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Abstract:
Overreactions and other behavioral effects in stock prices can best be examined by adjusting for the changes in fundamentals. We perform this by subtracting the relative price changes in the net asset value (NAV) from that of the market price (MP) daily for 134,406 data points of closed end funds trading in US markets. We examine the days before and after a significant rise or fall in price deviation and MP return and find evidence of overreaction in the days after the change. Prior to a spike in deviation we find a gradual two or three day decline (and analogously in the other direction). Overall, there is a characteristic diamond pattern, revealing a symmetry in deviations before and after the significant change. Much of the statistical significance and the patterns disappear when the subtraction of NAV return is eliminated, suggesting that the frequent changes in fundamentals mask behavior effects. A second study subdivides the data depending on whether the NAV or MP is responsible for the spike in the relative difference. In a majority of spikes, it is the change in market price rather than NAV that is dominant. Among those spikes for which there is little or no change in NAV, the results are similar to the overall study. Furthermore, the upward spikes are preceded by one or two days of declining market price while NAV rises slightly or is relatively unchanged. This suggests that a cause of the spike may be due to over-positioning of traders in the opposite direction in anticipation.

Overreaction, Price deviation, Diamond pattern, Overpositioning, Market dynamics, Financial markets, Behavioral finance, Closed-end funds

Abstract:
A system of nonlinear asset flow differential equations (AFDE) gives rise to an inverse problem involving optimization of parameters that characterize an investor population. The optimization procedure is used in conjunction with daily market prices and net asset values to determine the parameters for which the AFDE yield the best fit for the previous n days. Using these optimal parameters the equations are computed and solved to render a forecast for market prices for the following days. For a number of closed-end funds, the results are statistically closer to the ensuing market prices than the default prediction of random walk. In particular, we perform this optimization by a nonlinear computational algorithm that combines a quasi-Newton weak line search with the BFGS formula. We develop a nonlinear least-square technique with an initial value problem (IVP) approach for arbitrary stream data by focusing on the market price variable P since any real data for the other three variables B, zeta_1 and zeta_2 in the dynamical system is not available explicitly. We minimize the sum of exponentially weighted squared differences F[K] between the true trading prices from day i to day i n-1 and the corresponding computed market prices obtained from the first row vector of the numerical solution U of the IVP with AFDE for ith optimal parameter vector where {K} is an initial parameter vector. Here, the gradient (F(x))is approximated by using the central difference formula and step length s is determined by the backtracking line search. One of the novel components of the proposed asset flow optimization forecast algorithm is a dynamic initial parameter pool which contains most recently used successful parameters, besides the various fixed parameters from a set of grid points in a hyper-box.

numerical nonlinear optimization, inverse problem of parameter estimation, asset flow differential equations, financial market dynamics, market return prediction algorithm, data analysis in mathematical finance and economics, out-of-sample prediction

Abstract:
We study overreaction and the cumulative effect of the consecutive local overreaction patterns in financial markets. The 'overreaction diamond' pattern [1] is one of the key components of a financial market bubble. The cumulative effect of the consecutive short term overreactions arising from the deviation of stock prices from their fundamentals can be explained by attribution theory, feedback traders, affect and representativeness theories, and reference points in investments. We study large set of financial data and propose a data mining method by exploiting the relative cumulative sentiment of the investors. This leads to a potential for the implementation of suitable algorithms and the preparation of software packages that can be useful for prediction of various stages of overreaction and bubbles.

data mining, overreaction, computational finance software, financial bubble, prediction, financial markets

Abstract:
In this study I apply forward sensitivity analysis to the dynamical system of nonlinear asset flow differential equations (AFDE). I find that all parameters in AFDE are needed and can be estimated from market prices and net asset values data. Moreover, the market price is the most fluctuating state variable and the coefficient for the trend-based investors' sentiment is the dominant parameter. Furthermore, I define and compare the extreme value based volatilities of market price and net asset value for closed-end funds. I find that the extreme value based volatility of market price is higher than that of net asset value for the vast majority of closed-end funds for both overlapping and non-overlapping cases.

parametric sensitivity analysis, extreme value based volatility, nonlinear dynamical systems, numerical solution of differential equations market dynamics, mathematical finance and economics, quantitative finance

Abstract:
We present a new profitable trading and risk management strategy with transaction cost for an adaptive equally weighted portfolio. Moreover, we implement a rule-based expert system for the daily financial decision making process by using the power of spectral analysis. We use several key components such as principal component analysis, partitioning, memory in stock markets, percentile for relative standing, the first four normalized central moments, learning algorithm, switching among several investments positions consisting of short stock market, long stock market and money market with real risk-free rates. We find that it is possible to beat the proxy for equity market without short selling for S&P 500-listed 168 stocks during the 1998-2008 period and Russell 2000-listed 213 stocks during the 1995-2007 period. Our Monte Carlo simulation over both the various set of stocks and the interval of time confirms our findings.

portfolio risk management, algorithmic trading, out-of-sample prediction, long memory in stocks, adaptive learning algorithm, market timing, principal component analysis, simulation