# Price Between Coupon Dates

You can calculate the price of a bond for dates between coupon dates by

1) Using the __PRICE__ function.

2) Using the __YIELD__ function - uses clean price as an argument

SS

### What is the Clean Price ?

Also known as the **Flat Price**, **Quoted Price**

This is the price excluding any accrued income

Traders usually quote clean prices

### What is the Accrued Interest ?

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.

questions - how many days in a year

questions - how many days in a month

Accrued interest is reinvested at exactly the same rate throughout the life of the whole bond.

We obviously need a way of calculating the yield on all the days in between the coupon dates as well.

When an investor sells a bond in between coupon dates this investor receives a proportion of the next coupon payment.

This amount is known as the accrued income.

This is the accrued income on the next coupon payment.

If you buy or sell a bond it matures you will most likely catch the bond between coupon payments.

If you are selling you are entitled to the price of the bond plus the accrued interest that the bond has earned up to that point.

The buyer compensates you for this by adding the accrued interest to the current price.

This is the amount of the coupon payment that the holder of the bond has earned since the last coupon payment

SS - equation

Include only one of the two bracketing dates

If this is the first coupon, use the dates date instead of the previous coupon date.

SS - Equation

coupon days accrued - COUPDAYBS

number of days in period - COUPDAYS

The interest earned between coupons is simple interest and not compounded

### What is the Dirty Price ?

Also known as the **Street Price**, **Full Price**.

Dirty Price = Clean Price + Accrued

bond price including any accrued income.

Bond market convention is to always quote the clean price.

This is the price paid by the buyer to the seller.

This is the price without any accrued

When investors buy a bond, they pay the dirty price (or gross price)

The dirty price is the clean price plus the accrued.

### Example 1

A corporate bond has a 10% coupon and a maturity date of 1 March 2020.

It has a current dirty price if £118.78

The settlement date is 17 July 2014

SS - excel

settlement date

maturity date

frequency - 2 semi-annual

Day Convention / Basis

Coupon Rate

Coupon Days Accrued

Number of Days in Period

Quoted Dirty Price

Accrued Interest

Clean Price

Yield to Maturity (Yield)

### Ex Dividend Period

This is the period between when a coupon is announced and when it is actually paid

If a bond trades in this period, it is the seller who receives the next coupon.

### Cum Dividend Period

This is the period between the coupon payment date and the next ex-dividend date.

### Example

Investor 1 buys a bond from Investor 2, 10 days before a coupon is paid

Investor 1 will receive the entire coupon

Investor 1 must pay Investor 2 most of the accrued interest.

### Important

There is an inverse relationship between price and yield. The higher the yield, the lower the price.

Bloomberg screen - DCX

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