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Low volatility investing became somewhat fashionable in recent years. In general there are two approaches to this:

  1. Ranking stocks of a certain universe by either stand-alone volatility or by beta and forming portfolios of these. In this case correlation are not directly addressed, which could be an advantage if they are unstable.

  2. Applying an optimization $ w^T \Sigma w \rightarrow \text{Min} $ under constraints (max weights absolute, relative to index and so forth). An example for this approach is MSCI Europe Minimum Volatility.

For quite a while research by investment banks warns that low vol stocks are too expensive already (looking at P/E), that the low vol market is too crowded and that the draw down reduction property has weakened.

In my mind this can be true in the case (1) but too much less extent in case (2). Case (2) for me still makes sense in the spirit of stochastic portfolio theory.

Are there openly available sources to check whether low vol indices constructed in the sense of (2) are expensive? Can we find data to check it for indices, funds, ETFs? How do you think about (2) as a general strategy that does not need a low vol anomaly to work well (improve average annual return by reducing risk)?

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For example iShares has ETFs following MSCI Europe as well as MSCI Europe Minimum Volatility indices. The P/E ratio (as of 23.11.16) for MSCI Europe ETF was 16.87, while the figure for MSCI Europe Minimum Volatility ETF was 18.16.

Thus one could argue that the Min vol index is more expensive. It is another topic, whether it makes sense to use direct P/E comparisons to compare cheapness of different indices. For example, the min vol index could include "better" companies on average, and thus paying more for them might be totally appropriate, and wouldn't automatically mean that low vol stocks were overpriced.

Rob Arnott has recently argued (among other things) that low volatility is expensive, while Cliff Asness of AQR strongly disagrees about his usage of value metrics (such as P/E or P/B) in comparing cheapness of different equity factors/styles. One of the articels on the argument.

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