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Factors

#### Analysing the cycle

As we are seeking precise quantitative metrics for performance, risk, and forecasting we almost inevitably turn to one of the key tools used by investment professionals: the factor model. This is a brief and superficial skim of the topic, avoiding math to sketch the key concepts.

- About factors:
The factors described here come from statistical techniques applied to the entire set of over 100 indexes of monthly returns

Factors come automatically ranked in order of decreasing importance, and they are statistically uncorrelated (independent)

It turns out that just 3 factors ‘explain’ about 80-90% of past performance, meaning that systematic (not random) risk and return is dominant

Each area is ‘decomposed’ into a mixture (linear combination) of these factors, so by weighting and adding we get very close to the index

- About these factors
The first factor is ‘the market’ - we see in the barchart that all our 9 cases contribute positively to it

The second factor is the difference between performance of low-priced (e.g. Northern) areas and high-priced (London) areas, as in the barchart

The third factor is the difference between mid-priced (e.g. Midlands) areas and the average of low and high-priced areas, as in blue

The data tells us that the latter 2 are cyclical, about 16-17 years, have similar amplitude, and that factor 3 ‘leads’ factor 2 by a quarter cycle

It will be evident to STEM students that these are a bit/a lot like sin and cos waves

It will be clear to traders, portfolio managers, and financial analysts that these are like ‘shift’ ‘twist’ and ‘butterfly’ on the yield curve, only here along the ‘\(£/m^2\) curve’

- Why do we care?
The factors so far have not helped much *but* if we can understand ‘what they are’ we can understand 80-90% of market behaviour

[spoiler alert] It will turn out that they are almost entirely a reflection of price