## What Is an Average Price?

The average price of an asset or security is taken as the simple arithmetic average of closing prices over a specified time period, or over specific periods of duration intraday. For an intraday average price, when adjusted by trading volume, the volume-weighted average price (VWAP) can be derived.

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.

### Key Takeaways

- Average price is the mean price of an asset or security over some period of time.
- For intraday averages, the volume-weighted average price, or VWAP, is an important metric for traders and investors.
- For technical traders, moving averages (MAs) are used for a variety of trend and reversal indicators.
- A bond's average price is computed from its face value and market price and is used to derive its yield to maturity (YTM).

## Understanding 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.

## Example of Average Price in Bonds

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 follows:

- 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 six years to mature. Annual coupon payments will thus be 5% x $1,000 face value of corporate bond = $50. YTM is as follows:

- $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.

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.

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.

## Volume-Weighted Average Price

The volume-weighted average price (VWAP) is a trading benchmark used by traders that gives the average price a security has traded at throughout the day, based on both volume and price. It is important because it provides traders with insight into both the trend and value of a security.

Large institutional buyers and mutual funds use the VWAP ratio to help move into or out of stocks with as small of a market impact as possible. Therefore, when possible, institutions will try to buy below the VWAP, or sell above it. This way their actions push the price back toward the average, instead of away from it.

Retail traders tend to use VWAP more as a trend confirmation tool, similar to a moving average. When the price is above VWAP they look only to initiate long positions. When the price is below VWAP they only look to initiate short positions.

VWAP is calculated by adding up the dollars traded for every transaction (price multiplied by the number of shares traded) and then dividing by the total shares traded.

$\text{VWAP}=\frac{\sum\text{Price * Volume}}{\sum\text{Volume}}$