Fooled by Randomness
----Zhengyuan Zhu (Y12)
“Humans are often unaware of the existence of randomness. They tend to explain random outcomes as non-random. ” 1
People don’t understand how things are just random and try to make sense out of them. They would be making models out of stock data and look at how the pattern in the data is and forecast the future stock price, which exactly analysts and investors are doing in the investment banks. Is there really a sort of pattern and tendency behind the security price or just randomness? In this article, we would like to use some A-Level mathematics to make a sense of it. In order to understand how security prices work in the market, we need to understand the meaning of the term of the Efficient Market Hypothesis (EMH). It is a theory that states markets efficiently incorporate all public information. Security prices accurately reflect available information and respond rapidly to new information as soon as it becomes available 2 . The idea is that, if the market is really efficient, then any change from day to day has to be due only to news. However, news is essentially unpredictable. Thus, security prices have to do a random walk through time, which means any future movement in them is always unpredictable and changes are purely random. The random walk process can be described as follows: E(ε) = 0, for i ≠ s Using A-level statistics, we know that the mean of is zero and they are uncorrelated with any other previous values, meaning that is random. To test whether the stock market is really efficient, we are using the method called “auto-regression”, which is combined with PMCC (S1) and testing for zero correlation (S3). Autoregressive processes are used by investors to investigate the pattern in data. Auto-regressive models take into account past movements and future values are estimated based on the past values. E(ε i ε s ) = 0, Y t = Y t−1 + ε t ⟹ Y t − Y t−1 = ε t
1 Taleb, N. N. (2008) Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets. 2nd edn. New York: Random House Publishing Group 2 Efficient-market hypothesis (2015) in Wikipedia. Available at: http://en.wikipedia.org/wiki/Efficient- market_hypothesis (Accessed: 12 April 2015)
1
Made with FlippingBook - Online Brochure Maker