Technology-related weighted momentum
factor.formula
The formula for calculating the degree of scientific and technological relevance (cosine similarity):
The formula for calculating the technology-related weighted momentum factor is:
in:
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is the technological correlation between company i and company j in period t, with a value range of [0,1]. The larger the value, the higher the technological correlation. Here, the cosine similarity of the patent distribution vector is used to measure the degree of technological correlation between the two companies.
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is the N-dimensional patent distribution vector of company i in period t. N represents the number of major technology categories of the Patent and Trademark Office. The k-th element $T_{itk}$ in the vector represents the proportion of the number of applications for technology patents in the k-th category of company i in the past five years to the total number of applications. This vector reflects the patent distribution of the company in different technical fields.
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Represents the inner product of the patent distribution vectors of company i and company j, which is used to calculate the similarity of the vectors.
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The L2 norm (Euclidean norm) of the patent distribution vector representing company i, which is the square root of the sum of the squares of the elements of the vector, is used to normalize the vector so that its length is 1.
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is the rate of return of company j in period t, usually a simple rate of return or a logarithmic rate of return.
factor.explanation
This factor is based on the following assumptions: a company's technological progress will have a spillover effect, affecting other companies with a high degree of technological relevance, thereby changing the fundamentals of these companies and ultimately reflecting them in their stock prices. Empirical studies have shown that there is a lag-lead relationship between the target company's stock return and the previous returns of its technologically affiliated companies, that is, the changes in the previous returns of companies with a high degree of technological relevance to the target company have predictive power for the target company's future returns. Therefore, the returns of affiliated companies weighted by technological relevance can effectively construct a momentum factor to capture investment opportunities brought about by this technological spillover effect. The construction logic of this factor is that if other companies with technological relevance to the target company have achieved higher returns in the previous period, then the target company may also achieve higher returns in the future.