### Modeling Cyclical Markets – Part 1

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The proverbial wisdom is that there are two types of stock market cycles – secular and cyclical. I argued previously that secular cycles not only lacked statistical basis to be credible, but their durations of 12 to 14 years are also impractical for most investors. We live in an internet age with a time scale measured in nanoseconds. Wealth managers often turn over their portfolios after only a few years. Simply put, secular cycles can last longer than financial advisors can retain their clients.

The second type of cycle is called a “cyclical market” and is believed to comprise both primary and secondary waves. Economic cycles are thought to drive primary waves. According to the National Bureau of Economic Research (NBER), the average economic cycle length is 4.7 years, which would be more suitable for the typical holding periods of most investors.

To succeed in accumulating wealth in bull markets and preserving capital in bear markets, we must first define and detect primary and secondary markets. In this article, I present a modeling approach to spot primary cycles. Modeling secondary market cycles will be the topic of Part 2.

**Common flaws in modeling financial markets**

Before presenting my model on primary markets, I must digress to discuss two common mistakes in modeling financial markets. For example, when modeling secular market cycles and market valuations, analysts use indicators such as the Crestmont P/E, the Alexander P/R and the Shiller CAPE (cyclically adjusted price-earnings ratio). By themselves, these indicators are fundamentally sound. It's the modeling approach using these indicators that is flawed.

Models on valuations and secular cycles cited above share two assumptions. First, they assume that the amplitude (scalar) of the indicators can be relied on to indicate market valuations and secular outlook. Extremely high readings are interpreted as overvaluations or cycle crests, and extremely low readings, undervaluation or cycle troughs. Second, it's assumed that mean reversion will always drive the extreme readings in the models back into line.

Figure 1A shows the S&P 500 from 1881 to mid-2016 in logarithmic scale. Figure 1B is the Shiller CAPE overlay. The solid purple horizontal line is the mean from 1881 to 1994 and has a value of 14.8. The upper and lower dashed purple lines represent one standard deviation above and below the mean of 14.8, respectively. The solid brown line to the right is the mean from 1995 to mid-2016 and has a value of 26.9. The upper and lower dashed brown lines are one standard deviation above and below the post-1995 mean of 26.9, respectively. One standard deviation above the pre-1995 mean is 19.4 and one standard deviation below the post-1995 mean is 20.4. The data regimes in the two adjoining timeframes do not overlap. The statistically distinct nature of the two regimes invalidates the claim by many secular cycle advocates and CAPE-based valuations practitioners that the elevated CAPE readings after 1995 are just transitory statistical outliers and will fall back down in due course.

Let's examine the investment impacts from these two assumptions. The first assumption is that extreme amplitudes can be used to track cycle turning points. Figure 1B shows that both high and low extremes are arbitrary and relative. As such, they cannot be used as absolute valuation markers. For example, after 1995, the entire amplitude range has shifted upward. Secular cyclists and value investors would have sold stocks in 1995 when the CAPE first pierced above 22, exceeding major secular bull market crests in 1901, 1937 and 1964. They would have missed the 180% gain in the S&P 500 from 1995 to its peak in 2000. More recently, the CAPE dipped down to 13 at the bottom of the sub-prime crash. Secular cycle advocates and value investors would consider a CAPE of 13 not cheap enough relative to previous secular troughs in 1920, 1933, 1942, 1949, 1975 and 1982. They would have asked clients to switch from stocks to cash only to miss out the 200% gain in the S&P 500 since 2010. These are examples of huge upside misses caused by the first flawed assumption used in these scalar-based models.