[ptype]

This is the case of most market cap indices. There is no problem with that unless the history is revised. You could replicate the same performance in your own stock account. (Not sure what you mean by "without realising losses"?)

[brudgers]

Dow Jones 'performance' is based on a price-weighted average. If a $2 per share stock goes to $1, $200 per share stock going to $201 offsets the loss.

If $400 were allocated equally among the two stocks, an actual investor would lose 25% ($100) while the Dow showed no movement.

[ptype]

Yes, so you should not allocate the $400 equally across the shares to match the performance of the index. You should buy an equal number of shares of each stock. It may not be a greatly constructed index by modern standards but to my understanding you can in theory get the same performance yourself.

[brudgers]

Buying an equal number of shares does not track the DJIA either. Apple closed at 126.6 the day it replaced ATT. ATT closed at 33.48.

[ptype]

I struggle to see why that is a problem? You will need to rebalance the portfolio, yes.

[brudgers]

The DJIA replaced each share of ATT with a share of Apple on a ledger. Without additional investment or buying and selling other assets, there's no way to replicate that in a portfolio due to the difference in share price. Essentially, the DJIA pumped in an ~300% increase in equity value on the ATT shares...or divided among thirty companies a 10% profit.