The bond makes annual coupon payments. These results also demonstrate that there is an inverse relationship between yields and bond prices:. For a bond that makes semi-annual coupon payments, the following adjustments must be made to the pricing formula:. As an alternative to this pricing formula, a bond may be priced by treating the coupons as an annuity; the price is therefore equal to the present value of an annuity the coupons plus the present value of a sum the face value.

This method of valuing bonds will use the formula: The bond in the previous example can be priced using this alternate bond valuation formula as follows:. A zero-coupon bond does not make any coupon payments; instead, it is sold to investors at a discount from face value. The difference between the price paid for the bond and the face value, known as a capital gain , is the return to the investor. The pricing formula for a zero coupon bond is:. What is the market price of this bond? In order to be consistent with coupon-bearing bonds, where coupons are typically made on a semi-annual basis, the yield will be divided by 2, and the number of periods will be multiplied by There are different types of yield measures that may be used to represent the approximate return to a bond.

These include:. This equals the rate of return earned by a bond holder known as the holding period return if:. It is impossible to solve for the yield to maturity algebraically; instead, this must be done using a financial calculator or Microsoft Excel. The variables in brackets fv, type and guess are optional values; the value of type is set to zero if it is not specified.

Guess can be used to provide an initial estimate of the rate, which could potentially speed up the calculation time. Note that either pv or fv must be negative, and the other must be positive. The negative value is considered to be a cash outflow, and the positive value is considered to be a cash inflow. Also note that entering semi-annual periods and coupon payments will produce a semi-annual yield; in order to convert this into an annual yield on a bond-equivalent basis , the semi-annual yield is doubled.

For a bond that is callable, the yield to call may be used as a measure of return instead of the yield to maturity. The process is similar to computing yield to maturity, except that the maturity date of the bond is replaced with the next call date. This is because yield to call is based on the assumption that the bond will be called on the next call date.

The face value is replaced with the call price since this is the amount that the investor will receive if the bond is called. What is the yield to call? In this case, the bond will mature in eight years, but it can be called in three years. The yield to call is computed as follows:.

- Bond Prices, Rates, and Yields - Fidelity?
- 1) What are Bonds?.
- What is Coupon Rate?.

The current yield is simpler measure of the rate of return to a bond than the yield to maturity. The current yield is computed as:.

## An Introduction to Bonds, Bond Valuation & Bond Pricing

This measure has the benefit of simplicity. It suffers from the drawback that it does not account for the time value of money. Excel contains a set of specialized bond functions that can be used to account for several complications that arise in bond pricing, such as day-count conventions.

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Money market instruments e. Note that the settlement date and maturity date are represented as numerical values in Excel. The date January 1, is represented as 1; all later dates represent the number of days that have passed since January 1, As an example, suppose that a bond is sold on June 15, with a maturity date of June 15, What is the price of the bond?

Note that the price of the bond is entered as Also note that represents June 15, and represents For example,.

## Bond price relations

This article is one part of a series on fixed income portfolios. Other articles in this series include:. Call us: These include: Face Value Coupon Rate Coupon Maturity Call Provisions Put Provisions Sinking Fund Provisions a Face Value The face value also known as the par value of a bond is the price at which the bond is sold to investors when first issued; it is also the price at which the bond is redeemed at maturity.

The U. Treasury Treasury securities are issued by the U.

### Mutual Funds and Mutual Fund Investing - Fidelity Investments

Treasuries can be classified by their maturities as follows: Treasury bills — the maturity is one year or less; the currently available maturities are 4 weeks, 13 weeks, 26 weeks and 52 weeks Treasury notes — the maturity ranges between 1 and 10 years; the currently available maturities are 2, 3, 5, 7 and 10 years Treasury bonds — the maturity ranges between 20 and 30 years; the currently available maturity is 30 years Another key difference between these securities is that Treasury bills are sold at a discount from their face value and redeemed at face value; Treasury notes and bonds are sold and redeemed at face value and pay semi-annual coupons to investors.

These results show the following important relationship: The bond in the previous example can be priced using this alternate bond valuation formula as follows: The pricing formula for a zero coupon bond is: In order to be consistent with coupon-bearing bonds, where coupons are typically made on a semi-annual basis, the yield will be divided by 2, and the number of periods will be multiplied by 2: As market interest rates change, a bond's coupon rate—which, remember, is fixed—becomes more or less attractive to investors, who are therefore willing to pay more or less for the bond itself.

Let's look at an example. After evaluating your investment alternatives, you decide this is a good deal, so you purchase a bond at its par value: What if rates go up? Now let's suppose that later that year, interest rates in general go up. What if rates fall? It would be priced at a premium, since it would be carrying a higher interest rate than what was currently available on the market. Of course, many other factors go into determining the attractiveness of a particular bond: But the important thing to remember is that change occurs in market interest rates virtually every day.

The movement of bond prices and bond yields is simply a reaction to that change. The illustration is approximate and is not intended to represent the return of any particular bond or bond fund.

Bond values fluctuate in response to the financial condition of individual issuers, changes in interest rates, and general market and economic conditions. Mutual fund investing involves risks, including the possible loss of principal, and may not be appropriate for all investors. Stock values fluctuate in response to the activities of individual companies and general market and economic conditions.

Bond values fluctuate in response to the financial condition of individual issuers, general market and economic conditions, and changes in interest rates. Changes in market conditions and government policies may lead to periods of heightened volatility in the bond market and reduced liquidity for certain bonds held by the fund. In general, when interest rates rise, bond values fall and investors may lose principal value.

Interest rate changes and their impact on the fund and its share price can be sudden and unpredictable. Funds that concentrate their investments in a single industry may face increased risk of price fluctuation over more diversified funds due to adverse developments within that industry.

### How price is measured

Foreign investments are especially volatile and can rise or fall dramatically due to differences in the political and economic conditions of the host country. These risks are generally intensified in emerging markets. Smaller- and mid-cap stocks tend to be more volatile and less liquid than those of larger companies.