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Index funds are (slightly below) average by definition. The index itself defines the average (it's the benchmark that all funds use to measure performance), so

Index funds are (slightly below) average by definition. The index itself defines the average (it's the benchmark that all funds use to measure performance), so a fund perfectly tracking the index has almost zero alpha. The "almost" is whatever fees the index fund charges, which lead the funds returns to be slightly below the average if they otherwise track perfectly. Edit: Just to add, by the above definition, where you take the total return on the index as the average, most investors do significantly worse than average, a few do a lot better than average and investors in index funds make almost exactly the average.

soVeryTired 8y ago
But the parent's comment was "you cannot beat the market on average (since the index funds are the average)". If you take a particular index fund to define an average then this just asserts that you can't beat a particular index. GP might be trying to argue that alpha generation is a zero-sum game, but alpha and beta are notoriously slippery concepts. If you want to define beta as the index return, I think you're going to have a hard time convincing me that alpha is zero sum without assuming the EMH or something similar.
- throwawaymath 8y ago
  Yes, the point you're referencing is wrong. Your last point is correct. We can't extrapolate the fact that indices are designed to return averages of some market to the claim that indices can't be beaten without assuming the EMH first.
- kgwgk 8y ago
  > alpha generation is a zero-sum game This is a mathematical fact. Let’s say you do better than the market because you deviate from the market weights. For each position that you have, relative to the market, there is someone somewhere that holds the complementary position. Because the agregate of all the positions is the market portfolio, by definition.
- lmm 8y ago
  > GP might be trying to argue that alpha generation is a zero-sum game, but alpha and beta are notoriously slippery concepts. If you want to define beta as the index return, I think you're going to have a hard time convincing me that alpha is zero sum without assuming the EMH or something similar. Alpha is zero sum because the total return of the market is the total return of the market. So the money-weighted average return to stockholders must equal the money-weighted average growth of stocks.

soVeryTired 8y ago

But the parent's comment was "you cannot beat the market on average (since the index funds are the average)". If you take a particular index fund to define an average then this just asserts that you can't beat a particular index. GP might be trying to argue that alpha generation is a zero-sum game, but alpha and beta are notoriously slippery concepts. If you want to define beta as the index return, I think you're going to have a hard time convincing me that alpha is zero sum without assuming the EMH or something similar.

throwawaymath 8y ago
Yes, the point you're referencing is wrong. Your last point is correct. We can't extrapolate the fact that indices are designed to return averages of some market to the claim that indices can't be beaten without assuming the EMH first.
kgwgk 8y ago
> alpha generation is a zero-sum game This is a mathematical fact. Let’s say you do better than the market because you deviate from the market weights. For each position that you have, relative to the market, there is someone somewhere that holds the complementary position. Because the agregate of all the positions is the market portfolio, by definition.
lmm 8y ago
> GP might be trying to argue that alpha generation is a zero-sum game, but alpha and beta are notoriously slippery concepts. If you want to define beta as the index return, I think you're going to have a hard time convincing me that alpha is zero sum without assuming the EMH or something similar. Alpha is zero sum because the total return of the market is the total return of the market. So the money-weighted average return to stockholders must equal the money-weighted average growth of stocks.