There are four different groups of Bond Functions. The first of these are the oBond3 functions which have no preset conventions allowing complete customization of all parameters. The next are the oBond2 functions which have some of the conventions preset to allow for simplified use followed by the oBond1 functions which have further simplification. Finally there are the sovereign bond functions which have all relevant conventions pre-defined. For further information on the generic bond functions: For further information on the sovereign bond functions.

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Generally, the issuer sets the price and the yield of the bond so that it will sell enough bonds to supply the amount that it desires. The higher the credit rating of the issuer, the lower the yield that it must offer to sell its bonds. A change in the credit rating of the issuer will affect the price of its bonds in the secondary market: The other factors that determine the price of a bond have a more complex interaction. When a bond is first issued, it is generally sold at par , which is the face value of the bond.

The par value is the principal, which is received at the end of the bond's term, i. Sometimes when the demand is higher or lower than an issuer expected, the bonds might sell higher or lower than par. In the secondary market, bond prices are almost always different from par, because interest rates change continuously. When a bond trades for more than par, then it is selling at a premium , which will pay a lower yield than its stated coupon rate, and when it is selling for less, it is selling at a discount , paying a higher yield than its coupon rate.

When interest rates rise, bond prices decline, and vice versa. Bond prices will also include accrued interest, which is the interest earned between coupon payment dates. Clean bond prices are prices without accrued interest; dirty bond prices include accrued interest. A bond pays interest either periodically or, in the case of zero coupon bonds, at maturity. Therefore, the value of the bond is equal to the sum of the present value of all future payments — hence, it is the present value of an annuity , which is a series of periodic payments.

The present value is calculated using the prevailing market interest rate for the term and risk profile of the bond, which may be more or less than the coupon rate. For a coupon bond that pays interest periodically, its value can be calculated thus:. What is the present value of the payments? The following table shows the amount received each year and the present value of that amount.

As you can see, the sum of the present value of each payment equals the par value of the bond. Note that the above formula is sometimes written with both C and r divided by 2; the results are the same, since it is a ratio. Then, since there are 10 semiannual payment periods , the market interest rate is divided by 2 to account for the shorter period:. Case 2: In the primary bond market , where the buyer buys the bond from the issuer, the bond usually sells for par value, which is equal to the bond's value using the coupon rate of the bond.

However, in the secondary bond market, bond price still depends on the bond's value, but the interest rate to calculate that value is determined by the market interest rate, which is reflected in the actual bids and offers for bonds. Additionally, the buyer of the bond will have to pay any accrued interest on top of the bond's price unless the bond is purchased on the day it pays interest.

When bond prices are listed, the convention is to list them as a percentage of par value, regardless of what the face value of the bond is, with being equal to par value. This pricing convention allows different bonds with different face values to be compared directly. Thus, a point's actual value depends on the face value of the bond. No commission is charged when buying or selling bonds.

A bond dealer makes money through the spread —the difference between the bid price , which is what the dealer is willing to pay for a bond, and the ask price , which is what the dealer is selling the bond for. Another reason for this convention is that a point is not equal to a dollar, but a decimal base would still be more convenient. The pricing convention is to list the point after a dash.

The integer point value, in this case , is known as the handle. When traders negotiate, the handle is usually known and not expressed. Listed bond prices are clean prices aka flat prices , which do not include accrued interest. Most bonds pay interest semi-annually. For settlement dates when interest is paid, the bond price is equal to the flat price.

Between payment dates, accrued interest must be added to the flat price, which is often called the dirty price aka all-in price , gross price:. Accrued interest is the interest that has been earned, but not paid, and is calculated by the following formula:. When you actually buy a bond on the secondary market, you would have to pay the former owner of the bond the accrued interest. If this were not so, you could make a fortune buying bonds right before they paid interest then selling them afterward.

Because the interest accrues every day, the bond price increases accordingly until the interest payment date, when it drops to its flat price, then starts accruing interest again. In calculating the accrued interest, the actual number of days was counted from the last interest payment to the value date. There are 2 other methods where each month counts as 30 days, regardless of the number of days in the month and each year is considered to have days.

So, under these methods, there is always 3 days between February 28 and March 1, because each month counts as 30 days, including February, even though February has either 28 or 29 days. By the same reasoning, there are 25 days between January 15 and February 10, even though there are actually 26 days between those dates. When figuring accrued interest using any day-count convention, the 1 st day is counted, but not the last day. So in the previous example, January 15 is counted, but not February This is determined thus:.

The number of days are then divided by , then multiplied by the coupon rate to determine the accrued interest:. Corporate and Municipal Bonds. As already stated, most bond markets outside of the U. How much must you pay? If the settlement date fell on a interest payment date, the bond price would equal the listed price: Since the settlement date was 31 days after the last payment date, accrued interest must be added.

Using the above formula, with days between coupon payments, we find that:. In most cases, it will be more convenient to use a spreadsheet, such as Excel, that provides several functions for determining the number of days or the dirty bond price, with the settlement and maturity dates expressed as either a quote e. Search Help for more information. To calculate the accrued interest on a zero coupon bond , which pays no interest, but is issued at a deep discount, the amount of interest that accrues every day is calculated by using a straight-line amortization , which is found by subtracting the discounted issue price from its face value, and dividing by the number of days in the term of the bond.

This is the interest earned in 1 day, which is then multiplied by the number of days from the issue date. Interest accrues on bonds from one coupon date to the day before the next coupon date. However, some bonds have a so-called ex-dividend date aka ex-coupon date , where the owner of record is determined before the end of the coupon period, in which case, the owner will receive the entire amount of the coupon payment, even if the bond is sold before the end of the period.

The ex-dividend period aka ex-coupon period is the time during which the bond will continue to accrue interest for the owner of record on the ex-dividend date. The ex-dividend date and the ex-dividend period are misnomers, since bonds pay interest and not dividends, but the terminology was borrowed from stocks, since the concept is similar. Although ex-coupon is more descriptive, ex-dividend is more widely used.

If a bond is purchased during the ex-dividend period, then any accrued interest from the purchase date until the end of the coupon period is subtracted from the clean price of the bond. In other words, the accrued interest is negative. Only a few bonds have ex-dividend periods, which are usually 7 days or less. Microsoft Excel has several formulas for calculating bond prices and other securities paying interest, such as Treasuries or certificates of deposit CDs , that include accrued interest, if any.

Using the Microsoft Excel Date function , with format DATE year,month,day , to calculate the maturity date by adding 90 days to the issue date , and choosing the banker's year of days by omitting its value from the formula, yields the following results:. Par Value: Using the above formula, with days between coupon payments, we find that: Using the Microsoft Excel Date function , with format DATE year,month,day , to calculate the maturity date by adding 90 days to the issue date , and choosing the banker's year of days by omitting its value from the formula, yields the following results: Calculates the price, given the yield.

## Bond Basics

We are using the following form field to detect spammers. Please do leave them untouched. Otherwise your message will be regarded as spam. We are sorry for the inconvenience. Please note that the vocabulary items in this list are only available in this browser. Once you have copied them to the vocabulary trainer, they are available from everywhere.

This page contains a bond pricing calculator which tells you what a bond should trade at based upon the par value of the bond and current yields available in the market. It returns a clean price and a dirty price market price and calculates how much of the dirty price is accumulated interest.

Treasury Bonds are medium to long-term debt securities that carry an annual rate of interest fixed over the life of the security, payable semi-annually. There is an active secondary market for Treasury Bonds. Syndicated issues of Treasury Bonds are conducted from time to time. Similar to most fixed income securities trading in Australia, Treasury Bonds are both quoted and traded on a yield to maturity basis rather than on a price basis.

### Cum Coupon

This suite of functions is designed to be as generic as possible, covering a wide range of various bond conventions and allowing the user maximum flexibility over the input parameters. The functions allow for interest payments to be calculated as level coupon, or as day count based like the fixed leg of a swap. For level coupon interest payments, all regular cash flows are the same and are calculated based on the number of periods per year as follows: For day count based cash flows, each cash flow is calculated based on the year fraction of the coupon period. This year fraction is the accrual factor from the period start date to the period end date of the coupon period, and interest payments are calculated as follows: The price from yield calculation is slightly different depending on which type of cash flow is used.

### Bond Pricing

Would you like to her bond or politely? Would you like to the bond or politely? What is its price? What was the total return, capital return and income return? Calculate your answers as effective annual rates. Bonds X and Y are issued by the same US company. Which of the following statements is true? Give your answer as an effective annual rate, which is how the above bond yields are quoted. Bonds A and B are issued by the same company. They have the same face value, maturity, seniority and coupon payment frequency.

### Bond Function Parameters

Generally, the issuer sets the price and the yield of the bond so that it will sell enough bonds to supply the amount that it desires. The higher the credit rating of the issuer, the lower the yield that it must offer to sell its bonds. A change in the credit rating of the issuer will affect the price of its bonds in the secondary market: The other factors that determine the price of a bond have a more complex interaction. When a bond is first issued, it is generally sold at par , which is the face value of the bond. The par value is the principal, which is received at the end of the bond's term, i.

## Does the Settlement Date Have to Occur Before the Ex-Dividend Date to Receive a Dividend?

To determine whether you should get a dividend, you need to look at two important dates. They are the "record date" or "date of record" and the "ex-dividend date" or "ex-date. When a company declares a dividend, it sets a record date when you must be on the company's books as a shareholder to receive the dividend. Companies also use this date to determine who is sent proxy statements, financial reports, and other information. Once the company sets the record date, the ex-dividend date is set based on stock exchange rules. If you purchase a stock on its ex-dividend date or after, you will not receive the next dividend payment. Instead, the seller gets the dividend. If you purchase before the ex-dividend date, you get the dividend. XYZ also announces that shareholders of record on the company's books on or before September 18, are entitled to the dividend. The stock would then go ex-dividend one business day before the record date.

### Bond valuation

Object com. Serializable A fixed coupon bond. A fixed coupon bond is a financial instrument that represents a stream of fixed payments. The payments consist two types: The periodic payments are made n times a year with a fixed coupon rate at individual coupon dates. The nominal payment is the unique payment at the final coupon date. The periodic coupon payment schedule is defined using PeriodicSchedule. The payment amount is computed with fixedRate and notionalAmount. The nominal payment is defined from the last period of the periodic coupon payment schedule and notionalAmount.

Cum coupon is how bonds are sold in secondary markets when the buyer receives the current payment of the bond as part of the sale.

### Frequently Asked Questions- Individual Investors

The fund's total annual operating expense ratio. It is gross of any fee waivers or expense reimbursements. It can be found in the fund's most recent prospectus. The market value-weighted average maturity of the bonds and loans in a portfolio, where maturity is defined as the stated final for bullet maturity bonds and loans. The lowest potential yield that can be received on a bond without the issuer actually defaulting. The YTW is calculated by making worst-case scenario assumptions on the issue by calculating the return that would be received if the issuer uses provisions, including prepayments. When aggregating YTW for a portfolio level statistic, the weighted average of the YTW and market value for each security is used. A bond's annual return based on its annual coupon payments and current price as opposed to its original price or face. The formula for current yield is a bond's annual coupons divided by its current price. When aggregating Current Yield for a portfolio level statistic, the weighted average of the Current Yield and market value for each security is used. Incorporates the effect of embedded options for corporate bonds and changes in prepayments for mortgage-backed securities. The market weighted average rate of return anticipated on the bonds held in a portfolio if they were to be held to their maturity date. Also known as Standardized Yield An annualized yield that is calculated by dividing the net investment income earned by the fund over the most recent day period by the current maximum offering price. The sum of the most recent 12 dividends within the past days divided by Net Asset Value per share, expressed as a percentage. Performance quoted represents past performance, which is no guarantee of future results.

### Bond Function Parameters

Also known as the Flat Price , Quoted Price This is the price excluding any accrued income Traders usually quote clean prices. Accrued Interest is the interest that adds up ie accrues each day between coupon payments. The accrued interest represents the unpaid part of the coupon since the last interest payment. In the US and Canadian bond markets the accrued interest is added to the quoted price of the bond so it represents the total amount you will actually pay. In most European markets the accrued interest is not added to the quoted price of the bond. Accrued interest is reinvested at exactly the same rate throughout the life of the whole bond.

The ex-dividend date is the day on which all shares bought and sold no longer come attached with the right to receive the most recently declared dividend. To determine whether you are entitled to the next cash or stock dividend , you need to know two important dates -- the " record date " or "date of record" and the "ex-dividend date" or "ex-date. When a company declares a dividend , it sets a record date when you must be on the company's books as a shareholder to receive the dividend. Once the company sets the record date, the stock exchanges fix the ex-dividend date. The ex-dividend date is normally two business days before the record date. If you purchase a stock on or after its ex-dividend date, you will not receive the next dividend payment. Instead, the seller gets the dividend. If you purchase before the ex-dividend date, you will get the dividend. XYZ also announces that shareholders of record on the company's books on or before August 10, are entitled to the dividend. The stock would then go ex-dividend two business days before the record date. In a nutshell, if you buy a stock before the ex-dividend date , then you will receive the next upcoming dividend payment. If you purchase the stock on or after the ex-dividend date, you will not receive the dividend. With a large dividend, the price of a stock may move up by the dollar amount of the dividend as the ex-dividend date approaches and then fall by that amount after the ex-dividend date. A stock that has gone ex-dividend is marked with an " x " in newspapers on that day.

**VIDEO ON THEME: Coupon Bonds**

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