to sell their bond at a discount on the secondary market if they wanted to dispose of their investment.

The table below shows how the discounted cash flows of a 5% bond would adjust if market participants could get a 10% interest rate elsewhere.

Discounted cash flow for a 5% bond with a 10-year maturity adjusted for a 10% interest rate

In this case, the 5% bond would be discounted by the market to the point where its present value, based on its future cash flows, is proportionate to the cash flows of the newer bond. The table above shows that a bond with a 5% interest rate would be adjusted to a market value of £693 because investors discount its cash flows by 10% – the interest rate on the newer bond. This is the maximum that investors would be willing to pay for the bond based on its projected future earnings according to the discounted cash flow.

This new value is calculated by adding up all of the discounted cash flows of the current bond using a 10% yield rate. For the purpose of this example, we would divide the £50 coupon by an annual return of 10% (1.10) to the power of the number of years the investor would be waiting for the cash flow. For the first year, this would give us £45.45 – which is the adjusted return for the 5% bond now that new bonds with a 10% interest rate have been released into the market.

To get the second year’s return, we would divide £50 by 1.10 to the power of two; for the third year, we would do the same to the power of three and so on. The final year is £1050 divided by 1.10 to the power of ten, because this is the year in which the trader would receive back their initial investment for the bond, as well as the coupon payment.

In selling their bond at a discount, the trader would be losing money. However, they would be receiving instant capital with which they could take a position on another investment which could yield higher returns than their 5% bond, given the existence of 10% bonds on the market.

What happens to bond prices when interest rates fall?

If a trader held a bond with a 10% interest rate, but a new bond was issued with an interest rate of 5%, they would be able to sell their bond at a premium on the secondary market if they wanted to dispose of their investment. The table below shows how the bond’s price would adjust as market participants’ expectations for returns shift from 10% to 5%.

Discounted cash flow for a 10% bond with a 10-year maturity adjusted for a 5% interest rate

The bond would trade at a premium because the market would adjust the price of the 10% bond to a point where its present value, based on its future cash flows, is proportionate to the lower cash flows that investors could expect from the newer bond.

In this example, the table above shows that a bond with a 10% interest rate and an initial value of £1000 would be adjusted to a value of £1386 on the secondary market according to the discounted cash flows of the new 5% bond.

This price will become what investors are willing to pay for the 10% bond on the secondary market. As with the previous example, the figure of £1386 is calculated by adding up the discounted cash flows of the current bond using a 5% interest rate.

For the purposes of this example, we would divide the £100 coupon by an annual return of 5% (1.05) to the power of the number of years the investor would be waiting for the cash flow. This would give us an adjusted return of £95.24 for the first year. To get the second year, we would divide £100 by 1.05 to the power of two; for the third year we would do the same to the power of three and so on. The final year is £1100 divided by 1.05 to the power of ten, because this is the year in which the trader would receive back their initial investment for the bond, as well as the coupon payment.

In selling the bond at a premium, the trader would be gaining more profit than their initial investment would have yielded. As a result, they could reinvest this new capital into other opportunities in an attempt to get higher returns than are currently available on the 5% bonds.

Bonds and interest rates: what do traders need to bear in mind?

Perhaps the most important thing for a trader to bear in mind when trading bonds is that any changes in interest rate expectations will affect the return on their bonds – whether that change is positive or negative.

Additionally, bonds with a longer maturity will be more affected by any changes in interest rates because of the way that investors discount their cash flows. Bonds with longer maturities tend to offer higher yields to compensate the investor for interest rate risk. In this article, the bonds in both examples had a 10-year maturity for the sake of simplicity.

You can also speculate on the inverse relationship between long-term interest rates and bond prices with IG’s government bond futures markets. Here, you can trade on government bonds with either a spread betting or CFD account, which both enable you to speculate on which way you think bond prices will move.

You would go short if you think that a bond will fall in value or long if you thought that it will rise.