# Understanding Bond Prices: Quotes and Calculations | CFA Level I Fixed Income

In this lesson, we will discuss the difference between a bond’s quoted price and the price paid by investors. Additionally, we’ll learn how to estimate the price and market discount rate of a bond through matrix pricing. To help you better understand these concepts, we will cover the flat price and full price of a bond and provide examples to illustrate the calculations.

## Bond Flat Price vs. Full Price

When investing in bonds, it’s essential to understand the difference between a bond’s full price (also called dirty price) and its flat price (or clean price). The full price is the price an investor pays or receives for a bond when a trade is made, ignoring the effect of the spread. Meanwhile, the flat price is quoted by bond dealers without considering accrued interest.

Full price = Flat price + Accrued interest

In summary, the difference between the full price and the flat price of a bond is the accrued interest.

## Calculating Bond Full Price, Flat Price, and Accrued Interest

To calculate the full price of a bond, we first determine its value on the last coupon date. After finding this value, we adjust it based on the number of days since the last coupon date to get the full price. The accrued interest can then be calculated as the coupon payment times the proportion of the period that has elapsed. Finally, the flat price is found by subtracting the accrued interest from the full price.

EXAMPLE

Suppose a bond with a market discount rate of 12.6% is traded on June 1st. The coupon payment dates are April 1st and October 1st. How do we calculate the full price, flat price, and accrued interest of this bond?

Full Price: – Value of the bond on the last coupon date (April 1st): \$936.67 – Adjust this value for 61 days since April 1st: Full price = \$955.94

Accrued Interest: \$50 × 61/183 = \$16.67

Flat Price: \$939.27 (Full priceAccrued interest)

## Actual-Actual and 30/360 Methods

There are two methods to calculate the bond prices and accrued interest: the actual-actual method and the 30/360 method.

The actual-actual method uses the actual number of days between coupon payments and the actual number of days between the last coupon date and the settlement date. This method is often used with government bonds.

On the other hand, the 30/360 method assumes 30 days in each month and 360 days in a year. This method is most often used for corporate bonds.

EXAMPLE

As you can see, understanding the difference between the full price and the flat price of a bond is essential in bond trading. By using the actual-actual method or the thirty three-sixty method, you can accurately calculate bond prices, accrued interest, and determine the appropriate quoted price for various types of bonds.

So far, we’ve discussed how to use a bond’s market price to calculate its yield-to-maturity. But what if we don’t have either the price or the yield? This often happens with non-publicly traded bonds or new bond issues. In such situations, we can use matrix pricing to estimate the bond price based on the quoted prices of comparable bonds.

## Matrix Pricing

Matrix pricing involves finding the market prices of actively traded bonds with similar credit quality and using their yields to estimate the yield of the bond in question.

## Pricing New Bond Issuance

Another method for pricing bonds is by estimating the required yield spread over the benchmark rate. The benchmark rate is typically the yield-to-maturity on a government bond with a similar time-to-maturity. The yield spread accounts for additional risks associated with the bond relative to the government bond. Here’s an example:

EXAMPLE

## Conclusion

That wraps up our discussion on bond prices, quotes, and calculations. By understanding matrix pricing and how to estimate yield spreads and benchmark rates, you’ll be better equipped to navigate the world of fixed income. Next up, we’ll explore different yield measures for various types of bonds and money market instruments. Stay tuned!

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