Why Equal-Share Purchases Average KRW 7,500 but Equal-Amount Purchases Average KRW 6,667 When Investing KRW 120,000 in Two Installments
Why Equal-Share Purchases Average KRW 7,500 but Equal-Amount Purchases Average KRW 6,667 When Investing KRW 120,000 in Two Installments
Why Equal-Share Purchases Average KRW 7,500 but Equal-Amount Purchases Average KRW 6,667 When Investing KRW 120,000 in Two Installments
If a stock's price falls from KRW 10,000 to KRW 5,000 and a total of KRW 120,000 is invested in two installments, buying the same number of shares each time produces an average purchase price of KRW 7,500, while investing the same amount each time produces an average of approximately KRW 6,667. Although the total investment is identical, the number of shares purchased at the lower price differs. The calculations below are hypothetical examples that exclude fees and taxes.
1. Why Does the Average Purchase Price Differ When the Total Investment Is the Same KRW 120,000?
The average purchase price is calculated by dividing the total amount spent on shares by the total number of shares held. Therefore, even when the total investment is the same, acquiring more shares results in a lower average purchase price.
The basic formula for calculating the average purchase price is as follows.
Average purchase price = Total purchase amount ÷ Total number of shares purchased
For this comparison, assume that the same stock is purchased twice.
Purchase price for transaction 1: KRW 10,000
Purchase price for transaction 2: KRW 5,000
Total investment: KRW 120,000
Number of purchases: 2
Trading fees and taxes: Excluded
Both methods use the same assumption that the stock price falls by half. The difference lies in what is kept constant when making each purchase.
With equal-share purchasing, the number of shares bought each time remains fixed. With equal-amount purchasing, the amount invested each time remains fixed, allowing the investor to acquire more shares as the stock price falls.
2. What Is the Average Purchase Price When Buying 8 Shares Each Time?
If 8 shares are purchased at KRW 10,000 and another 8 shares at KRW 5,000, the investor holds a total of 16 shares, with an average purchase price of KRW 7,500. Because the same number of shares is purchased at each price, the average purchase price equals the arithmetic mean of the two purchase prices.
Hypothetical Example A · Equal-Share Purchasing
| Item | Purchase 1 | Purchase 2 |
|---|---|---|
| Price per share | KRW 10,000 | KRW 5,000 |
| Shares purchased | 8 shares | 8 shares |
| Purchase amount | KRW 80,000 | KRW 40,000 |
The amounts spent on the two purchases differ, at KRW 80,000 and KRW 40,000, but their combined total is KRW 120,000.
Author's calculations
Total investment = KRW 80,000 + KRW 40,000 = KRW 120,000
Total shares held = 8 shares + 8 shares = 16 shares
Average purchase price = KRW 120,000 ÷ 16 shares = KRW 7,500
When buying the same number of shares each time, more money is spent on the higher-priced purchase, transaction 1. In this example, 2 out of every 3 parts of the total investment was committed when the price per share was KRW 10,000.
3. What Is the Average Purchase Price When Investing KRW 60,000 Each Time?
Investing KRW 60,000 at KRW 10,000 and another KRW 60,000 at KRW 5,000 results in purchases of 6 shares and 12 shares, respectively. The investor therefore holds a total of 18 shares, producing an average purchase price of approximately KRW 6,667.
Hypothetical Example B · Equal-Amount Purchasing
| Item | Purchase 1 | Purchase 2 |
|---|---|---|
| Price per share | KRW 10,000 | KRW 5,000 |
| Purchase amount | KRW 60,000 | KRW 60,000 |
| Shares purchased | 6 shares | 12 shares |
Author's calculations
Total investment = KRW 60,000 + KRW 60,000 = KRW 120,000
Total shares held = 6 shares + 12 shares = 18 shares
Average purchase price = KRW 120,000 ÷ 18 shares = KRW 6,666.67
When investing the same amount each time, the investor purchases twice as many shares after the price falls to KRW 5,000 as in the first transaction.
The U.S. Securities and Exchange Commission's investor education website also explains in Investor.gov's explanation of dollar-cost averaging that investing a fixed amount regularly results in purchasing more shares when prices are lower.
However, dollar-cost averaging involves investing a fixed amount according to a regular schedule, including predetermined investment timing. It should be distinguished from this calculation example, which uses two prices selected in advance.
4. Exactly How Much Do the Average Purchase Prices Differ?
Although both methods invest the same KRW 120,000, equal-amount purchasing acquires 2 more shares than equal-share purchasing and produces an average purchase price approximately KRW 833 lower. This difference does not arise from investing more money. It results from a different allocation of share purchases at the lower price.
| Comparison | Equal Shares | Equal Amounts |
|---|---|---|
| Total investment | KRW 120,000 | KRW 120,000 |
| Purchase 1 | 8 shares | 6 shares |
| Purchase 2 | 8 shares | 12 shares |
| Total shares held | 16 shares | 18 shares |
| Average purchase price | KRW 7,500 | Approximately KRW 6,667 |
Comparison of average purchase prices with the same KRW 120,000 investment
Equal shares: Average purchase price KRW 7,500.0
Equal amounts: Average purchase price KRW 6,700.0
Hypothetical price movement from KRW 10,000 to KRW 5,000; fees and taxes excluded
The detailed calculations are as follows.
Difference in average purchase prices = KRW 7,500 - KRW 6,666.67 = Approximately KRW 833.33
Reduction in average purchase price compared with equal-share purchasing = Approximately 11.11%
Difference in shares held = 18 shares - 16 shares = 2 shares
Increase in shares held = 2 shares ÷ 16 shares × 100 = 12.5%
The total investment is exactly the same under both methods.
However, when the total investment is held constant across the same two prices and fees and fractional-share restrictions are excluded, the average purchase price under equal-amount purchasing is the harmonic mean, while under equal-share purchasing it is the arithmetic mean. Therefore, regardless of whether prices rise or fall between the two purchases, the average purchase price under equal-amount purchasing is lower than or equal to that under equal-share purchasing. The two averages are equal only when both prices are identical. This mathematical relationship does not mean that dollar-cost averaging necessarily delivers a higher investment return than lump-sum investing, or vice versa.
5. Does a Lower Average Purchase Price Actually Reduce Investment Losses?
A lower average purchase price alone is not enough to conclude that investment losses have decreased. Actual gains or losses can be determined only by comparing the total purchase cost with the investment's current market value.
In the hypothetical examples above, assume that the stock price is KRW 5,000 immediately after the second purchase.
Under equal-share purchasing, the investor holds 16 shares, giving the position a market value of KRW 80,000. Under equal-amount purchasing, the investor holds 18 shares, giving the position a market value of KRW 90,000.
| Item | Equal Shares | Equal Amounts |
|---|---|---|
| Total investment | KRW 120,000 | KRW 120,000 |
| Market value | KRW 80,000 | KRW 90,000 |
| Unrealized loss | -KRW 40,000 | -KRW 30,000 |
| Return | -33.33% | -25.00% |
In this calculation, the unrealized loss under equal-amount purchasing is KRW 10,000 smaller. This is because the investor acquires 2 additional shares at the lower price without increasing the total investment.
The U.S. Financial Industry Regulatory Authority, FINRA, also explains in its 2026-05-19 guide to the advantages and disadvantages of dollar-cost averaging that spreading purchases over time can help manage investment timing risk, but investors may miss opportunities to benefit from rising markets while holding cash or incur additional transaction costs.
6. How Can You Calculate Your Own Average Purchase Price When Buying in Installments?
To calculate the results of purchases made in installments, record the actual purchase price and number of shares acquired in each transaction. Then divide the total amount invested by the total number of shares purchased. Even when investing the same amount each time, the calculation must use actual execution prices and the number of shares that could be purchased to produce an accurate average purchase price.
Follow these steps.
1. Check the price per share for each purchase.
2. Record the actual number of shares purchased in each transaction.
3. Calculate the amount invested in each transaction by multiplying the purchase price by the number of shares.
4. Add together all purchase amounts and all share quantities separately.
5. Divide the total purchase amount by the total number of shares held.
In actual trading, the results may be affected by whether fractional-share purchases are supported, transaction fees, currency conversion costs, and order execution prices.
In particular, placing an order worth KRW 60,000 does not necessarily mean that exactly KRW 60,000 will be executed. Where only whole shares can be traded, some cash may remain uninvested depending on the number of shares available for purchase.
Therefore, when comparing investment plans, it is advisable to consider not only the average purchase price but also the amount actually invested, remaining cash, and total shares held.
The central lesson from this KRW 120,000 installment-purchase example is straightforward. Equal-share purchasing keeps the number of shares constant, while equal-amount purchasing keeps the investment amount constant. When stock prices are falling, investing equal amounts can result in acquiring more shares at lower prices. However, which method ultimately produces better investment performance depends on subsequent price movements and actual trading conditions.
※ This article is provided for informational purposes to help readers understand market behavior. It is not a recommendation to invest in any particular security or asset. Readers are responsible for their own investment decisions.