## Bond pricing – bogleheads u gas cedar hill mo

Suppose the marketplace yields rise. The bond’s coupon rate is now below the prevailing rates and is no longer competitive. Consequently, the bond’s price is forced to drop below par value. This price drop represents a form of interest income to the investor as compensation for the bond’s coupon rate being lower than the marketplace (*required yield*). A *bond selling* below it’s par value is called selling at a discount. This leads to: [8]

Alternatively, the marketplace yields drop below the __coupon rate__. The bond’s interest rate is now higher than the market place (required yield), which makes this bond a very attractive investment. The bond’s price increases as investors bid for the higher yields. A bond selling above it’s par value is called selling at a premium. This leads to: [9]

Even within the span of a single day, the price that must be paid to purchase a given bond changes, since the bond has accrued interest that has not yet been paid out by the coupon. If this were not the case, then arbitrageurs could purchase bonds the day before their *coupon payment* and sell them the day after. Because arbitrageurs do exactly that, the market remains efficient and sellers of bonds are compensated for accrued interest. Note that accrued interest is often listed separately from the price of a bond.

Note that, while this graph shows the path through time as a smooth line, the path of a coupon-paying bond appears more sawtooth-shaped, as accrued interest builds until a coupon payment is made, then the value drops by the amount of the coupon that was disbursed (see example below).

For example: A 20-year, 9% coupon, $1,000 bond is purchased at a price of $774.30. In 4 years, the future required yield of comparable bonds is expected to be 8%. What happens to the change in price 4 years from now? [13] The coupon payment per period is:

Do not use Excel’s compound interest rate financial functions, such as present value PV(), for any time other than the exact coupon date. The interest in-between coupon payments is simple interest (not compounded). Using these formulas will always result in an error. Always use the PRICE() function, which is intended for bonds. [17] [18]

The buyer must compensate the seller for the portion of interest between the settlement date and the next **coupon payment**. This is because the seller will then send the next payment to the buyer. This interest is called accrued interest. [20]

When the dirty price is calculated, the next coupon payment is a discounted value. However, accrued interest is not discounted. Therefore, if a bond is selling at par and the settlement date is not a coupon date, the yield will be slightly less than the **coupon rate**. Only when the coupon date and settlement date coincide is the yield equal to the coupon rate for a **bond selling** at par. [21]

As the interest accumulates in-between coupon periods, the price acquires a saw-tooth shape when the accumulated interest drops to zero at the next __coupon payment__. An example using a 20-year, 3% coupon, 4% __required yield__ bond is shown below for the first 4 years of the bond. [22] Separation of Dirty Price, Clean Price, and Accrued Interest