### 金融代写|金融计量经济学代写Financial Econometrics代考|Random Walk Hypothesis

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• Statistical Inference 统计推断
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• (Generalized) Linear Models 广义线性模型
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• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 金融代写|金融计量经济学Financial Econometrics代考|Background

The basic idea is that movement of the stock prices are unpredictable and random. Jules Augustin Frédéric Regnault, a French stock broker’s subordinate primarily explained the rationale behind the stock prices stochastic movements using a random walk model. Jules in his book titled ” Calcul des chances et philosophie de la bourse” states that “l’écart des cours est en raison directe de la racine carrée des temps”. 1 Which means “the price difference is a direct result of the square root of the times” and it clearly indicates that the stock prices movement follows a stochastic process. Later it becomes the foundation of Louis Bachelier PhD thesis titled “Th’corie de la Sp’eculation”. Louis often credited as the first person to introduce advanced mathematics into the field of finance. He established a mathematical model of the stochastic process (known as Brownian motion) for valuing the stock options. For a longer period of time Louis’ contribution was overlooked or ignored as his study applied mathematics into the field of finance. Possible reason could be during the nineteenth century the field of interdisciplinary research was not developed or quite accustomed. Then in 1964, Paul H. Cootner, a professor of MIT Sloan School of Management in his book titled “The Random Character of Stock Market Prices” educes the ideas on the stochastic process of stock prices movements. Later on the same ideas are well established by the several known scholars namely Eugene Fama, Burton Malkiel, and others.

## 金融代写|金融计量经济学Financial Econometrics代考|What Is Random Walk Hypothesis and Its Implications

Random walk hypothesis assumes that price movements of individual securities in the stock markets follow a random walk and successive price movements are independent to each other. Therefore, the random walk hypothesis posits that it is impossible to forecast the stock prices movements. Random walk hypothesis also suggests that it is impossible to beat the market by the market participants in the long run. Outperformance of the market by an investor is only possible by taking an extra amount of risk. The Random Walk hypothesis is heavily criticized on several grounds such as market participants differ in terms of the amount of time they spend in the financial market. Then several numbers of the known and unknown factors are responsible for driving the stock prices (Maiti, 2020). It is often not likely to detect the associated trends or patterns that might exist in the stock prices movements due to the presence of several such distinct factors. To test the random walk hypothesis in practice, Wall Street Journal (WSJ) initiated the “Dart Throwing Investment Contest” in the year 1988. Two groups were formed: one group belongs to the professional investors whereas other belongs to the dummy. Professional investors group consists of the professionals working with NYSE whereas WSJ staff groups as the dummy. In other words professional investors represent “skill” whereas dummy represents “luck”. Professional investors selected stocks based on their skills whereas dummy made their selection of stocks based on the outcome of the dart throwing (luck). After 100 contests the outcomes come as following: professional investors won 61 times or skill wins 61 times versus luck. However, professional investors (skill) are able to beat the market (DJIA) 51 times out of 100 . Dart Throwing Investment Contest does not provide any ultimate consensus on “luck versus skills”. The current consensus is that the random walk hypothesis is linked to the efficient market hypothesis (EMH). Mathematically a simple random walk model with a drift is represented by following Eq. (2.1):
$$\text { Price }{t}=\text { Price }{t-1}+\alpha_{t}$$
$/ / \operatorname{Mean}(\mu)$ is zero and standard deviation $(\sigma)$ is constant where
Price $_{t}$ represents current stock price at time ( $\left.t\right)$
Price $_{t-1}-$ represents stock price at time $(t-1)$
$\alpha_{t}$ represents the drift term

## 金融代写|金融计量经济学Financial Econometrics代考|Efficient Market Hypothesis

Efficient market hypothesis assumes that the security prices reflect all available information and follow a random walk. However, the strength of these assumptions depends on the form of EMH as explained by Fama (1970). Thus, the direct implication of EMH is that it is impossible to beat the market steadily merely by ensuing a specific risk adjusted strategy. Fama (1970) labels efficient market hypothesis into three types based on the level of the relevant information as weak, semi-strong and strong forms of EMH, respectively. Weak forms of EMH assume that all historical stock prices information is impounded in the current price of the stock. Then a semi-strong form of EMH assumes that all publicly available information in addition to those historical stock prices information are well impounded in the current price of the stock. Finally, strong forms of EMH assume that all available information both private (insider information) and public is fully impounded in the current price of the stock. The joint hypothesis problem makes it difficult to test the EMH. The argument put forward as the EMH could only be tested with the help of a market equilibrium model (Asset pricing model). The EMH basically tests whether the properties of expected returns suggested by the assumed market equilibrium model (asset pricing model) are noticed in actual returns. If the tests reject, then it is difficult to interpret whether the rejection is made due to the inefficiency of the market or a bad market equilibrium model (asset pricing model). Fama (1970) stressed that the EMH is always tested jointly along with the market equilibrium model and vice versa. Thereafter significant number of studies are done on EMH and asset pricing. All of these studies unanimously emphasized that the $\mathrm{EMH}$ is very simple in principle but testing it proved to be difficult. Both the random walk hypothesis and efficient market hypothesis have significant importance in applied financial econometrics study as both of them could provide some relevant information on relative market efficiency. Still distinct views exist on whether markets are really efficient? There are several studies that evidence support for EMH such as on an average mutual funds do not able to outperformed the market. Then “Dart Throwing Investment Contest” results show that the performance of skills versus luck are quite similar in beating the market. On the other hand, there are group of studies that evidence against EMH is as follows: presence of stock market anomalies, presence of excessive volatility in the stock market, behavioural finance theories, and others.

## 金融代写|金融计量经济学Financial Econometrics代考|What Is Random Walk Hypothesis and Its Implications

价格 吨= 价格 吨−1+一个吨
//意思是⁡(μ)是零和标准偏差(σ)是常数，其中

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