 Dollar Cost Averaging - Maple Help

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Dollar Cost Averaging

Main Concept

Dollar cost averaging is a method of investing in the stock market that minimizes risk and is based on simple statistics. The idea behind this technique is to purchase a fixed dollar amount of stocks at regular intervals rather than all at one time. The idea is that when the stock is cheaper, more stock will be bought for the same price and when the cost is higher, less stock will be bought. The best way to learn about dollar cost averaging is through examples. Example 1

Suppose Alice has $1000 that she wants to invest in stocks which currently cost$10 per share. She will either invest it as a lump-sum (all at once), or she will try dollar cost averaging by buying stocks each quarter (4 times a year). If she invests it all right away, she will purchase $1000 ÷$10 = 100 shares. Suppose that at the end of the year each share is now worth $16 for a profit of$600.

If instead she used dollar cost averaging, she would at first buy $1000 ÷ 4 =$250 worth of stocks at $10 a share for 25 shares. Now suppose that after the first quarter, the stock is worth$5. She still buys $250 worth of shares, but this time it amounts to$250 ÷ $5 = 50 shares. At the next quarter the stock returns to$10 a share, and so she again buys 25 shares. At the final quarter stocks jump to $16 per share and she buys$250 worth, which amounts to $250 ÷$16 =$15.625$ shares. She thus owns 25 + 50 + 25 + $15.625$ = 1$15.625$ total shares which are currently worth $16 each, so their net worth is 1$15.625$ ×$16 = $1850 and so she has a$850 profit - even higher than the lump-sum method!

 Current After ${\mathbf{1}}^{\mathbf{st}}$ Quarter After ${\mathbf{2}}^{\mathbf{nd}}$ Quarter After ${\mathbf{3}}^{\mathbf{rd}}$ Quarter $10$5 $10$16

Of course, dollar cost averaging does not always produce a higher profit. Typically, dollar cost averaging can be more effective if the market is quite volatile, whereas if the market is expected to have steady and consistent growth with low volatility then the lump sum method may be better. Example 2

Consider the same example as above, except this time the share value at the end of each quarter is given by

 Current After ${\mathbf{1}}^{\mathbf{st}}$ Quarter After ${\mathbf{2}}^{\mathbf{nd}}$ Quarter After ${\mathbf{3}}^{\mathbf{rd}}$ Quarter $10$12.50 $12.50$16

It is clear that the lump-sum method yields the same profit of $600, but what about the dollar cost averaging method? Immediately Bob would buy 25 shares at$10 per share. At the end of the first and second quarters, he buys 20 shares at $12.50 apiece for$250 in each case. In the final quarter, the price jumps to $16 per share and for that price he can buy $15.625$ shares. At the end of the year, Bob now owns 25 + 20 + 20 + 15.625 = 80.625 shares which is worth$16 × 80.625 = $$1290$, which is not as high a profit as the lump-sum method would have given him, but it's still a sizeable profit. The dollar cost averaging method is clearly not always superior to the lump-sum method, but it does reduce some of the effects of fluctuations in the market. Statistically, for a market which is 50% likely to go up or down, the dollar cost averaging method, on average, has a higher return than the lump-sum method. However, in an increasing market, the lump-sum method usually has a higher return but can suffer from volatility. The demonstration below illustrates the difference between the lump-sum and dollar cost averaging methods. Notice that when the lump-sum method loses money, the averaging method usually does not lose as much money. In this way the averaging method reduces the variance of the potential return. Note that because there are assumptions in this model, it is not guaranteed to be reflective of real life. This model operates under the assumptions that 1) No commission is charged for buy/selling stocks. 2) The market is simulated by geometric Brownian motion. 3) The market is volatile but tends to increase by about 10% over 50 years. The markers indicate when you bought stock according to the dollar cost averaging settings. Risk Level High RiskMedium RiskLow Risk Buying Frequency times per year Contribution Amount$ Length of Investment years

Lump-sum

 Total Invested $Final Return$ Net Profit $Dollar cost averaging  Total Invested$ Final Return $Net Profit$ More MathApps