Three Fundamental Factors and their Analytical Proxies

The 3 fundamental factors and the financial or analytical proxies that capture these factors in a quantitative measure:

There are certain firm characteristics, known as style anomalies, which appear to be proxies for risk. The traditional Capital Asset Pricing Model does not capture these anomalies. The three fundamental factors that we deal with are moment, size and value. These fundamental characteristics could essentially be responsible for a portion of the shares returns.

The momentum anomaly says that have outperformed the market over the past 12 months are likely to continue outperforming in the near future.  This is often caused by investors overreacting in the short run. A proxy used to measure this momentum factor would be relative price appreciation.

Size is one of the more common fundamental factors. This anomaly says that the smaller firms tend to outperform the larger firms (inverse relationship between firm size and stock returns). This is measures by market capitalisation, and was first demonstrated by Banz (1981). Small companies grow more easily than larger companies, as relatively they could achieve a much larger growth percentage relative to a large company, even with much smaller revenues. These small companies are therefore able to grow faster than the larger companies, and this is reflected in their stock performance. This higher return, does, however come with higher risk. 


Value anomaly indicates that under-priced stocks typically outperform in the long term. This is also knows as the book-to-market effect. This effect compares the book value of a company to the companies price of its stock (inverse of price to book ratio). The bigger the book-to-market ratio is, the more fundamentally cheap the investigated company is.
Pure value effect portfolios are created as long stocks with highest book-to-market ratio.

The two primary approaches to investigating style anomalies are portfolio sort, and regression-based methods.
1.     The portfolio sorting approach sorts shares monthly into fractiles on the basis of one or more firm characteristics. The difference between the payoff at the top and bottom fractiles represents the payoffs to the characteristics in question.
2.     The second approach is to fit a univariate regression of realised share returns against firm characteristics in order to establish whether certain characteristics are able to explain or predict share returns.


https://etfs.wisdomtree.eu/Documents/761%20-%20Smart%20Beta%202%200%20-%204%2013%2015.pdf 
https://www.sciencedirect.com/science/article/pii/S0304405X12000931

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