How do you calculate the average share price?
| Date |
Total Amount |
Price per Share |
Number of Shares |
| 1/15/2006 |
$100
|
$10
|
10
|
| 2/15/2006 |
$100
|
$5
|
20
|
| Total |
$200
|
 |
30
|
What is the average share price?
There are several ways to calculate the average or mean. Â
The Arithmetic mean is the “Sum of the samples divided by the number of samplesâ€.
Arithmetic Mean = (X1 +Â .. + Xn) / n
1. The arithmetic mean of the share price, with each transaction (rate) treated as a sample: Â
There were two transactions (rates), one at $10 per share, and one at $5 per share.
Arithmetic Mean = (10 + 5) / 2 = $7.5 / share (WRONG)
2. The arithmetic mean of the share price, with each share price treated as a sample:
There were 30 shares purchased, 10 shares at $10 per share, and 20 shares at $5 per share.
Arithmetic Mean = (10 * 10 + 5 * 20) / 30 = $6.67 / share (CORRECT)
The Harmonic mean is the “Number of samples divided by the sum of the samples reciprocalsâ€.
Harmonic Mean = n / (1/X1 + … + 1/Xn)
3. The harmonic mean, with each transaction (rate) treated as a sample:There were two transactions (rates), one at $10 per share, and one at $5 per share.
Harmonic Mean = 2 / (1/10 + 1/5) = $6.67 / share (CORRECT)
In finance, the harmonic mean is used to calculate the average cost of shares purchased over a period of time. For example, an investor purchases shares at a rate of $1000 per month for three months. If the spot prices at execution time are as follows: Â
Then the average price the investor paid is $8.926 per share. However, if the investor purchased 1000 shares per month, the arithmetic mean would be used.
The harmonic mean is used to calculate of the average of several rates.