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A eficiência do critério de Kelly: teste comparativo com índices de ações
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Abstract(s)
Segundo Damodaran (2009), o risco é o principal impulsionador da evolução humana,
desde as primeiras ferramentas criadas até a terapia genética. Como é sabido, o maior receio de
um investidor, é perder o investimento, isso significa que os investidores procuram sempre
métodos de se protegerem do risco a que estão expostos quando fazem uma aplicação
financeira.
Neste sentido o objetivo deste trabalho é testar o critério de Kelly, para perceber se com
a sua adoção existe uma maximização do lucro e mitigação das perdas.
Para demonstrar a eficiência do critério de Kelly foram aplicados alguns testes práticos
do seu funcionamento, nomeadamente testes de Monte Carlo.
Para responder ao objetivo do trabalho desenvolveu-se uma análise comparativa de
investimentos em alguns dos principais índices de mercado, para o período de 2001 a 2020.
Para isso, foi testado um investimento anual de 10.000,00€ no PSI20, FTSE100 e Dow Jones,
e posteriormente foi feito o mesmo exercício, mas utilizando o critério de Kelly como base para
o investimento.
Após esta análise, concluiu-se que para o PSI20 embora o índice tenha tido uma queda
de quase 60% no decurso das duas últimas décadas, com a adoção do critério de Kelly existem
ganhos de aproximadamente 4% no investimento. Nos casos do FTSE100 e do Dow Jones,
houve uma diferença, pois ambos os índices tiveram uma evolução positiva, e um investidor
que aplicasse o seu capital nestes dois índices teria tido ganhos superiores ao obtido através da
aplicação do critério de Kelly. Porém é importante sublinhar, que com a adoção do critério de
Kelly tanto no caso do FTSE100 que teve ganhos de aproximadamente 5% como no Dow Jones
que teve ganhos de aproximadamente 50%, nos períodos de queda dos índices, esta foi muito
menor por conta da proteção que o critério de Kelly dá ao investidor.
According to Damodaran (2009), risk is the main driver of human evolution, since/from the first tools created to gene therapy. As is known, the biggest fear of an investor is to lose the investment, which means that investors always look for methods to protect themselves from the risk they are exposed to when making a financial investment. In this sense, the objective of this work is to test the Kelly criterion, to see if with its adoption there is a maximization of profit and mitigation of losses. To demonstrate the efficiency of the Kelly criterion, some practical tests of its operation were carried out, namely Monte Carlo tests. To respond to the objective of the work, a comparative analysis of investments in some of the main market indices was developed, for the period from 2001 to 2020. For this, an annual investment of € 10,000.00 was tested in PSI20, FTSE100 and Dow Jones , and later the same exercise was performed, but using the Kelly criterion as base for the investment. After this analysis, it was concluded that for the PSI20, although the index has fallen by almost 60% over the last few decades, with the adoption of the Kelly criterion, there were gains of approximately 4% in investment. In the cases of the FTSE100 and the Dow Jones, it was different, as both had a positive evolution, and an investor who put his capital in these two indices would obtain higher gains if he used the Kelly criterion. However, it is important to emphasize that with the adoption of the Kelly criterion, both in the case of the FTSE100, which had gains of approximately 5%, and in the Dow Jones, which had gains of approximately 50%, in periods of falling indices this was much lower due to the protection that the Kelly criterion gives the investor.
According to Damodaran (2009), risk is the main driver of human evolution, since/from the first tools created to gene therapy. As is known, the biggest fear of an investor is to lose the investment, which means that investors always look for methods to protect themselves from the risk they are exposed to when making a financial investment. In this sense, the objective of this work is to test the Kelly criterion, to see if with its adoption there is a maximization of profit and mitigation of losses. To demonstrate the efficiency of the Kelly criterion, some practical tests of its operation were carried out, namely Monte Carlo tests. To respond to the objective of the work, a comparative analysis of investments in some of the main market indices was developed, for the period from 2001 to 2020. For this, an annual investment of € 10,000.00 was tested in PSI20, FTSE100 and Dow Jones , and later the same exercise was performed, but using the Kelly criterion as base for the investment. After this analysis, it was concluded that for the PSI20, although the index has fallen by almost 60% over the last few decades, with the adoption of the Kelly criterion, there were gains of approximately 4% in investment. In the cases of the FTSE100 and the Dow Jones, it was different, as both had a positive evolution, and an investor who put his capital in these two indices would obtain higher gains if he used the Kelly criterion. However, it is important to emphasize that with the adoption of the Kelly criterion, both in the case of the FTSE100, which had gains of approximately 5%, and in the Dow Jones, which had gains of approximately 50%, in periods of falling indices this was much lower due to the protection that the Kelly criterion gives the investor.
Description
Keywords
Critério de Kelly Risco financeiro Mercado financeiro Bolsas de valores Kelly criterion Financial risk Financial market stock exchanges