Index investment is whether the average?

“We take the average market (all investors) When are long-term holding and has an index fund”

There is this story.I am also saying things like this.
However, it is not I think this is, not accurate to think about it a little.

I’ll try a simple simulation.

[Prerequisite of model to use in the simulation]
And market is made up of four stock 4 A, B, C, and D
· A, B, C, stock price at some point in the (T0) is the same all D
→ The evenly investment A, B, and CD in the stock price index simple average
· Market capitalization in T0 is, A = 400, B = 300, C = 200, D = 100 (the overall market = 1000)
Index investment is assumed index investment of the following two types of
1. total investment index
2. simple average stock price index investment
Share index of the operation of each one by 10%
→ ratio of active management 80%

It is the Nikkei average TOPIX, the simple average of the “close” in the Nikkei average and the TOPIX index is a representative of the (reference) Japanese stocks, the market capitalization of “close”.

I will try to the simulation of four patterns under the above conditions.
«If the stock small pattern 1 >> market capitalization has risen
«If the pattern 2» stock market capitalization is large rises
«If the stock small pattern 3» market capitalization fell
«If the pattern 4» stock market capitalization is large fell

«If the stock small pattern 1 >> market capitalization has risen

Market average + 10%
Market capitalization index + 10%
Simple average index + 25%
Active + 8.1%

I became such a result.
It is a market capitalization index = market average, but the simple average index is higher than the market average as large as + 25%.And active is below the market average and + 8.1%.
Given in active vs the entire index, [+ 17.5% (index) vs + 8.1% and (active)] is.

«If the pattern 2» stock market capitalization is large rises

Market average + 40%
Market capitalization index + 40%
Simple average index + 25%
Active + 41.9%

Simple average index is far below the market average and + 25% now, active were higher than the market average and + 41.9%.
Given in active vs the entire index, [+ 32.5% (index) vs + 41.9% and (active)] is.

A bonus, I’ll try to verify even if the stock price falls.

«If the stock small pattern 3» market capitalization fell

-5% Market average
Market capitalization index -5%
Simple average index -12.5%
Active -4.1%

It is a market capitalization index = average market as usual, but the simple average index is significantly lower than the market average and -12.5%, active were higher than the market average and -4.1%.
Given in active vs the entire index, [- 8.75% (index) vs -4.1% and (active)] is.

«If the pattern 4» stock market capitalization is large fell

-20% Market average
Market capitalization index -20%
Simple average index -12.5%
Active -20.9%

Simple average index is significantly higher than the market average and -12.5%, active in performance worse than the market average of -20.9%.
Given in active vs the entire index, [- 16.25% (index) vs -20.9% and (active)] is.

Given the results of this simulation, assets of the operator so that the entire 40% + market capitalization of the “market will become + 40%.Passive and because average + 40%, active overall + 40%.Story that “seems to be a little different.

Became so long and …… likely be able to follow the market average in the case of a pure market capitalization index, so far this time.