[Illustration] Verification of the effect of time variance of investment (dollar cost average method)

Financial Planner

“Time dispersion” is one of the ways to reduce the risk of investment. It is also called the dollar cost ad average method. I will actually illustrate through simulation what kind of profit and loss will occur when stock prices move against this method realized by investing.

The difference between a bulk purchase for a simple price movement and a new one is explained in the following article.

This time, I would like to look at the effect of the new work and the profit and loss of the operation from a viewpoint a little different from the above article.

Effect of time variance “build-up”

In this simulation, the first stock price is set at about 100 yen per share, assuming a movement to return to the first stock price at the end after a change of within plus or minus 20 yen, and in that price movement, I will set it up for three years by 10,000 yen each month. In other words, the investment amount will be 360,000 yen in total, and if you buy it in bulk and sell it in bulk at the end, the profit and loss will be 0.

We will consider what kind of profit and loss will ultimately be caused by the fresh effect, and what kind of profit and loss will occur during the period.

Price Movement Pattern 1: Sign Curve

As shown below, let’s assume a price movement like a sign curve that comes down after going up and returns to the end.

The following table summarizes the stock price at the time of each purchase of 36 times and the number of shares purchased accordingly.

Number of purchasesStockNumber of shares that can
be bought for 10,000 yen
Amount of investmentValue of the ratingIncome
1100.0100.010,000.10,000.0
2101.898.320,00020,178178
3103.596.630,00030,520520
4105.195.140,00040,995995
5106.693.850,00051,5601,560
6107.892.860,00062,1592,159
7108.891.970,00072,7292,729
8109.591.380,00083,2033,203
9109.991.090,00093,5103,510
10110.090.9100,000103,5853,585
11109.891.1110,000113,3673,367
12109.291.6120,000122,8062,806
13108.492.3130,000131,8641,864
14107.393.2140,000140,519519
15105.994.4150,000148,767-1,233
16104.495.8160,000156,622-3,378
17102.797.3170,000164,119-5,881
18101.099.0180,000171,313-8,687
1999.2100.8190,000178,281-11,719
2097.4102.6200,000185,115-14,885
21.95.8104.4210,000191,923-18,077
2294.2106.1220,000198,828-21,172
2392.9107.7230,000205,959-24,041
2491.7109.0240,000213,451-26,549
2590.9110.1250,000221,435-28,565
2690.3110.8260,000230,036-29,964
2790.0111.1270,000239,365-30,635
2890.1111.0280,000249,513-30,487
2990.4110.6290,000260,545-29,455
3091.1109.7300,000272,499-27,501
3192.1108.6310,000285,375-24,625
3293.3107.2320,000299,140-20,860
3394.7105.6330,000313,721-16,279
3496.3103.8340,000329,010-10,990
3598.0102.0350,000344,867-5,133
3699.8100.2360,000361,1191,119
The last value100.0360,000361,7761,776

In the first ups and downs, we are profitable, but then if we fall a little past the peak, we are beginning to lose money. Profits have been positive in the end somehow, but the investment amount is about 0.5% of 360,000 yen. Because there is an error such as rounding at the time of calculation, it is good to think that the last plus is almost nothing.

When the profit and loss at the time of the build-up is reflected in the graph of the price movement, it looks like the following figure.

In fact, it will be painful in the feelings of the person who is investing because the operation situation is longer in the negative period than the positive period. In a phase that continues to decline, I think it is important to have a mental that continues to endure believing that it will return to the original stock price.

Even if you know that it is good because you can buy a lot of shares only when the stock price is going down, which is commonly said, if you see a large loss, you may not be able to wipe your anxiety and stop investing. However, if the stock price returns in the end in this way, stopping investment there is the worst possible scenario of the biggest loss.

Price Movement Pattern 2: Negative Sign Curve

As shown below, assume a price movement that is the reverse phase of the sine curve.

The following table summarizes the stock price at the time of each purchase of 36 times and the number of shares purchased accordingly.

Number of purchasesStockNumber of shares that can
be bought for 10,000 yen
Amount of investmentValue of the ratingIncome
1100.0100.010,000.10,000.0
298.2101.820,00019,822-178
396.5103.630,00029,474-526
494.9105.440,00038,982-1,018
593.4107.050,00048,387-1,613
692.2108.560,00057,746-2,254
791.2109.670,00067,126-2,874
890.5110.580,00076,605-3,395
990.1111.090,00086,263-3,737
1090.0111.1100,00096,178-3,822
1190.2110.8110,000106,425-3,575
1290.8110.2120,000117,066-2,934
1391.6109.1130,000128,146-1,854
1492.7107.8140,000139,692-308
1594.1106.3150,000151,7081,708
1695.6104.6160,000164,1724,172
1797.3102.8170,000177,0377,037
1899.0101.0180,000190,23410,234
19100.899.2190,000203,66813,668
20102.697.5200,000217,22817,228
21104.295.9210,000230,78620,786
22105.894.5220,000244,20424,204
23107.193.3230,000257,34227,342
24108.392.4240,000270,05830,058
25109.191.6250,000282,21932,219
26109.791.1260,000293,70333,703
27110.090.9270,000304,40834,408
28109.991.0280,000314,25434,254
29109.691.3290,000323,18833,188
30108.991.8300,000331,18831,188
31107.992.7310,000338,26228,262
32106.793.7320,000344,45424,454
33105.395.0330,000349,84219,842
34103.796.5340,000354,53414,534
35102.098.1350,000358,6708,670
36100.299.8360,000362,4182,418
The last value100.0360,000362,4181,760

We lost in the first phase of the decline, but when we recover after that, we are starting to make a profit. As with Pattern 1, the final investment amount is about 0.5% positive for 360,000 yen.

When the profit and loss at the time of the build up is reflected in the graph of the price movement, it looks like the following figure.

In the first phase of stock price sinking, even if the stock price does not return to 100 yen, the operating situation has been positive from the part of about 93 yen. It can be said that this is a big effect by the build up.

If the price eventually declines to the original stock price, you won’t get much profit, but if the stock price can sell near its peak, you’ll get a big profit.

Price Movement Pattern 3: Cosine Curve

Let’s assume the case of the price movement which becomes a cosine curve as shown below.

The following table summarizes the stock price at the time of each purchase of 36 times and the number of shares purchased accordingly.

Number of purchasesStockNumber of shares that can
be bought for 10,000 yen
Amount of investmentValue of the ratingIncome
1110.090.910,000.10,000.0
2109.891.020,00019,985-15
3109.491.430,00029,899-101
4108.692.140,00039,688-312
5107.593.050,00049,305-695
6106.394.160,00058,714-1,286
7104.895.570,00067,891-2,109
8103.197.080,00076,827-3,173
9101.498.690,00085,530-4,470
1099.6100.4100,00094,024-5,976
1197.8102.2110,000102,350-7,650
1296.1104.0120,000110,568-9,432
1394.5105.8130,000118,752-11,248
1493.1107.4140,000126,987-13,013
1592.0108.8150,000135,371-14,629
1691.0109.9160,000144,004-15,996
1790.4110.6170,000152,989-17,011
1890.0111.1180,000162,423-17,577
1990.0111.1190,000172,394-17,606
2090.3110.7200,000182,973-17,027
2190.9110.0210,000194,211-15,789
2291.8108.9220,000206,134-13,866
2393.0107.5230,000218,739-11,261
2494.4105.9240,000231,995-8,005
2596.0104.2250,000245,839-4,161
2697.6102.4260,000260,176176
2799.4100.6270,000274,8874,887
28101.298.8280,000289,8279,827
29103.097.1290,000304,83414,834
30104.695.6300,000319,73219,732
31106.194.2310,000334,33724,337
32107.493.1320,000348,46928,469
33108.592.2330,000361,95431,954
34109.391.5340,000374,63234,632
35109.891.1350,000386,36536,365
36110.090.9360,000397,04137,041
The last value110.0360,000397,04737,047

During the first half of the decline, losses increased to a maximum of 10% of the investment amount, but the subsequent recovery in stock prices resulted in a profit of about 10%.

When the profit and loss at the time of the build up is reflected in the graph of the price movement, it looks like the following figure.

When purchased in bulk for the first time, the stock price is always lower than the first value, so there is always a loss, but even if the stock price does not completely recover due to the effect of the build up, profit and loss has changed to positive at the stage of about 97 yen.

Price Movement Pattern 4: Minus Cosine Curve

Let’s assume a price movement that is the reverse phase of the cosine curve, as shown below.

The following table summarizes the stock price at the time of each purchase of 36 times and the number of shares purchased accordingly.

Number of purchasesStockNumber of shares that can
be bought for 10,000 yen
Amount of investmentValue of the ratingIncome
190.0111.110,000.10,000.0
290.2110.920,00020,01818
390.6110.330,00030,123123
491.4109.440,00040,380380
592.5108.250,00050,843843
693.7106.760,00061,5521,552
795.2105.070,00072,5302,530
896.9103.280,00083,7803,780
998.6101.490,00095,2865,286
10100.499.6100,000107,0117,011
11102.297.9110,000118,9008,900
12103.996.3120,000130,88210,882
13105.594.8130,000142,87212,872
14106.993.6140,000154,77514,775
15108.092.6150,000166,49216,492
16109.091.8160,000177,92317,923
17109.691.2170,000188,97018,970
18110.090.9180,000199,54619,546
19110.090.9190,000209,57619,576
20109.791.2200,000219,00019,000
21109.191.7210,000227,77917,779
22108.292.5220,000235,89915,899
23107.093.5230,000243,36613,366
24105.694.7240,000250,21710,217
25104.096.1250,000256,5126,512
26102.497.7260,000262,3382,338
27100.699.4270,000267,807-2,193
2898.8101.2280,000273,049-6,951
2997.0103.0290,000278,218-11,782
3095.4104.8300,000283,476-16,524
3193.9106.5310,000288,998-21,002
3292.6108.0320,000294,961-25,039
3391.5109.3330,000301,539-28,461
3490.7110.3340,000308,893-31,107
3590.2110.9350,000317,172-32,828
3690.0111.1360,000326,496-33,504
The last value90.0360,000326,490-33,510

Contrary to Pattern 3, profits of up to 10% of the investment amount were generated in the first half, but in the end there was a loss of less than 10%.

When the profit and loss at the time of the build up is reflected in the graph of the price movement, it looks like the following figure.

When purchasing in bulk, the operating profit and loss is positive because it always has a higher value than the first stock price, but in the build up, the profit and loss are negative at the stage where the stock price is about 101 yen.

Summary

In order to verify the effect of build up investment (time variance) (dollar cost average method), I examined the patterns of four price movements using tri-functions.

In this four patterns where the first and last stock prices are the same, focusing only on the final profit and loss results in the following results:

Final gains and losses
Pattern 11,776
Pattern 21,760
Pattern 337,047
Pattern 4-33,510

Considering the expected value as these four patterns occur with an equal probability, the profit and loss will be +1,768 yen for the case of the build-up purchase. Considering the ratio of the investment amount of 360,000 yen, it is only about 0.5%, and considering that it also includes errors such as rounding at the time of calculation, it is not considered to be a big difference. From the results of the previous article, I have found that there is no significant difference in expectations when comparing bulk purchases.

The most convenient scenario for a fresh case is the price movement that rises after falling like pattern 3. In order to make the most of such a sharp effect, it is not to quit because it is scared in the falling phase. It is important to think of the decline as an opportunity to prepare for a subsequent backlash. Even if it does notrecover to the original stock price after the decline phase, you will understand in this illustration that the operating profit and loss will be positive if it recovers even a little.