What is an 'Average Price'

The average price of a bond is calculated by adding its face value to the price paid for it and dividing the sum by two. The average price is sometimes used in determining a bond's yield to maturity where the average price replaces the purchase price in the yield to maturity calculation.

BREAKING DOWN 'Average Price'

In basic mathematics, an average price is a representative measure of a range of prices that is calculated by taking the sum of the values and dividing it by the number of prices being examined. The average price reduces the range into a single value, which can then be compared to any point to determine if the value is higher or lower than what would be expected. In situations where there is a range of prices it can be useful to calculate the average price to simplify a range of numbers into a single value. For example, if over a four-month period you earned $104, $105, $110, and $115 from your investments, the average return on your portfolio will be ($104 + $105 + $110 + $115) / 4 = $108.50.

In the finance sector, the average price is mostly attributed to bonds. Bondholders that want to know the total rate of return they will get from a bond that is held until maturity can calculate a metric known as the yield to maturity (YTM). An estimate of the yield to maturity can be calculated using the bond’s average rate to maturity (ARTM). The ARTM determines the yield by measuring the proportion of the average return per year to the average price of the bond. For a coupon bond, the yield to maturity can be calculated as:

YTM = C + [(F – P)/n] ÷ (F + P)/2

Where C = coupon rate

F = face value

P = purchase price

n = number of years

For example, consider an investor that purchased a corporate bond at a premium to par for $1,100 and annual coupon rate of 5% with 6 years to mature. Annual coupon payments will, therefore, be 5% x $1,000 face value of corporate bond = $50. YTM is:

 = $50 + [($1,000 - $1,100)/6] ÷ ($1,000 + $1,100)/2

= $33.33 / $1,050 = 3.17%

The logic behind the formula is that the premium amount over par, that is, F – P = $1,000 - $1,100 = -$100 is divided over the number of years to maturity. Hence, -$100/6 = -$16.67 is the amount that reduces the coupon payment per year. Hence, even though the investor receives $50 coupon per year, his real or average return is $50 - $16.67 = $33.33 per year since he bought the bond for a price above par. Dividing the average return by the median or average price is the bondholder’s yield to maturity.

Note that if the bond was purchased at a discount to par, the investor’s average return per year will be higher than the coupon payment. Furthermore, if an investor bought the bond at par, his average return per year will equal the coupon rate. In this case, the YTM will also equal the coupon rate after dividing the average return per year by the average price of the bond.

Although the average price of a bond is not the most accurate method to find its YTM, it does give investors a rough and simple gauge to find out what a bond is worth.

RELATED TERMS
  1. Yield To Maturity (YTM)

    Yield to maturity (YTM) is the total return expected on a bond ...
  2. Current Yield

    Current yield is the annual income (interest or dividends) divided ...
  3. Bond Valuation

    Bond valuation is a technique for determining the theoretical ...
  4. Coupon Rate

    Coupon rate is the yield paid by a fixed income security, which ...
  5. Discount Bond

    A discount bond is a bond that is issued for less than its par ...
  6. Coupon

    A coupon is the annual interest rate paid on a bond, expressed ...
Related Articles
  1. Investing

    Comparing Yield To Maturity And The Coupon Rate

    Investors base investing decisions and strategies on yield to maturity more so than coupon rates.
  2. Investing

    Simple Math for Fixed-Coupon Corporate Bonds

    A guide to help to understand the simple math behind fixed-coupon corporate bonds.
  3. Investing

    Understanding the Different Types of Bond Yields

    Any investor, private or institutional, should be aware of the diverse types and calculations of bond yields before an actual investment.
  4. Investing

    How To Evaluate Bond Performance

    Learn about how investors should evaluate bond performance. See how the maturity of a bond can impact its exposure to interest rate risk.
  5. Managing Wealth

    How Bond Prices and Yields Work

    Understanding bond prices and yields can help any investor in any market.
  6. Investing

    Corporate Bonds: Advantages and Disadvantages

    Corporate bonds can provide compelling returns, even in low-yield environments. But they are not without risk.
RELATED FAQS
  1. Current yield vs yield to maturity

    Learn about the relationship between a bond's current yield and its yield to maturity, including how the market price of ... Read Answer >>
  2. What is the difference between yield to maturity and the coupon rate?

    A bond's coupon rate is the actual amount of interest income earned on the bond each year based on its face value. Read Answer >>
  3. Learn to Calculate Yield to Maturity in MS Excel

    Find out the best practices for most financial modeling to price a bonds, calculate coupon payments, then learn how to calculate ... Read Answer >>
  4. What does a negative bond yield mean?

    Find out what it means when a bond has a negative yield and what circumstances must arise for the yield to be negative when ... Read Answer >>
  5. How do I calculate yield to maturity of a zero-coupon bond?

    Find out how to calculate the yield to maturity of a zero-coupon bond, and learn why this calculation is simpler than one ... Read Answer >>
  6. What is the most common solvency ratios used in fundamental analysis?

    Learn about the difference between a bond's coupon rate and its yield rate, how the coupon rate influences market price and ... Read Answer >>
Trading Center