Bonds

The Yield on a Bond

The term “yield” is commonly used in the capital market to describe an investor’s return on investment for a given security, i.e., the profit or loss that an investor receives on the investment. An investor who bought a share for \$100 and sold it for \$120 earns \$20, meaning that the yield is 20%. Calculating a yield is usually simple according to the following formula:

R = (P – I)/I = P/I – 1

Where: R = Yield, I = Investment, and P = Proceeds.

For an investment involving shares, calculating the yield is fairly basic (as long as there are no interim payments), since the proceeds are simply divided by the total sum invested. In the case of bonds, however, there are almost always interim payments. Furthermore, these interim payments are disclosed at the beginning of the bond’s lifespan, and therefore they also affect the yield.

The various calculations required to establish the yield on a bond, and the factors affecting this yield (in addition to the time and risk factors mentioned above) will be discussed.

Cumulative Yield to Maturity

The cumulative yield to maturity reflects the total yield (profit) that the bond yields to the investor from the date of the calculation (date A) until the maturity date (date B).

The Sources of the Yield

Yield to maturity stems from two sources:

1. The coupons received - the interest payments.

2. Capital gain - the difference between the face value of the bond (\$1,000) and its price on the calculation date since the bondholder will receive the bond’s face value on the maturity date.

Examples:

• If the bond price on the calculation date is \$940, then the capital gain is \$60.
• If the bond price on the calculation date is \$920, then the capital gain is \$80.

The Yield to Maturity is Known in Advance at All Times

The cumulative yield to maturity is always disclosed in advance because the profit from each source is known:
1. The number of coupons that the investor will receive, the amounts, and the date on which they are received.

2. The capital gain.

For example, assume that face value bonds worth \$1,000 have been purchased for \$950, which will mature in three years. The bond pays 8% annual interest twice each year (i.e., each payment is \$40). The sources of the bond’s yield are:

1. 6 biannual coupons of \$40 each.

2. A \$50 capital gain.

A List of the Data for Calculating the Yield

The explanation will be accompanied by the three rectangles in the following diagram.

In order to calculate the cumulative yield to maturity, the receipts expected on the maturity date are listed in Rectangle A, and the expenditures in Rectangle B. The expenditures consist of a single figure, i.e., the price of the bond on the date of the calculation. The assumption is that the bond is bought on that date (even if it was purchased previously).

The total profit, which represents the difference between the two rectangles, is indicated in Rectangle C.

Fluctuations in the Cumulative Yield

Since the price of the bond (Rectangle B) changes from time to time in the course of trading, the capital gain (i.e., the difference between the price of the bond and \$1,000) changes accordingly, and consequently the cumulative yield to maturity also changes from moment to moment.

Transition from Cumulative Yield to Maturity to Annualized Yield to Maturity

The “annualized yield to maturity” reflects the average annual percentage profit that the bond will provide its holder each year until the maturity date.

In the previous example, the bond was purchased for \$950, and the bondholder received \$1,240 at the end of three years. In order to obtain the annualized yield, the following question must be answered: What would be an appropriate annual interest rate for someone investing \$950 today who wishes to receive \$1,240 at the end of three years? If the answer is 9.3%, then the annualized yield is 9.3%, meaning that someone depositing \$950 in a bond at 9.3% annual interest will also have \$1,240 at the end of three years. You can use the bond calculator to obtain the answer.

Using the annualized yield to maturity facilitates convenient comparisons between various U.S bonds since the cumulative yield on a bond with 10 years to maturity will always be greater than the cumulative yield on a bond with two years to maturity.

Publication of Yields in the Press

Various financial websites publish a table of bonds with the yield of every bond printed next to its name. Calculation of the yield is based on the bond price at the end of the day of trading. If the bond’s yield as published on these websites is 7%, then it means that the annualized rate of profit on that bond from the calculation date until the maturity date is 7%. If the market is offering a deposit with 6% annual interest, it is preferable to buy the bond. If 8% is offered, then the deposit is preferable to the bond.

Nominal Yield

Nominal yield refers to the rate at which the amount of money in any investment increases. For example, let us assume that 100 bonds are purchased on date A for \$100,000 (\$1,000 per bond). The bonds mature in one year (on date B) with a yield of 7%.

The yield means that the amount of money invested when purchasing the bonds on Date A increases by 7%. The investor will have \$107,000 at the end of the year. How much this \$107,000 can buy is a separate question.

The Yield on a Bond562