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"What is the chief tenet of MPT, of which passive index-investing is a consequence?"

Technically, indexing is a consequence of the Efficient Market Hypothesis (EMH), not Modern Portfolio Theory (MPT). When costs are included, the EMH implies that it is inefficient to attempt to outperform the market. This is supported by volumes of historical, empirical data about mutual fund performance and various academic papers. (This is not to say EMH is without issues - it certain has a number of them - but most of those deal with weaknesses of actual pricing of the market, and have less impact on the pricing of individual assets relative to the market.)

The problem with blind adherence to index investing is not that indexing is inherently bad. Indexing is eliminating the risks of stock- (or bond-) picking (and the associated transaction costs). I do it with a portion of my portfolio simply because the opportunity cost of doing appropriate research to do the picking impinges too much on my "free time" that I want to spend on a mountain or lake. It's lazy, but it is enormously effective at doing what it is designed to do: Track the market. However, it does *not* protect an investor from broad market declines, because by indexing one effectively buys the market.

This is actually where the danger arises... because the portion of EMH that deals with market efficiency (that market pricing is accurate to all news overall) has been shown to be incorrect. One counter example is the empirical evidence that shows value stocks outperform other stocks. This flaw in EMH which is most likely explained by people doing excessive extrapolation: [PDF warning] , which I read as very similar to your point that "estimates of the magnitude of tail events cannot be derived from the known sample of tail events".

Because indexing is buying a broad range of assets all at once, people may misinterpret that as appropriate diversification (one could say that they are misapplying MPT). Even if appropriately diversified (according to MPT) through indexes, one still suffers from the known flaws in MPT, which happen to also be weaknesses in EMH: namely those that behavioral economists have pointed out. It's especially interesting - in my opinion - that the Fed has recently noted some behavioral economics folks:

The reason this is so relevant is that we are up against points where models and empirical data fail. The Fed already had to go into "quantitative easing" to distort bond rates (since they couldn't lower the Fed funds rate below zero), and as has been recently pointed out either here or on METAR (I forget) is that we've now set a record for the steepness of the yield curve between the 2 year and 10 year bond. We are therefore beyond the empirical data that might make up models and if any large players are dependent upon those models, asset prices also bear a much larger "extrapolation risk" (not sure it has a better name) than they do in boring markets.

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