Following the established methodology for measuring document similarity (see Ash and Hansen, 2023 ), company similarity is measured as the cosine similarity of the numerical vectors to which the companies’ descriptions have been converted (using in turn each of the NLP methods introduced in Section 3):

$\cos \left(v_A,v_B\right)=\frac{v_A^T{v}_B}{\Vert v_A\Vert \Vert v_B\Vert }=\frac{{\displaystyle {\sum }_{i=1}^n{a}_i{b}_i}}{\sqrt{{\displaystyle {\sum }_{i=1}^n{a}_i^2}}\sqrt{{\displaystyle {\sum }_{i=1}^n{b}_i^2}}}$ (1)

where the vectors $v_A=\left(a_1,a_2,\cdots ,a_n\right)$ and $v_B=\left(b_1,b_2,\cdots ,b_n\right)$ correspond to the vectorised business descriptions of company A and company B, respectively. Table 1 and Table 2 present descriptive statistics for the similarity measure for the S&P 500 and respectively the STOXX Europe 600 companies and illustrate the potential for divergence (and contest) across the three NLP methods. Pairwise correlations are positive for all the methods but moderate: for the S&P 500 companies in the 0.43 - 0.69 range and similarly, the range is 0.41 - 0.65 for the European companies.

The proven ( Ibriyamova et al., 2017 , 2019 ) and persistent ( Pungulescu and Stolin, 2023 ; Pungulescu, 2024 ) link between pairwise return correlations and the similarity of the respective companies’ business descriptions (with the returns of more similar companies being more correlated), can be leveraged by constructing minimum semantic concentration portfolios (see Ibriyamova et al., 2019 , for the theoretical exposition). The minimum semantic concentration portfolio weights

Table 1. S&P 500: Cosine similarities.

The table reports descriptive statistics (mean, standard deviation, minimum and maximum) of the pairwise cosine similarities of the business description of the S&P 500 companies, as well as their correlations.

Table 2. STOXX Europe 600: Cosine similarities.

The table reports descriptive statistics (mean, standard deviation, minimum and maximum) of the pairwise cosine similarities of the business description of the STOXX Europe 600 companies, as well as their correlations.

are given by $\frac{{\left(S^{T}S\right)}^{-1}1}{1^T{\left(S^{T}S\right)}^{-1}1}$, where S^TS, the matrix of cosine similarities, takes on

the role that the variance-covariance matrix, Σ, plays in finding the minimum variance portfolio weights. Pungulescu (2022b) compares the minimum variance and the minimum semantic concentration portfolios constructed from the Dow Jones Industrial Average constituent companies over 16 years and finds that the minimum semantic concentration portfolio outperforms the minimum variance portfolio 66% of the time.

In this paper, three NLP methods are placed in a “horse race” that attempts to find which of them results in a minimum semantic concentration portfolio with lower variance. Similar comparisons have been conducted in the related literature for different text analysis methods to show both that text analysis is apt to extract meaningful information from unstructured data as well as to rank the various methods. For instance, Ash and Hansen (2023) compare 10 different algorithms in terms of their ability to quantify similarities between companies using the Risk Factors section of the 10-K reports (required by the U.S. Securities and Exchange Commission) as input text, and Ibriyamova et al. (2017) task 4 measures of proximity for pairs of companies with predicting stock return correlations and find that the measure based on semantic fingerprinting performs best.

To test the ability of each of the three NLP methods to provide diversification benefits, for each day, a set of 25 and respectively 50 constituent companies of S&P 500 and STOXX Europe 600 indices is randomly selected and minimum semantic concentration portfolios are constructed based on the cosine similarities of their business descriptions vectorised using each of the NLP methods, in turn⁸. These portfolios are held for the next 60, 120 and 240 days and the standard deviations of their returns are calculated over these holding periods. Time series of standard deviations of the returns of the portfolios’ constructed on any given day are obtained in this fashion and the procedure is repeated 100 times. Table 3 and Table 4 compare the performance of 100 times series of standard deviations of returns of portfolios constructed using 25 constituents of the S&P 500 and respectively the STOXX Europe 600 indices. The comparison includes a portfolio with randomly chosen weights (RND) and five minimum semantic concentration portfolios based on our NLP methods: semantic fingerprinting (SF), three variants of BERT (resulting in vectors of differing lengths), and GPT. The results show how many times (out of 100), the time series of standard deviations of returns of portfolios with weights computed using a given method (SF, BERT, GPT, RND) and held for a particular number of days (60, 120, 240) has a lower mean (statistically significant at 10%) than the other methods. As expected, the portfolios using randomly chosen weights are without exception ‘beaten’ by all the minimum semantic concentration portfolios, illustrating the potential diversification benefits of using text analysis in the context of portfolio management. For portfolios of 25 constituent companies of the S&P 500 (see Table 3 ), using BERT 328 results in portfolios with a higher number of “wins” (counts with time series of standard deviations of portfolio returns that are significantly lower, on average, than for the portfolios constructed using the other methods). A close second is the NLP solution provided by GPT followed by semantic fingerprinting (SF). The two remaining BERT variants (with vectors of 1024 and respectively 768 positions) are in the last places. For portfolios of 25 constituent companies of the STOXX Europe 600 (see Table 4 ), BERT 1024 and semantic fingerprinting (SF) lead in a closely contested race (they are only one “win” apart), BERT 328 is a distant third and GPT comes in second to last. The difference between the performances of the BERT variants is suggestive of one of the potential pitfalls of using pre-trained models, as the best choice is by no means evident a priori and the wrong choice is clearly costly. The end-user is faced with the task of running extensive comparisons and/or further training and fine-tuning any chosen model.

For portfolios of 50 constituent companies of the S&P 500 (see Table 5 ), SF results in portfolios with the same number of “wins” as BERT 328 and they both outperfom GPT (albeit slightly), whereas for European companies, semantic fingerprinting (SF) wins clearly, followed at considerable distance by BERT 1024 (see Table 6 ). GPT manages to “beat” BERT 328 on this occasion and BERT 768 fares worst.

Table 3. S&P 500: Minimum semantic concentration portfolios: 25 companies.

This table reports the number of times out of 100, that the time series of standard deviations of portfolio returns has a lower mean (statistically significant at 10%) than the given alternatives. Each day a set of 25 companies is randomly selected from the S&P 500 constituents and combined into portfolios using either random weights (RND) or minimum semantic concentration weights (based on the cosine similarities of business descriptions vectorised using three different NLP methods: SF, BERT, GPT). The standard deviation of each portfolio constructed on a given day is calculated assuming the portfolio is held for the subsequent 60, 120 and respectively 240 days.

Table 4. STOXX europe 600: Minimum semantic concentration portfolios: 25 companies.

This table reports the number of times out of 100, that the time series of standard deviations of portfolio returns has a lower mean (statistically significant at 10%) than the given alternatives. Each day a set of 25 companies is randomly selected from the STOXX Europe 600 constituents and combined into portfolios using either random weights (RND) or minimum semantic concentration weights (based on the cosine similarities of business descriptions vectorised using three different NLP methods: SF, BERT, GPT). The standard deviation of each portfolio constructed on a given day is calculated assuming the portfolio is held for the subsequent 60, 120 and respectively 240 days.

Table 5. S&P 500: Minimum semantic concentration portfolios: 50 companies.

This table reports the number of times out of 100, that the time series of standard deviations of portfolio returns has a lower mean (statistically significant at 10%) than the given alternatives. Each day a random set of 50 companies is randomly selected from the S&P 500 constituents and combined in portfolios using either random weights (RND) or minimum semantic concentration weights (based on the cosine similarities of business descriptions vectorised using three different NLP methods: SF, BERT, GPT). The standard deviation of each portfolio constructed on a given day is calculated assuming the portfolio is held for the subsequent 60, 120 and respectively 240 days.

Table 6. STOXX europe 600: Minimum semantic concentration portfolios: 50 companies.

This table reports the number of times out of 100, that the time series of standard deviations of portfolio returns has a lower mean (statistically significant at 10%) than the given alternatives. Each day a random set of 50 companies is randomly selected from the STOXX Europe 600 constituents and combined in portfolios using either random weights (RND) or minimum semantic concentration weights (based on the cosine similarities of business descriptions vectorised using three different NLP methods: SF, BERT, GPT). The standard deviation of each portfolio constructed on a given day is calculated assuming the portfolio is held for the subsequent 60, 120 and respectively 240 days.