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- 저자 : 김규태 ( Gyu Tai Kim ) (검색결과 19 건)
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김규태 ( Gyu Tai Kim ),정수희 ( Su Hee Jung ) 한국경영공학회 2012 한국경영공학회지 Vol.17 No.1
Investment and risk always go together. Namely, the high investment rate of return is followed by the high risk. Therefore, we need to take a proper measure to minimize the risk and simultaneously to maximize the investment rate of return. To solve and optimize this problem, we hedge the risk using the diversified investment instead of the entire investment at a time. Accordingly, we determine the optimal allocation of the investment capital to minimize the investment risk. In this paper, we discuss the Kelly criterion. The Kelly criterion is adopted to determine the optimal fixed fraction that is contributed to maximizing the geometric mean of the return over a long period of time. The criterion is implemented with the concept of the flaws of averages, especially with the Jensen`s inequality assuming that the function employed has a type of convexity. Finally, we illustrate it with a numerical example.
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The Investment Size Matter with the Kelly Criterion
Gyu-Tai KIM(김규태) 조선대학교 지식경영연구원 2008 기업과 혁신연구 Vol.1 No.2
대부분의 투자자들이 생각하듯이 투자 규모의 크기와 이익성이 선형적 관계를 이루고 있다는 고정적 관념이 사실일까 이러한 일반적 관념에 ? 반하여 본 연구에서 논하게 될 켈리기준에 의하면 투자 규모의 크기와 이익성 상호간에는 선형적 관계가 아닌 비선형적 관계가 성립된다고 한다. 켈리기준의 비선형적 관계성을 염두에 둔다면 투자자들은 투자 할당문제에 있어서 매우 신중한 투자활동을 취해야 할 것이다. 즉, 특정한 투자 자산에 대한 투자의 수익성을 극대화하기 위한 최적의 투자 할당액이 얼마이어야 하는지를 모든 투자자들은 결정해야 한다. 최적의 투자할당 문제를 다루는 것이 켈리기준의 궁극적인 목표라고 할 수 있다. 투자의 규모의 크기와 수익성의 상호관계성에 대한 켈리기준의 새로운 개념이 1956년에 주요 학회지에 발표되었음에도 불구하고 아직까지 이와 관련된 연구를 지속적으로 수행하고 있는 그룹은 극소수의 연구자들로 구성되어 있을 뿐이고 금융학 분야에서도 아직 심도있게 연구가 진행되고 있지 않고 있다. 이러한 사실로 인하여 본 연구에서는 켈리기준이 무엇이고 어떻게 실현되는지를 수리적 예제를 통하여 보여주고 있다. 그리고 다양한 종류의 켈리기준을 이해하기 쉽게 단계적으로 수리적 모형을 유도하였고 특히 Aristotle의 켈리기준을 확장하여 새로운 켈리기준을 소개하고 있다. 마지막으로 삼성전자와 현대자동차의 주식을 토대로 구성된 사례연구를 통하여 켈리기준의 실질적 사용예를 보여주고 있다. 그 결과는 일반적으로 수용될 수 있는 자본 할당률 범위 내에서 최적의 투자 할당액이 존재하지 않는 것으로 판명되었다. As currently most of investors suppose, is it true that there exists an outrightly linear relationship between the investment size and profitability?. On the contrary to the general conception about the relationship, the Kelly criterion which will be discussed in this paper says that such a relationship is destroyed in a real investment world. With this assertion in mind, the investors should be careful to make a decision on the investment size. That is, they should be concerned with how much must be made to maximize the profitability of their investment. It is also inferred from the assertion that there must be an optimal amount of the investment size to maximize the profitability. Finding this optimal point is one of the major objectives of the Kelly criterion. Even though the criterion was published in 1956 and had been regarded to provide a useful guideline for the investors, not only has it been studied by a extremely small group of the researchers, but it has also been rarely known to a finance community in a world. For these observations, this paper will discuss what the Kelly criterion is and illustrates it with a numerical example. Finally, it is concluded with the discussion of the future research directions, mainly oriented with the real investment case.
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정수희(Su-Hee Jung),김규태(Gyu-Tai Kim) 대한산업공학회 2008 대한산업공학회 추계학술대회논문집 Vol.2008 No.11
Black and Scholes published the seminal paper "The Pricing of Option and Corporate Liabilities" in 1973. The Black-Scholes model marked an epoch in trading options in an orderly market with well-defined contracts in 1973. And thanks to their contribution, much research on valuing options has been actively conducted. For instance, Cox, Ross, Rubinstein proposed a binomial lattice option pricing model in 1976. In Korea, the option market was introduced with the KOSPI200 stock index option at the 7th day of July in 1997. Since then, the option market has been steadily growing. As the option market grows, it is required that the investors obtain an accurate option value. However, it is not easy to get the accurate option value mainly due to the volatility of the options. In this thesis, we will analyze the option pricing models to compare the theoretical option values with the option prices trading in a real market. As the option pricing models to provide a theoretical option values, Black-Scholes and a binomial lattice option pricing models, most widely used, will be employed and a Monte Carlo simulation will be performed for option price presumption and analysis. For the empirical analysis purpose, we will use the KOSPI200 stock index option data from January to December in 2006. The data was collected from a daily closing stock and option prices. For the comparison purpose, we will conduct a statistical analysis with the data collected to take a validity test.
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정수희(Su-hee Jung),김규태(Gyu-tai Kim) 대한산업공학회 2010 대한산업공학회 추계학술대회논문집 Vol.2010 No.11
In general, the purpose of the investment is to amass the more wealth in the future on the basis of a current investment capital. If any investment alternative will generate certainly a profit as a 100 percentage in the future, we will invest all capital into that alternative to make a money as much as possible. But in reality, all future values according to the current investment act have an uncertainty. Therefore to achieve a goal of the investment rate of return uncertain investment environment, we need to take a proper measure to minimize the uncertainty. To solve this problem, we generally construct the optimal portfolio to minimize the uncertainty. Namely, it means we optimize an allocation rate of investment capital for the diversified investment. In this paper, discuss the Kelly criterion which is the one of the method to determine the optimal allocation of the investment capital. The Kelly criterion determines the optimal fixed fraction that is contributed to maximize the geometric expected value of the return over a long period of time. In this paper, we describe what the Kelly criterion is. Then, we will construct the optimal portfolio from the KOSPI 200 using the Kelly criterion.
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