Investors using dollar-cost averaging (DCA) often want to know exactly what average price they’re paying per share. Because investments are made over time at different prices, it can be easy to lose track of what’s going on.

Formula and Calculation Breakdown

To calculate the average of a ratio like price per share, financial experts often use the harmonic mean, whose formula is shown here:

It looks intimidating at first, but the math behind it is straightforward.

In this formula, H is the average price-per-share paid over a period of time. n is the number of periods (in this case,  months) and x1, x2, x3, x4….xn are the various prices-per-share actually paid. Because the Xs in this equation are ratios (price per share) we need to use the harmonic mean to calculate the correct average amount.

Let’s take a simple hypothetical example. Say you  have $3,000 to invest, but are concerned about putting the money in the market all at once. Instead, you decide to invest $1,000 per month for the next three months.

Right now the ETF you’re interested in buying is trading at $50 per share, so with your $1,000 you buy 20 shares. Next month when you check back, the ETF is trading for $40 per share. Since we didn’t invest all at once you can buy more shares with your $1,000. So this month at $40 per share we buy 25 shares with our $1,000.

Finally when you check back again in our final month, the price has stabilized at $40 per share so you buy another 25 shares. So you’re fully invested, but what average price per share did you actually pay? To figure this out we can use the formula above.

You made three transactions at different prices, so this formula helps determine what average price you paid using only the price-per-share in the denominator of the calculation. The number in the numerator is the number of months we invested, in this case three. This calculated average number also corresponds with what we know.

You paid $3,000 over three months and as a result you have 70 shares (20+25+25),which is $3,000/70 or $42.86 per share.

Investing, simplified

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