Why will the holder of a broad-based index fund, by definition, achieve the average return for the market? A Random Walk Down Wall Street (2015 11 ed, but an 2019 ed. is upcoming). pp. 271 Bottom – 272 Top.


    All “smart beta” strategies represent active management rather than indexing. Capitalization-weighted portfolios are the market. If you believe a subset of securities will give you superior returns, you are counting on some “dumb” investors to hold portfolios producing poorer returns. Some “smart beta” advocates have been quite explicit in suggesting who these dumb investors might be. They claim that the investors in traditional capitalization index funds are the dumb beta investors, since by holding the broad index they will be holding a number of overvalued growth stocks. But that argument must be false. $\color{red}{\text{The holder of a broad-based index fund will by definition achieve the average return for the market.}}$ If “smart beta” funds generate above average returns, it can’t be at the expense of traditional index-fund investors—it must be at the expense of all active managers who do not hold the market portfolio.


For simplicity, suppose that a country’s economy has only 2 types of ETF: 

i. 1 broad-based, whose return I'll call $r_B$ + 

ii. 1 Smart Beta one that's a subset of securities without some (overvalued) growth stocks, whose return must be higher than the broad-based fund's (say $2\% + r_B$).

Then the average return of ETFs is $1\% + r_B$, which nobody achieves (as my imaginary economy has only 2 types of ETF). 


So how's the red sentence true? 
How's the bolded sentence true? Wouldn’t fund ii's higher return 'be at the expense of traditional index-fund investors'?
1. The Red Sentence

Because it is market-weighted, the market portfolio is the average of what's going on. It is the default scenario, in which you don't need to trade to maintain your asset allocation.

As soon as someone trades and diverge from this default scenario, one of the two parties will lose, relative to the market (they can both be better off, but one of them will underperform).

In addition, your setup with two funds cannot work. The smart beta index is going to trade. With whom? Not with the market-weighted fund: he does not need to trade (the weights basically adjust all by themselves with the price changes, he only needs to reinvest dividends). Therefore if there are two funds only in your universe, and one of them holds the market portfolio, then the second either holds nothing, or he holds the market portfolio as well. If he holds any other security, then the market portfolio funds cannot hold all securities with market-weights.

2. The Bold Sentence

I think this sentence is wrong. It confuses return and performance. Performance is the efficiency of the process which generates return from risk. Basically, you input risk, and you output return. That's what investing is all about.

The claim behind smart betas is that the market portfolio is not correctly diversified. Basically, you get exposure for some risk without being paid for it. This can be shown quite intuitively : equally-weighted portfolios overperform market-cap weighted portfolios (Platen and Rendek, 2010, Platen and Rendek, 2012). That's because it gives you exposure non non-rewarded risks!

To sum up: the market-weighted portfolio does give you the average return. It can be outperformed by other strategies. Your example is too simple to work.