Algorithmic Trading

• Study notes on various topics

Algorithmic Trading

• Algorithmic trading, also known as automated or black-box trading, utilizes computer programs to execute trades based on predefined instructions or mathematical models, considering factors like price, timing, and quantity.

Algorithmic Trading Advantages

• Reduced transaction costs through minimized market impact and improved execution prices.
• Faster order execution compared to human traders, crucial in fast-moving markets.
• Simultaneous order execution across multiple markets, impossible for human traders.
• Reduced errors by eliminating human factors like mistyping or emotional decisions.
• Increased trading opportunities with 24/7 market monitoring.
• Backtesting capabilities to evaluate performance and identify weaknesses.

Algorithmic Trading Disadvantages

• Susceptibility to system errors like software bugs or hardware failures.
• Reliance on models, which may be wrong or outdated, leading to model risk.
• The potential for over-optimization, resulting in poor performance on live data.
• Significant market impact from large algorithmic orders.
• Exposure to regulatory risk, where new rules could limit algorithms' use.
• The need for continuous monitoring and maintenance.

Types of Algorithmic Trading Strategies

• Trend Following takes advantage of existing market trends.
• Mean Reversion capitalizes deviations from an asset's average price.
• Arbitrage exploits the price differences of the same asset in different markets.
• Market Making provides liquidity by placing bid and offer orders.
• Statistical Arbitrage uses statistical models to identify and capitalize on pricing discrepancies.
• Execution Algorithms optimize the execution of large orders to minimize market impact.

Order Execution

• Order execution involves completing buy or sell orders by matching them with counterparties and settling the transactions either manually or electronically, often automated with algorithms.

Order Placement Considerations

• Order Size: The number of shares or contracts to be traded.
• Price: The price at which the order should be executed.
• Timing: The time at which the order should be executed.
• Order Type: The type of order to be used (e.g., market order, limit order, stop order).
• Venue: The exchange or trading venue where the order should be executed.

Types of Orders

• A Market Order executes immediately at the best available price, offering a high probability of execution but potentially at a less favorable price.
• A Limit Order executes only at a specified price or better, allowing price control but with the risk of non-execution.
• A Stop Order triggers when the price reaches a specific level (stop price), usable for limiting losses or protecting profits but can be sensitive to temporary fluctuations.
  • Buy Stop Order is an order to purchase a security, and is only executed when the price rises to the stop price
  • Sell Stop Order is an order to sell a security, and is only ecuted when the prices falls to the stop price
• Combining the features of stop and limit orders, a Stop-Limit Order becomes a limit order once the stop price is reached, but may not execute if the market moves quickly past the limit price.
• Other Order Types
  • Day Order is an order that is only good for the day it is placed.
  • Good-Til-Canceled (GTC) Order is an order that remains in effect until it is executed or canceled.
  • Immediate-or-Cancel (IOC) Order must be executed immediately, and any portion that cannot be executed is canceled.
  • Fill-or-Kill (FOK) Order is an order that must be executed in its entirety immediately, or it is canceled.
  • All-or-None (AON) Order is an order that must be executed in its entirety, but not necessarily immediately.

Order Execution Algorithms

• Volume-Weighted Average Price (VWAP) matches an order to the stock's volume-weighted average price over a specific period.
• Time-Weighted Average Price (TWAP) matches a specific stock against the the time-weighted average price of a stock over a determined duration.
• Percentage of Volume (POV) executes a fixed percentage of the market volume over a specified period
• Implementation Shortfall minimizes the difference between the actual execution price and the theoretical price when the order was placed.
• Dark Pools executes orders privately without publicly displaying order information.

Algorithmic Trading Example

• Algorithm: Create an algorithm to buy a stock when its 50-day moving average crosses above its 200-day moving average (a "golden cross"),
• Fetch daily price data for the stock.
• Calculate the 50-day and 200-day moving averages.
• If the 50-day moving average crosses above the 200-day moving average, place a buy order.
• Monitor the position and sell when the 50-day moving average crosses below the 200-day moving average (a "death cross").
• To minimize market impact, use a VWAP algorithm to execute buy and sell orders over one hour.

Order Execution Example

• Scenario: An investor wants to buy 1,000 shares of a stock trading at $50.
• Order Placement: The investor places a limit order to buy 1,000 shares at $49.95.
• Order Routing: The broker routes the order to an exchange or trading venue where it can be matched with a seller.
• Order Matching: The order is matched with a seller willing to sell 1,000 shares at $49.95.
• Settlement: The transaction is settled, and the investor receives the 1,000 shares of stock.

High-Frequency Trading (HFT)

• High-Frequency Trading (HFT) relies on extremely high speeds, high turnover rates, and short-term positions.
• HFT is leveraged in market making, arbitrage, and exploiting short-term price discrepancies.
• HFT is controversial as it may destabilize markets and create unfair advantages.

Algorithmic Trading Regulations

• Subject to regulations that designed to prevent market manipulation and ensure fair trading practices.
• Regulations vary by country and may include:
• Registration requirements for algorithmic traders.
• Testing and certification requirements for algorithms.
• Monitoring and surveillance of algorithmic trading activity.
• Restrictions on certain types of algorithmic trading strategies.

Equations Diferenciales de Primer Orden

• A differential equation is an equation that contains derivatives of one or more dependent variables with respect to one or more independent variables.

Classification by Type:

• An ordinary differential equation (ODE) an equation contains ordinary derivatives of one or more dependent variables with respect to a one independent variable
• A partial differential equation (PDE) an equation contains partial derivatives of one or more dependent variables with respect to two or more independent variables

Classification by Order:

• The order of a differential equation is the order of the highest derivative that appears in the equation.

Classification by Linearity:

• Linearity can be described in the formula below:

a_n(x) \frac{d^n y}{dx^n} + a_{n-1}(x) \frac{d^{n-1} y}{dx^{n-1}} + \dots + a_1(x) \frac{dy}{dx} + a_0(x)y = g(x)

• A differential equation is linear if:
• The dependent variable "y" and all its derivatives are of the first degree (the power of each term in "y" is 1).
• Each coefficient depends only on the independent variable "x".
• Example:
• Ordinary differential equation, of first order, linear:

\frac{dy}{dx} + P(x)y = Q(x)

Types of Solution:

• Explicit Solution: A solution in which the dependent variable is expressed only in terms of the independent variable and of constants.
• Implicit Solution: A relation G(x,y) = 0 that defines one or more explicit solutions in an interval I.
• Particular Solution: It is a solution free of arbitrary parameters.
• General Solution: It is a solution that contains all the solutions of the differential equation within a certain domain.

Economics

• Economics studies how societies use scarce resources to produce valuable goods and services and distribute them among different individuals.

Scarcity and Efficiency

• Goods are limited because society makes less than people need.
• Scaricity implies that choices must be made.
• Efficiency refers to obtaining the maximum profit that one can output using less resources.

Microeconomics and Macroeconomics

• Microeconomics deals with the behavior of things such as markets, companies, and households.
• Macroeconomics examines the performance of the economy.

The Logic of Economics

• Economists use the scientific approch to understadn economic life. This implicates using phenomena and the economic use of scientific and historical data to ananlyze them.
• Econometrics is a use of statistical to analyze ecoomic data and test theories.

Common Fallacies in Economic Reaoning

• The Post Hoc Fallacy, "because one event occurred after another, the first caused the second."
• The fallacy of composition, what is that one part of system that its true if also true of the whole.
• The Ceteris Paribus Fallacy, where factos aren't kept constant when evaluating variables.

Positive vs. Normative Economics

• Postitive economics is about facts and behavior.
• Normative economics involves value judgements.

Problems of Economic Organization

• What goods and services are made?
• How are these goods produced
• For whom are these products made for?

Technological

• Every economy runs on a limited amount of supplies: work, capital, land, and technology.
• The production possibilities frontier (PPF) displays max amounts of goods and services that the the economy can output from the available limited supplies.

Features in Production Power

• Hows the maximun anount of product that is supplied to consumers vs what a market can provide as a business.
• Represents the choices available to a society.

Economy Resources

• Cycles in Economy
• Not having enough supplies
• Discrimination amongst consumers

Matrixes

• Elements in index $i$ and $j$ are called $a_{ij}$

Operations

• Adding and subtracting from each other can only work if elements are of the same type
• Scalar multiuplication work by multiplicating a matrix against a scalar
• The amount of columns available can be matrixed if number of columns of fist matrix is eaual to the number of arows in the second

Special Matrixes

• Square Matrix occurs a matrix containing an equal set of arows and columns.
• An equality matrix containing ones is a diaganol
• Transponat of matrix is signified as $A^T$

Chemical Engineering Thermodynamics

• VLE= Vapor Liquid Equilibrium

Vapor Pressure

• $P^{sat}$: The pressure by vapor.
• Vaporization: Liquid becomes vapor.
• Evaporation: Vaporization that takes place at surface.
• Boiling: Vaporization that takes place to the entirety of all liquids.
• Sublimation: Solid becomes vapor.

Vapor Liquid Terms

• Saturated Vapor: Vapor at saturation, meaning any shift in temperature or pressure results in condensations.
• Superheated Vapor: Temperatures are over saturated tempeture under the said pressure.
• Saturated Liquid: A liquid at the satiuration point, any change in temperature or pressure causes liquid to change into vapor.

Types of Equations Listed to Calculate Phase Transition

• Vapor and Temp
• Clapeyron
• Clausius-Clapeyron
• Riedel Equation
• Antoine Equation

Acetric Factor Equation

• Kenneth Pitzer - (1955)

Equation - Phase

Example

• An example can be made to try to determine of freedom of liquid in various temperatures

Clinical Guidelines

Types of Clinical Treatments

• Glycine Enema is a formula made of protein used for treatment.
• It increases blood flow allowing new protection agents amongst the blood.
• Decreases inflammation and oxidiation in the intestines to prevent injuries.

Reasons For Use

• Ulcerative Colitis
• Radiation Proctitis
• Diversion Proctitis

Preperation and Appliction

• Duration if treatment is a four week cycle after a daily application for 30 mins.

Git Basics Learning

• Setting up the repository
• Committing a change
• Exploring the history
• Tracking changes
• In this lab you will need to download and install Git
• You will have to also congfigure local user name and email
• You have to create a local repository to commit changes to a local project
• Track changes in repositories via git log to observe changes, and add new file, or add new material.