Let me clarify with an example. A hedge fund manager doesn't beat the S&P 500 consistently every year but when he does, his fund returns 80% vs. the S&P's 10%. Thus, even if he exited all his positions, his returns would still be higher than SPY for the next few years. ( i.e. Disregard annualized performance. I'm talking about multiple on invested capital at the end of say 50 years).

 
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I think you are messing up your math. Annualized performance (you can discuss if compounded, I.e. reinvested returns or not) is a metric that will give you that answer. If a fund underperforms for 10yrs and then has an 80% vs 10% yr, you will still see who “outperforms” based on annualized returns (that is the “lump sum” paid at the end, basically take $100 invested in both, annualized return when looking at the compounded metric is going to tell you which returns more money - that is how the math works). Although, in general, a good actively managed fund doesn’t make it all up in one year, but rather has consistent returns over time (outside of tail risk funds, etc).

Additionally, your example isn’t very likely, a more likely scenario is that a HF or actively managed fund outperforms during big downturns in the s&p and underperforms during outperformance by the s&p. 

What you normally see with actively managed funds (the “good” ones) is better ratio, fewer (and less severe) drawdowns, and uncorrelated to major indices (I.e. diversifying to a portfolio of equities or most major asset classes). 

 

looking at ex US data for passive vs active is an interesting exercise - i think for a lot of economies that cannot be expected to post strong long term secular growth (europe, japan), there is actually a decent case for active management if you have to have exposure to the region

 

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