This research paper focuses on the study of Gordon’s mathematical model as a practical application for determining the expected value of securities. The overall research problem is to find an optimal algorithm for predicting the value of securities in an investment portfolio that makes sense to investors. Although not always evident, the article is filled with systematic comparisons between two investment strategies: in value for low-grade stocks and in growth with long-term upside prospects. Asness et al. (2020) turn to Gordon’s well-known model for total value and create two variations for it: for value stocks and growth stocks.

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Manipulating the formula mathematically, the authors arrive at a single model in which the maximum value of the stock is determined by the value spread and the growth spread. The authors use three components (E/P, B/P, and S/P) for which a value spread function is subsequently created to form a composite stock value function. Based on the fact of market research and stock picking from 1981 to 1999, several investment portfolios with different strategies are created as a sample: a growth portfolio and a value portfolio. Thus, the innovation of the proposed function is to use two spreads at once, value and growth, as opposed to only unidirectional models. This allows for a single model that will demonstrate the ability to predict the expected value of securities statistically and economically meaningfully versus growth.

Having created the mathematical model, Asness et al. decided to investigate it to test its effectiveness and efficiency in solving original problems. Several conclusions were drawn by the developers regarding the use of the new function. First, its application to a sample of securities yielded a maximum return of 52 percent, which is even higher than the historical return. Consequently, the proposed formula allows for a more accurate and optimistic valuation of securities.

Secondly, the use of the formula makes it possible to find the optimal time for the value of the stock. This, according to the authors, occurs when the value spread is extremely large, and the growth spread is the smallest. Third, it is confirmed that the refined R2 for the correlation was not very high and was only 38.7%, which hints at the non-ideality of the model. Recognizing this feature, Asness et al. plot the comparison of actual and predicted values for the twelve-month return period and show that there are generally good patterns of agreement between the two plots. Thus, the overall conclusion of the article is that the proposed model shows a return on value versus growth.

A close reading of the proposed article legitimately raises several issues of critical reflection. First of all, the authors did not use complicated mathematics, but rather, all of the features they presented are clear and accessible to the reader with a mathematical background. In addition, Asness et al. used years of return for a particular period as a benchmark, which means that it is not unlikely that this model may not be suitable for other time periods: this requires a number of additional tests. In addition, any mathematical conclusions made by the authors are based on the use of the Gordon model, which has serious limitations. For example, the model is only used for dividend-paying companies, and the predictive economic growth of a company, overall, is infinite, although this is not always possible.

Finally, although the authors make accessible use of the mathematical apparatus, their explanations and notations are not always clear to the reader, which can lead to a “snowball” effect on perception. Thus, the article offered for reading is helpful and shows one of the methods developed for predicting the future value of securities, but the format and methods used do not always seem reasonable.

## Reference

Asness, C. S., Friedman, J. A., Krail, R. J., & Liew, J. M. (2000). Style timing: Value versus growth. *The Journal of Portfolio Management, 26*(3), 50-60.

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