Forget dollar cost averaging. This is value averaging

Chanced upon this term called value averaging while reading The Four Pillars of Investing by William Bernstein. The man credited with value averaging Michael Edleson, introduced in his book with the same name. Dollar cost averaging helps you buy more when price is low, and less when the price is high. Value cost averaging claims to be able to do it even better.

Suppose I have $1,200 to invest into an index fund. Using dollar cost averaging, I might choose to put in $100 every month over the course of 12 months. Here is a hypothetical scenario.

Month
Price
Number of units
1
10
10
2
20
5
3
25
4
4
20
5
5
10
10
6
25
4
7
20
5
8
20
5
9
10
10
10
5
20
11
5
20
12
20
5

The average price over the one year is 15.83, and the total units bought is 103. If you had simply used $1,200 to buy the units at 15.83, you would only have bought 76 units ($1,200 / 15.83 = 75.79).

What is value averaging?

Value averaging is different in that you do not put in the asme $100 every month. However, you would make the total value of your investments be equal to $100 in the first month, $200 in the first month, and so on.

Using the example, in the first month, we bought 10 units at $10 each. Coming to the second month, these 10 units would be worth $200 ($20 x 10 units). Since the total value is now $200, we do not purchase any shares this period. In the third period, my current holdings of 10 units is now worth $250. Since the total value of my shares need to be $300 in my third month, I will buy 2 units of shares at $25 each, making a total of $300 in value (the original $250 + $50 from 2 units purchased).

If we were to use value averaging, this would be the replicated table.


Month
Price
Existing units
Existing value
Required value
Required top up
Units to buy
Total units now
Total value now
1
10
0
0
100
100
10
10
100
2
20
10
200
200
0
0
10
200
3
25
10
250
300
50
2
12
300
4
20
12
240
400
160
8
20
400
5
10
20
200
500
300
30
50
500
6
25
50
1,250
600
0
0
50
1,250
7
20
50
1,000
700
0
0
50
1,000
8
20
50
1,000
800
0
0
50
1,000
9
10
50
500
900
400
40
90
900
10
5
90
450
1,000
550
110
200
1,000
11
5
200
1,000
1,100
100
20
220
1,100
12
20
220
4,400
1,200
0
0
220
4,400

Using this method instead, the total units bought would have been 220. This is even higher as compared to 103 (by dollar cost averaging).

An alternative to dollar cost averaging

Evidently, the calculations might be a little messy, given that numbers will not be so nice in the market. Personally, I think it is an interesting concept, but might be a little complicated for some. Feel free to comment if you need any clarifications, I will be happy to explain!
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19 February 2016 at 08:25 delete

Hi Jason,

I received your email this morning, but couldn't find it when I wanted to reply it. If I remember correctly, your question was about how do we know decide on how much is the increment amount?

It is a good question, and I had to do some additional research on it. According to the Bogleheads wiki page, the increment depends on how much money you want to have at the end of your investment period. For instance, if you want to have $10,000 at the end of 5 years, then you will calculate out an increment amount based on that. Yes, it is very formula based.

This is the formula given, Vt = C * t * (1+R)t, where we will set R=(r+g)/2. These are the rest of the definitions:

t = Time period (can be months, quarters, years, etc.)
Vt = Target value of investment at time period t
C = Target initial contribution per period
r = Expected rate of growth per period of investment
g = Expected rate of growth per period of contribution
R = Average rate of growth of investment and contribution

In our case, r and g should be the same number, which means that R is also the same as r and g. It should be the long run expected return of your portfolio. You can find the full explanation in this very well written wiki page: https://www.bogleheads.org/wiki/Value_averaging.

I understand that it might be calculative, and more tedious that simple Dollar Cost Averaging. If it was me, I would simply use the increment as the amount I would have put into DCA.

In the blog post, that would have given a cost of $1,660, which is slightly higher than the $1,200 for DCA. However, the average cost for each unit is $7.54 instead of $15.83 for DCA.

Hope it clarifies!

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