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Register a new userGeneralized framework for applying the Kelly criterion to stock markets
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We develop a general framework for applying the Kelly criterion to stock markets. By supplying an arbitrary probability distribution modeling the future price movement of a set of stocks, the Kelly fraction for investing each stock can be calculated by inverting a matrix involving only first and second moments. The framework works for one or a portfolio of stocks and the Kelly fractions can be efficiently calculated. For a simple model of geometric Brownian motion of a single stock we show that our calculated Kelly fraction agrees with existing results. We demonstrate that the Kelly fractions can be calculated easily for other types of probabilities such as the Gaussian distribution and correlated multivariate assets.
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In this paper, we study the Kelly criterion in the continuous time framework building on the work of E.O. Thorp and others. The existence of an optimal strategy is proven in a general setting and the corresponding optimal wealth process is found. A simple formula is provided for calculating the optimal portfolio for a set of price processes satisfying some simple conditions. Properties of the optimal investment strategy for assets governed by multiple Ornstein-Uhlenbeck processes are studied. The paper ends with a short discussion of the implications of these ideas for financial markets.
The influence of Commodity Trading Advisors (CTA) on the price process is explored with the help of a simple model. CTA managers are taken to be Kelly optimisers, which invest a fixed proportion of their assets in the risky asset and the remainder in a riskless asset. This requires regular adjustment of the portfolio weights as prices evolve. The CTA trading activity impacts the price change in the form of a power law. These two rules governing investment ratios and price impact are combined and lead through updating at fixed time intervals to a deterministic price dynamic. For different choices of the model parameters one gets qualitatively different dynamics. The result can be expressed as a phase diagram. Meta-CTA strategies can be devised to exploit the predictability inherent in the model dynamics by avoiding critical areas of the phase diagram or by taking a contrarian position at an opportune time.
In this study, we have investigated empirically the effects of market properties on the degree of diversification of investment weights among stocks in a portfolio. The weights of stocks within a portfolio were determined on the basis of Markowitzs portfolio theory. We identified that there was a negative relationship between the influence of market properties and the degree of diversification of the weights among stocks in a portfolio. Furthermore, we noted that the random matrix theory method could control the properties of correlation matrix between stocks; this may be useful in improving portfolio management for practical application.
Different investment strategies are adopted in short-term and long-term depending on the time scales, even though time scales are adhoc in nature. Empirical mode decomposition based Hurst exponent analysis and variance technique have been applied to identify the time scales for short-term and long-term investment from the decomposed intrinsic mode functions(IMF). Hurst exponent ($H$) is around 0.5 for the IMFs with time scales from few days to 3 months, and $Hgeq0.75$ for the IMFs with the time scales $geq5$ months. Short term time series [$X_{ST}(t)$] with time scales from few days to 3 months and $H~0.5$ and long term time series [$X_{LT}(t)$] with time scales $geq5$ and $Hgeq0.75$, which represent the dynamics of the market, are constructed from the IMFs. The $X_{ST}(t)$ and $X_{LT}(t)$ show that the market is random in short-term and correlated in long term. The study also show that the $X_{LT}(t)$ is correlated with fundamentals of the company. The analysis will be useful for investors to design the investment and trading strategy.
Uncovering the risk transmitting path within economic sectors in China is crucial for understanding the stability of the Chinese economic system, especially under the current situation of the China-US trade conflicts. In this paper, we try to uncover the risk spreading channels by means of volatility spillovers within the Chinese sectors using stock market data. By applying the generalized variance decomposition framework based on the VAR model and the rolling window approach, a set of connectedness matrices is obtained to reveal the overall and dynamic spillovers within sectors. It is found that 17 sectors (mechanical equipment, electrical equipment, utilities, and so on) are risk transmitters and 11 sectors (national defence, bank, non-bank finance, and so on) are risk takers during the whole period. During the periods with the extreme risk events (the global financial crisis, the Chinese interbank liquidity crisis, the Chinese stock market plunge, and the China-US trade war), we observe that the connectedness measures significantly increase and the financial sectors play a buffer role in stabilizing the economic system. The robust tests suggest that our results are not sensitive to the changes of model parameters. Our results not only uncover the spillover effects within the Chinese sectors, but also highlight the deep understanding of the risk contagion patterns in the Chinese stock markets.
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