This morning’s Wall Street Journal described how “a $1.4 billion ETF gold rush” supposedly has disturbed the pricing of mining stocks around the world. $1.4 billion turns out to be the incremental cash flow into a single exchange-traded fund designed to track an index of the gold mining industry, including some relatively small-capitalization companies. These flows, it is argued, are another illustration of how passive management is disrupting market efficiency and creating a bubble, the economic effects of which some commentators consider to be even worse than Marxism.
I have no opinion on whether there is a bubble in gold shares at the moment; having one would require a knowledge of these stocks’ fundamental valuations relative to their market prices. But the bubble, if there is one, has nothing to do with passive management and is only tangentially related to the ETF in question. The bubble, if there is one, is being inflated by investors who’ve decided that they want to increase their exposure to gold.
If you doubt this, consider what would happen if no ETFs invested in gold stocks, but actively-managed mutual funds did. Then presumably the $1.4 billion that flowed into the gold ETF would have gone into an actively-managed fund. An active portfolio would almost certainly be less diversified than the ETF, which means that the same asset flows would have been directed to a smaller number of stocks where they would presumably have been even more disruptive.
When the technology bubble inflated in the late 1990s, the ETF industry was a negligible fraction of its current size. Bubbles inflate with greed and deflate with fear; whether the mechanism by which fear and greed are expressed is active or passive is a secondary issue. Focusing on an ETF rather than on the motives of its purchasers is the wrong diagnosis.
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What happens to the cumulative returns when the daily returns move in opposite directions? In this case, the magnitude of the returns matters, but not the order. If a market participant were to pursue both strategies, it would likely be a losing proposition in a choppy market. The only way to profit is by picking whether the larger absolute return will be positive or negative and using the standard long index for the larger absolute positive return and the inverse index, which is like a short position, for the larger absolute negative return. If the magnitudes of the opposite consecutive returns are the same, the directional order makes no difference, as shown in the first column of Exhibit 2, and there is a certain loss for both the standard and inverse indices. However, there is a chance to win if opting for only one strategy with a correct bet on the bigger absolute return, regardless of order.
What conclusions can be drawn for 2x leveraged indices when daily returns are compounded? Similar results are observed when comparing the standard indices to the 2x leveraged indices, which double the daily return. The compounded returns when there are two days of consecutive losses or gains show that the 2x leveraged version has a better payoff profile, since it loses less than double the standard index return but gains more than double. If a market participant is sure about commodity trends over time, then the 2x leveraged index may be a winning bet, even if the direction is uncertain.

