Relationship between coupon rate and bond price

Contents:
  1. Definition of 'Coupon Rate'
  2. Coupon Rate
  3. Why Do Bond Prices Go Down When Interest Rates Rise?

While the price of junk bonds typically follows economic conditions, just like stocks; the price of investment quality bonds is usually linked to interest rates. In fact, there is an inverse correlation between interest rates and bond prices which can be explained using two rules of thumb:.

The primary market is associated with the issuance of new bonds. These can be companies, or government agencies, that are raising funds through the sale of bonds. These investments are usually purchased through securities dealers. The secondary bond market is where issues are traded before they mature. Except where noted, most of the relationships explained in this article apply to the secondary market.

Explaining Bond Prices and Bond Yields

When a bond is first issued, it will pay a fixed rate of interest until maturity. That interest rate is referred to as the coupon rate. The coupon rate of any bond is a function of the credit risk of the issuer, as well as prevailing interest rates when the bond was first issued. Over time, interest rates will change, but the coupon rate will remain the same, as will the payments to the bondholder.

If interest rates fall, new bond issues will offer the market a lower coupon rate. The reverse is true if interest rates rise; coupon rates will increase. Since the coupon rate is fixed at a point in time, the price of bonds on the secondary market need to rise or fall to remain competitive with the primary market. In order to remain competitive with new issues, the bond would sell at a discount to its face value on the secondary market.

In order to remain competitive with new issues, the bond would sell at a premium to its face value on the secondary market. Buyers need to understand the bond's yield before purchasing the security. There is an inverse relationship between the yield and its price. As demonstrated in the examples provided above:. Another factor that will influence the price of a bond is its maturity date. That's because when a bond matures, the holder of the issue will receive a payment equal to its face value.

If the bond is selling at a premium to its face value, then the holder will receive less than the price paid. If the bond is selling at a discount, then the holder will be paid more than the price they paid. In other words, if the bond is selling at a discount or premium to its face value, then that difference in price will be another component of the bond's yield.

If the bond's maturity is in the distant future, this premium or discount will have less influence on the yield than if it matured in the near term. Once again, an example can be used to illustrate how the prices of bonds vary with maturities. At a practical level, investors will be more concerned about the bond yield to maturity than current yield.

All bonds are assigned ratings that qualify the quality of the issue. Ratings are standardized and assigned by credit rating agencies. The system used by each company to indicate the quality of a government or company's bond offering appears in the table below. Bond valuation is the determination of the fair price of a bond. As with any security or capital investment, the theoretical fair value of a bond is the present value of the stream of cash flows it is expected to generate.

Definition of 'Coupon Rate'

Hence, the value of a bond is obtained by discounting the bond's expected cash flows to the present using an appropriate discount rate. In practice, this discount rate is often determined by reference to similar instruments, provided that such instruments exist. Various related yield-measures are then calculated for the given price. If the bond includes embedded options , the valuation is more difficult and combines option pricing with discounting.

Depending on the type of option, the option price as calculated is either added to or subtracted from the price of the "straight" portion. See further under Bond option. This total is then the value of the bond. As above, the fair price of a "straight bond" a bond with no embedded options ; see Bond finance Features is usually determined by discounting its expected cash flows at the appropriate discount rate.

Coupon Rate

The formula commonly applied is discussed initially. Although this present value relationship reflects the theoretical approach to determining the value of a bond, in practice its price is usually determined with reference to other, more liquid instruments. The two main approaches here, Relative pricing and Arbitrage-free pricing, are discussed next. Finally, where it is important to recognise that future interest rates are uncertain and that the discount rate is not adequately represented by a single fixed number—for example when an option is written on the bond in question —stochastic calculus may be employed.

Conversely, if the market price of bond is greater than its face value, the bond is selling at a premium. Below is the formula for calculating a bond's price, which uses the basic present value PV formula for a given discount rate: [3] This formula assumes that a coupon payment has just been made; see below for adjustments on other dates. Under this approach—an extension, or application, of the above—the bond will be priced relative to a benchmark, usually a government security ; see Relative valuation.


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  • Why Do Bond Prices Go Down When Interest Rates Rise?.

Here, the yield to maturity on the bond is determined based on the bond's Credit rating relative to a government security with similar maturity or duration ; see Credit spread bond. The better the quality of the bond, the smaller the spread between its required return and the YTM of the benchmark. As distinct from the two related approaches above, a bond may be thought of as a "package of cash flows"—coupon or face—with each cash flow viewed as a zero-coupon instrument maturing on the date it will be received.

Thus, rather than using a single discount rate, one should use multiple discount rates, discounting each cash flow at its own rate. Under this approach, the bond price should reflect its " arbitrage -free" price, as any deviation from this price will be exploited and the bond will then quickly reprice to its correct level. Here, we apply the rational pricing logic relating to "Assets with identical cash flows". In detail: 1 the bond's coupon dates and coupon amounts are known with certainty. Therefore, 2 some multiple or fraction of zero-coupon bonds, each corresponding to the bond's coupon dates, can be specified so as to produce identical cash flows to the bond.

Thus 3 the bond price today must be equal to the sum of each of its cash flows discounted at the discount rate implied by the value of the corresponding ZCB. Were this not the case, 4 the arbitrageur could finance his purchase of whichever of the bond or the sum of the various ZCBs was cheaper, by short selling the other, and meeting his cash flow commitments using the coupons or maturing zeroes as appropriate. Then 5 his "risk free", arbitrage profit would be the difference between the two values. See under Rational pricing Fixed income securities. When modelling a bond option , or other interest rate derivative IRD , it is important to recognize that future interest rates are uncertain, and therefore, the discount rate s referred to above, under all three cases—i.

In such cases, stochastic calculus is employed.

Why Do Bond Prices Go Down When Interest Rates Rise?

The solution to the PDE—given in Cox et al. To actually determine the bond price, the analyst must choose the specific short rate model to be employed. The approaches commonly used are:. When the bond is not valued precisely on a coupon date, the calculated price, using the methods above, will incorporate accrued interest : i. The price of a bond which includes this accrued interest is known as the " dirty price " or "full price" or "all in price" or "Cash price".

The " clean price " is the price excluding any interest that has accrued. Clean prices are generally more stable over time than dirty prices. This is because the dirty price will drop suddenly when the bond goes "ex interest" and the purchaser is no longer entitled to receive the next coupon payment.