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### Patterns in financial markets relate to human behaviour, the business cycle, and longer inflation cycles

My post on Monday presented the results of some statistical analyses I ran on a database of monthly inflation-adjusted US equity and bond returns going back 170 years. Yesterday's post was for those who wanted or needed to understand randomness and the normal distribution in a more formal sense.

Today, I set out my thoughts about how the patterns identified in my analyses should be interpreted: what they mean for investors, how they can be used to improve portfolio returns, etc. This will involve reference to the normal distribution - randomness - and the patterns of momentum and mean reversion that were the subject of yesterday's explanatory post.

There are still a few charts in this post but many of them were introduced in Monday's and yesterday's posts and annotated further.

To recap, from 170 or so years of monthly inflation-adjusted equity and bond returns, I calculated, for each, the average monthly return - mean - and the variation - the standard deviation. I then constructed simulated equity and bond series, based on the means and standard deviations of the actual series. Because mean and standard deviation were the only parameters used to construct the simulated series, this guaranteed that they were random walks to which the actual series could be compared.

Then, from each of these four 170 year series - equities/actual, equities/simulated, bonds/actual, bonds/simulated - one hundred 30-year periods were selected at random - Chart 1 depicts how this was done with respect to the actual equity series.

The four sets of one hundred 30-year periods were then plotted on top of each other - Charts 2 to 5 below, along with the upper and lower 1 standard deviation ranges in red. If the 100 selected periods were all following random walks, 68pct of them would fall inside the red lines i.e., within +/- 1 standard deviation.

Charts 2 and 4 - the two simulated series - show that around two thirds of the series fall within the red lines which makes complete sense given that they were created from random walks i.e., 68pct should fall within +/- 1 standard deviation. I have annotated them with a green bell curve which represents a normal distribution i.e. a random walk.

Charts 3 and 5 show actual equities and bonds respectively.

With actual equities, for the first 4 or so years, more of the 100 periods were outside the red lines than there should have been if they were following a random walk. Thereafter, too few of them are outside the red lines. These two distinct periods have been annotated with red and blue bell curves representing, respectively, momentum and mean reversion patterns.

With actual bonds, for the first 15 or so years there is clear momentum pattern, followed by a number of years in which they are essentially following a random walk, then, around the 25 mark they start to exhibit mean reversion.

I find these results fascinating as although it is known, accepted, and understood that bond returns are lower than those from equities - 2.2pct versus 6.4pct - and that they are less volatile over short periods, the respective patterns that emerge in each over *longer* periods demonstrate a less well understood difference between the two asset classes.

Namely, that cycles on monthly scales in equity markets are much shorter than those in bonds, perhaps 4-6 years versus 25-30 years - in many respects this finding would have been evident by eyeballing Charts 1 and 2 in Monday's post but it is important that the data confirm the patterns/cycles.

The next question of course is what these two cycles relate to. The two underlying cycles that operate of these timescales are, respectively, the business cycle and the inflation cycle. Equities track the former, bonds the latter. But why don't equities track the inflation cycle *and* the business cycle? Perhaps because equities - companies - can do all sorts of things to counter the effects of inflation - they can raise prices, move production, cut investment, reduce workforces. Bonds, on the other hand, can do nothing. Their coupons and principle are fixed in nominal terms so are going to rise in real terms when inflation goes down and fall when it goes up. Even index-linked bonds, which you think might be immune, are subject to inflation cycles. This is because there is a high correlation between real yields and inflation. Rising inflation may not impact index-linked bonds in the same way it impacts straight bonds, but rising real yields do.

Furthermore, the business cycle and the longer-term inflation cycle can be connected with underlying human behaviour. The business cycle comprises an expansion and a contraction phase which are related to increases and decreases in spending. These spending patterns to a large extent are driven by changes in consumer confidence i.e., by human behaviour.

It is perhaps a bit harder to link the longer inflation cycle to human behaviour, but nonetheless possible. We can become complacent over a number of decades about the dangers of inflation, as indeed we may have done in recent decades up until two years ago. Complacency is a quintessentially human behavioural trait.

What about the implications for investors? First, since bonds exhibit multi decade-cycles, there are going to prolonged periods of negative real returns i.e., they are higher risk than many think. Moreover, we may well have entered one of these prolonged periods two years ago. Second, since companies - equities - are able to adapt to rising and falling inflation, one should really only be bearish on them when they are clearly above trend towards the end of the business cycle.

These are simple observations but ones that investors - active and passive - should be aware of.

Chart 1:

Source: Credit Suisse/Yahoo

Chart 2:

Source: Credit Suisse/Yahoo

Chart 3:

Source: Credit Suisse/Yahoo

Chart 4:

Source: Credit Suisse/Yahoo

Chart 5:

Source: Credit Suisse/Yahoo

The views expressed in this communication are those of Peter Elston at the time of writing and are subject to change without notice. They do not constitute investment advice and whilst all reasonable efforts have been used to ensure the accuracy of the information contained in this communication, the reliability, completeness or accuracy of the content cannot be guaranteed. This communication provides information for professional use only and should not be relied upon by retail investors as the sole basis for investment.

© Chimp Investor Ltd

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