Now, the initial assumption could very well hit a wall.
Either both are or none are.
Holding an asset for N days does not magically flip it from category to the other.
Yes, if the market is overall rising, then active trading should enjoy that overall rise just like buy and hold does.
But then why active trade? Because you think you can do better than passive. That part - the "doing better" part - is zero sum. In fact it's negative sum, because of transaction costs.
then consider just how much shares passive funds move all the time due to continuous rebalancing they do due to their self-imposed mandate. (reminder: etfs hold ~$5T worth of assets.)
One of the big selling points of passive, market weighted ETFs is their low turnover and high tax efficiency. Vanguard’s S&P 500 ETF (VOO) has an annual turnover of 4%, for example. That’s nothing compared to the turnover in an actively traded portfolio.
Sure they do a lot of trading volume to account for inflows and outflows from the ETF. But one of the very nice properties of market weighting is that there is hardly any rebalancing needed as individual assets drift in price.
https://web.stanford.edu/~wfsharpe/art/active/active.htm
That doesn't mean there haven't been long-running active strategies that have worked. But those have overperformed by grabbing returns from other actives underperforming, not the passives.
Let me try to poke some holes in the argument.
1. Market return (M) is a weighted combination of passive (P) and actively managed portfolio (A) returns:
M = (1-w)P+(w)A.
2. Passive investor achieves market return M by holding the whole market, so P = M.
3. To satisfy the equation, A must also be M, regardless of w.
The logical error is in the assumption that P = M. To make this a concrete programming problem: let's say at time t=1, immediately prior to the start of a trading period, a passive investor decides to construct a portfolio. The passive investor makes investment allocations based on the current set of market prices.
Subsequently, how can the passive investor possibly match market returns without w being 0, or the passive investor knowing exactly how the active investors will allocate their holdings? That information lies in the future - one only needs to go though the exercise of simulating market returns on a discrete time basis to realize that the passive investor cannot possibly allocate to achieve exactly market returns.
M[1] = (1-w[1])P[1]+w[1]A[1]
Because all he has to do is do absolutely nothing and he achieves that. The passive investor doesn't make choices, he buys a portfolio that has all the components of the index in the proportions at that point. Then the active traders trade among themselves and the prices move. And now the passive investor still holds all the components in the index at the proportions at t=2 because he hasn't traded, only the assets have changed value. You can observe this in practice. Index funds track their index incredibly well.
If passive investors make worse trades with outsiders than the active investors do, they will underperfom.
Some of the math surrounding the derivation of the weakest forms of EMT also relies on the assumption that everyone has access to the same information, which is patently false in the world we live in. Even retail traders sometimes have an information edge (e.g. working at a biotech company or a specialized industry like semiconductors)