Dollar cost averaging is a method of investing a certain amount on a regular basis, and it is said that the purchase price can be kept low on average in a changing price. Here, I will illustrate how effective it actually is, using specific examples.

### Change model of stock prices

Here, I define the trend of stock prices into eight simple patterns and actually calculate how low the average cost of each pattern and their total is by using dollar cost averaging.

As a setting here, the first stock price is set at 100 yen, and the change of 10 yen is repeated three times. Then, the end result is four patterns, but it can be divided into 8 patterns in the process of going there.

In dollar cost averaging, the same amount is invested in each of the reserves 1, 2, and 3 in the graph shown above.

This time, we will invest a total of 30,000 yen to verify how much profit or loss will come out at the time of sale.

### Purchased in bulk for the first time

If you first purchase a 100 yen stock in bulk using all 30,000 yen, you will have 300 shares. Therefore, the final profit and loss can be calculated by the amount of change in the stock price x 300 shares.

In addition, if all price movements of these eight patterns can occur with equal probability, the expected value will be the final profit and loss of 0 yen.

(+9000 x 1/8) + (+3000 x 1/8) + (+3000 x 1/8) + (-3000 x 1/8) + +3000 x 1/8) + (-3000 x 1/8) + (-3000 x 1/8) + (-9000 x 1/8) = 0

calculation of the expected value assuming that each of patterns occurs with an equal probability (1/8).

### Using dollar cost averaging

Using dollar cost averaging, the investment amount of 30,000 yen will be divided into three times, and shares will be purchased at a timing of 1,2,3 in reserve by 10,000 yen.

The number of shares purchased is determined by calculating the stock price of 10,000 yen at the timing of each reserve. By combining the number of shares purchased for three times and applying it to the stock price at the time of sale, the sale price can be obtained, so you can see the final profit and loss by looking at the difference between 30,000 yen. It should be noted that, here is calculated by rounding off the final profit and loss.

In addition, if all price movements of these eight patterns can occur with equal probability, the expected value will be the final profit and loss +1 yen. This is the relation of the fraction when rounded, and it is not possible to interpret that the expected value is large.

### Bulk Purchases and dollar cost averaging

Compare the final profit and loss of a bulk purchase with dollar cost averaging.

Bulk purchase | Dollar cost calculation | |

➀ | 9,000 | 5,652 |

② | 3,000 | 167 |

③ | 3,000 | 2,000 |

④ | -3,000 | -3,818 |

⑤ | 3,000 | 4,222 |

⑥ | -3,000 | -2,000 |

⑦ | -3,000 | 250 |

⑧ | -9,000 | -6,472 |

All in all, a bulk purchase is a higher risk and higher return than dollar cost averaging.

The characteristic of the dollar cost astration method seen from this result is that the width of profit and loss (risk) can be reduced. ➀ a simple rise or fall, such as the dollar and ⑧, dollar cost averaging will result in smaller profits and smaller losses.

Since it is difficult to aim for a big profit by dollar cost averaging, there may be an effect that the possibility of profit even a little as shown in ⑦ increases.In terms of whether it will eventually be positive or negative, the probability of ending up with a positive is 1/2 in the case of a bulk purchase, but 5/8 in the dollar cost average method.

### Summary

The profit and loss from the investment when the stock price transitioned randomly was compared with the case of using dollar cost averaging.

As a result, I found that dollar cost averaging has the effect of reducing the margin of profit and loss due to changes in stock prices, and ultimately increased the likeness to make even the slightest profit. However, it also lowers the likely possibility of a large profit, and if you think about it as an expectation, both will not change.

In my opinion, the biggest advantage of using dollar cost averaging is that you can invest whileleaving it alone. The fact that risk is reduced and is likely to end up with a positive result means you don’t have to observe daily stock price movements and predict what will happen in the future. In this embodiment, I assume that all changes in stock prices will move with equal probability, which is exactly equivalent to not predicting a change in stock prices. In other words, it will be left without effort.

Unless you’re a professional investor or a very free man, it’s impossible to understand what’s going on in the world and accurately predict changes in stock prices. In fact, even experts have announced their stock price forecasts and removed them, so I feel barren even trying to predict economic developments.

Since the total amount of population and money in the world continues to increase, I can agree with the opinion that stock prices as a whole will continue to rise, but with the amount of information of ordinary people, it is often not possible to trust the forecast of an increase in the price of individual stock prices. Then I think the better choice would be to invest in dollar cost averaging instead of focusing on tracking changes in stock prices.