Anna and Bob run active mutual funds; Carol runs a passive index fund and David runs a passive ETF. Suppose they are the only 4 participants in the market. If Anna outperforms the market, it must be the case that:

1. David underperforms the market

2. All of B, C, D underperform the market

3. Carol underperforms the market

4. Bob underperforms the market

Never mind. I figured it out. It's #4; Bob underperforms the market.

Explaination: if any active investor in any market earns higher returns than a passive index fund, those returns must be at the expense of another active investor.