Role of Mathematics and Statistics in Trading | Quantra Courses скачать в хорошем качестве

Role of Mathematics and Statistics in Trading | Quantra Courses

Find more courses on Quantra: https://quantra.quantinsti.com/ In this video we will explain the role of mathematics and statistics in trading using three applications. These applications are Technical indicators Financial time series analysis Quant trading strategy and performance analysis. Every trader at least once in their lifetime uses technical indicators to generate trading signals. It could be a simple moving average or complex indicators like the Ichimoku cloud. If you have noticed all these indicators are based on some mathematical formula. For example a simple moving average is the rolling average of prices over a period of time. What does rolling average mean? Let’s say you have the daily price data of a security and you need to calculate the moving average with period 5. The first moving average is calculated by taking the average of the first five day closing prices. Similarly the next moving average is calculated by taking the average of the next five closing prices and so on. Consider another technical indicator Bollinger Bands. It consists of three lines the upper middle and lower bands. How do these bands form? The middle band is the moving average of the prices over a time period. The upper and lower bands are calculated by adding and subtracting standard deviations to the moving averages respectively. The standard deviation tells how the prices are dispersed from its mean price. The moving averages and standard deviations are used to create Bollinger bands. So if you are doing technical analysis you will frequently find usage of such statistical and mathematical terms and understanding them are crucial for a thorough analysis of the strategy. The second application is time series analysis. Say you want to predict the future price of security using its past prices. For example the past 1 year price of stock Tesla is given to you and your task is to predict the next day's price. How do you do that? First you can find if there is any relationship between the past and current Tesla prices. To do that you can use autocorrelation and partial autocorrelation. Both are statistical measures that tell how the current price is related to the past price. If there is a relationship between past and current stock prices you can predict the future prices. This is done using a concept called autoregression. Autoregression is a time series model which is very similar to regression. It uses past stock prices as input to a regression equation to predict the future prices. Again the statistics come to the rescue and help in achieving the task of future price prediction. The third application is to create a trading strategy. You may have heard of a popular quant trading strategy known as pairs trading. In pairs trading we look for the stock pairs that have some correlation. Once we find correlated stock pairs we check whether the pair is cointegrated or not. To do that we perform statistical tests like ADF and Johansen. Once it is confirmed that chosen pairs are cointegrated we buy the underperforming stock and sell the overperforming one. Here we used the three terms. We used correlation which tells the statistical relationship between two random variables. Then we used cointegration followed by statistical tests to validate the cointegration between pairs. You created the pairs trading strategy and you are confident that it will give you a huge profit. But is there any method that validates the strategy will be profitable and reliable to put your hard-earned money? Yes mathematical formulas will tell you about the strategy performance. You can find out how strategy has performed over the period of time using cumulative returns. That is subtracting the initial value of the strategy from the final value and dividing it by the initial value. You can find out how volatile your strategy is by calculating the standard deviation of the cumulative returns. Similarly the performance metrics such as Sharpe ratio Sortino ratio Beta can be used to analyse the strategy. All are derived from some mathematical formula. So understanding these metrics and how they are calculated will definitely help you evaluate the strategy. If you have heard these terms for the first time you might be a little overwhelmed. There is no need to worry. In the Quantra courses we discuss the relevant mathematical formulas and statistical concepts before learning the trading strategy. We hope this clears how statistics and mathematics are used in quantitative trading and modelling. Happy learning! Quantra is an online education portal that specializes in Algorithmic and Quantitative trading. Quantra offers various bite-sized, self-paced and interactive courses that are perfect for busy professionals, seeking implementable knowledge in this domain. Find more info on - https://quantra.quantinsti.com/ Like us on Facebook:   / goquantra   Follow us on Twitter:   / goquantra