Last month I published an editorial in the Journal of Portfolio Management that turned out to be somewhat prescient. It deals with the VIX index and the problem on non-stationarity that I have addressed here before. The crux of the article follows.

## In my role as an academic, I play down the importance of stationarity to get on with research efforts. When I have to make investment decisions, it is the elephant in the room. In fact, the question of stationarity is so important that it often dominates my investment decision-making and as a result renders much academic research of little practical value. The point of this commentary is to argue that finance research needs to take the question of stationarity more seriously to be more useful to investors.

*The surprising behavior of the VIX index*

*The cross section of expected returns*

*Individual Stocks*

*returns*remained stationary while the company was continually transformed because stock returns depend on investor expectations. But it would be foolhardy for an investor to assume that the dramatic evolution of the firm did not have a major impact on investor perceptions, including investor estimates of risk, and thereby on stock returns.

*Smart beta and factor premiums*

*without*replacement. Every time say a red ball is drawn, the probability of drawing another red ball declines. For this reason, the distribution is non-stationary. The probability of drawing a red ball can be interpreted as the probability that a factor portfolio will earn excess returns. The more the valuation increases, the more red balls are drawn, and the less likely it will be that valuations will rise in the future.

*Conclusions and implications*

^{rd}digit of Pi has now become known as the Feynman point, but the six 9s have no meaning.