Chapter 5. Algorithmic Trading

Algorithmic trading is defined as the buying and selling of financial instruments using predefined rules called algorithms. Traders use predictive modeling, time series modeling, and machine learning to predict the price, return, or direction of movement of the asset.

Algorithms are developed by quantitative traders or quantitative researchers and tested on historical data. Algorithms go through rigorous testing before they are used for live trading. Technical indicator-based trading can also come under algorithm trading if it is fully automated. However, sometimes quantitative traders also use fundamental data such as market capitalization, cash flow, debt to equity ratio, and so on to define rules for algorithms. People are free to use any technique to define rules for algorithms. Very recently, investment or trading firms have started to dive deep into machine learning methods to predict price, return, or direction movement.

I will be covering machine learning...

Momentum or directional trading

Momentum trading is trading when the instrument is trending up or down or, in other words, continuation in the trend as like historical winners are expected to be winners and historical losers are expected to lose. You bet on the direction of the instrument and you aim for buying at a low price and selling at a high price. I will not cover the pros and cons and what the different types of momentum trading strategies are. It is left to the trader to devise any idea. I will cover how to implement momentum trading rules and backtest using historical data in R. Stock return depends on various factors, and later in this chapter, I will show you how to use the multifactor model which explains stock return.

Let me start with simple technical indicators.

Technical indicators are implemented in the quantmod package so I will be using quantmod for this:

> library('quantmod') 
>getSymbols("^DJI",src="yahoo") 
[1] "DJI" 
> head(DJI) 

We have...

Capital asset pricing model

The capital asset pricing model (CAPM) model helps to gauge risk contributed by security or portfolio to its benchmark and is measured by beta (). Using the CAPM model, we can estimate the expected excess return of an individual security or portfolio which is proportional to its beta:

Here:

• E(Ri): Expected return of security

• E(Rm): Expected return of market

• Ri: Rate of return of security

• Rf: Risk Free rate of return

• Rm: Benchmark or market return

• : Beta of the security

CVX is regressed against DJI using linear model as per equation 5.4.

Here I used zero as risk-free return in the following command:

>rf<- rep(0,length(dji))
>model <- lm((ret_cvx  -rf) ~ (ret_dji -rf) )
> model
Call:
lm(formula = (ret_cvx - rf) ~ (ret_dji - rf))
Coefficients:
(Intercept)  ret_dji
-0.0002013    1.1034521 

You can see the intercept term in the above result is alpha (-0.0002013) and coefficient for ret_dji is beta (1.1034521). However, you can also use the PerformanceAnalytics...

Multi factor model

The multi factor model can be used to decompose returns and calculate risk. The factors are constructed using pricing, fundamental, and analyst estimates data. I will use Systematic Investor Toolbox for this section.

The gzcon() function creates a connection and reads data in compressed format. Once we create a connection, we also have to close the connection.

The following commands explain this:

> con = gzcon(url('http://www.systematicportfolio.com/sit.gz', 'rb'))
>  source(con)
> close(con)

The following function is used to fetch Dow Jones components data from http://money.cnn.com and join() is taken from Systematic Investor Toolbox:

>dow.jones.components<- function(){
url = 'http://money.cnn.com/data/dow30/'
   txt = join(readLines(url))
   temp = gsub(pattern = '">', replacement = '<td>', txt, perl = TRUE)
   temp = gsub(pattern = '</a>', replacement = '</td>', temp, perl = TRUE) 
   temp = extract.table.from.webpage(temp, 'Volume...

Portfolio construction

Investors are interested in reducing risk and maximizing return of their investment and creating a portfolio does this job provided we have constructed it by keeping in mind the investor risk-return profile. I will guide you through creating an efficient frontier that can help you to measure risk with respect to your return expectation. For that, I will start extracting data for four securities. The first line of code creates a new environment to store data; the next few lines are for symbols list, data starting date, and extracting data using getSymbols():

>stockData<- new.env() 
> symbols <- c("MSFT","FB","GOOG","AAPL")
>start_date<- as.Date("2014-01-01")
>getSymbols(symbols, src="yahoo", env=stockData, from=start_date)
> x <- list()

The next for loop stores individual stock data in a list, and calculates the day's gain and a data frame consisting of closing prices of all stocks in portfolio:

>for (i in 1:length(symbols)) {
  x[[i]]...

Questions

1. How do you import stock data into the R workspace from Yahoo Finance?

2. How do you generate a momentum strategy using moving average crossover?

3. Which package helps to calculate the performance metrics of a strategy?

4. How do you calculate the covariance matrix for a portfolio consisting of five stocks?

5. Extract MSFT data from Yahoo and test that the closing price series is non-stationary.

6. Use the distance method to generate trading signals which exit when the spread reverts to mean.

7. How do you test a pair of stocks for co-integration and write code to test it?

8. How do you calculate hedge ratio and how does it helps in trading?

9. How do you calculate portfolio beta? Show it using an example.

10. How do you use the fundamental factor to create quantiles and quantile spread?

11. Write code to calculate portfolio expected _return and standard deviation.

12. How do you calculate the efficient frontier and plot it using the R command?

Summary

In this chapter, I presented different concepts of trading using R. I started with trend following strategy and explained in depth how the trading signals are generated and how various parameters related to its performance are captured. Momentum strategies was followed by pairs trading using three different methods. The first method covered was distance based pairs trading, the second was correlation based, and the third and final method was co-integration based pairs trading. Sometimes, trading in a portfolio is important to control the risk and reward ratio and for that I have covered capital asset pricing, the multi factor model, and portfolio construction. I used Systematic Investor Toolbox for implementing portfolio ideas.

In the next chapter, I will explain trading strategies using machine learning algorithms, which are gaining in popularity. Machine learning algorithms learn automatically from historical market behavior and try to mimic this behavior.