Algorithmic Trading Strategies and Execution

Algorithmic Trading

• Utilizes computer programs to automate trading processes.
• Aims to execute orders at the best possible price.
• Strategies include directional bets, market making, arbitrage, statistical arbitrage, index fund rebalancing, pairs trading, and execution algorithms.

Types of Trading

• Directional: Betting on the price direction of a stock.
• Market Making: Providing bid/ask quotes to profit from the spread.
• Arbitrage: Exploiting price differences of an asset in different markets.
• Statistical Arbitrage: Employing algorithms to identify statistical mispricing and using mean reversion strategies.
• Index Fund Rebalancing: Trading activities resulting from fund rebalancing.
• Pairs Trading/Correlation Trading: Betting on the convergence of correlated stocks when they deviate.
• Execution Algorithm: Using algorithms like VWAP, TWAP, POV, and IS to execute large orders.

Execution Algorithm

• Aims to execute large orders while minimizing market impact.
• Volume Weighted Average Price (VWAP): Executes orders based on historical volume patterns.
• Time Weighted Average Price (TWAP): Distributes the order execution evenly over a specified time.
• Percent of Volume (POV): Participates with a predetermined percentage of the market volume.
• Implementation Shortfall (IS): Designed to minimize costs and slippage.

Order Book

• A limit order book (LOB) is an electronic record of outstanding limit orders.

Order Book Events

• Limit Order: Order to buy/sell at a specific price, adding liquidity to the order book.
• Market Order: Order to buy/sell immediately at the best available price, removing liquidity.
• Cancel Order: Removal of a pre-existing limit order from the order book.

Order Book Example

• At a price of $100.01, there's a buy and sell size of 100 shares each.
• At a price of $100.00, there's a buy and sell size of 200 shares each.
• At a price of $99.99, there's a buy and sell size of 300 shares each.
• At a price of $99.98, there's a buy and sell size of 400 shares each.
• At a price of $99.97, there's a buy and sell size of 500 shares each.

Market Order: Buy 100 Shares

• Requires purchasing 100 shares at $100.01
• Results in a new best offer at $100.00

Market Order: Sell 300 Shares

• Requires selling 100 shares at $99.99
• Selling an additional 200 shares at $99.98.
• Results in the new best bid at $99.97.

Order Book Statistics

• Important statistics include best bid/ask, mid price, spread, book depth, order flow, and order size.
• Mid Price is the average of Best Bid and Best Ask
• Spread is the difference between Best Ask and Best Bid

Simple Trading Strategies

• Mean Reversion: A strategy that assumes prices will revert to their average value; short when z > threshold, long when z < threshold.
• Pairs Trading: Capitalizes on temporary divergence between correlated stocks; short the "expensive" stock and long the "cheap" stock.
• Delta One: Involves buying shares of a company before its S&P500 inclusion to profit from the anticipated price increase.
• Market Making: Quoting tight bid-ask spreads to repeatedly earn small profits.
• Arbitrage: Taking advantage of price discrepancies in different markets.

Basic Time Series Analysis

• Key components include trend, seasonality, cycle, and irregularity.
• Apply descriptive statistics and hypothesis testing to identify patterns, correlation, stationarity and volatility

Common Trading Signals

• Signals include Moving Averages, Bollinger Bands, MACD, RSI, Stochastic Oscillator, Ichimoku Cloud, and Fibonacci Retracement.

Back Testing

• Considers factors like Transaction Cost and Slippage.

Backtesting Metrics

• Total Return: Overall profit or loss over the backtesting period.
• Annualized Return: Average annual return of the strategy.
• Sharpe Ratio: Measures risk-adjusted return, calculated as $\frac{R_p - R_f}{\sigma_p}$.
• Sortino Ratio: Measures downside risk-adjusted return, calculated as $\frac{R_p - R_f}{\sigma_d}$.
• Maximum Drawdown: The largest peak-to-trough decline during a specific period. Calculated as $Drawdown = \frac{Current,Value - Peak,Value}{Peak,Value}$
• Win Rate: Percentage of profitable trades.
• Profit Factor: Ratio of Gross Profit to Gross Loss.

Overfitting

• Model performs well on training data but poorly on test data.
• Due to excessive complexity which captures noise
• Can be avoided by: keeping it simple, using cross-validation, regularization, and more data
• Use out-of-sample testing

Máquina de Aprendizaje Algoritmos

Clasificación

• Assigns an instance to a finite number of classes using training data consisting of labeled instances.
• Types: Logistic Regression, SVM, Decision Trees, Random Forests, Neural Networks

Regresión

• Predicts a continuous value using a training dataset of instances labeled with continuous values.
• Types: Linear Regression, Polynomial Regression, SVM, Decision Trees, Random Forests, Neural Networks

Agrupamiento

• The algorithm groups similar instances from a training dataset each unaassociated with a class label
• Types: K-Means, Hierarchical Clustering, DBSCAN, Spectral Clustering, GMM

Reducción de la dimensionalidad

• Reduces the number of features while preserving important aspects.
• Types: PCA, LDA, Autoencoders, t-SNE, Feature selection

Introduction to Algorithmic Trading

Algorithmic Trading

• Computer programs are employed to automate trading also known as automated trading or black-box trading.

Order Execution

• Objective is to get orders filled at the best possible price.

High-Frequency Trading (HFT)

• Characterized by its high speeds, high turnover rates, and high order-to-trade ratios and depends on co-location, DMA, complex algorithms
• DMA stands for direct market access

Advantages of Algorithmic Trading

• Reduced Transactions Cost
• Improved order execution
• Increased market efficiency
• Automation
• Backtesting

Disadvantages of Algorithmic Trading

• Model Risk: Possibility of algorithm based on a flawed model.
• Technical Risk: Possibility of technical problems ex. software bugs
• Market Risk: Flash crash
• Regulatory Risk: Possibility of change in regulation
• Increased Competition

Types of Algorithmic Trading Strategies

• Statistical Arbitrage is exploiting statistical relationships between different assets
• Market Making provides liquidity to the market by placing buy and sell orders
• Trend Following identifies and follows trends in the market
• Execution Algorithms optimize the execution of orders

Order Book

• A limit order book (LOB) is an electronic list of buy and sell orders for a specific security or financial instrument in order of price level

Components of an Order Book

• Bid: Buyer's highest price for a share
• Ask (Offer): Seller's lowest price for a share
• Bid Size: Shares buyers will buy for bid price
• Ask Size: Shares the sellers will sell for an ask price
• The mid-price is the middle between the bid and ask prices. The mid-price formula is $\text{Mid-Price} = \frac{\text{Bid} + \text{Ask}}{2}$

An example of an order book for a hypothetical stock

• At a price of $100.00 the size of the bid is 100 via order type being bid
• At a price of $99.99 the size of the bid is 50 via order type being bid
• At a price of $99.98 the size of the bid is 25 via order type being bid
• At a price of $100.01 the size of the ask is 30
• At a price of $100.02 the size of the ask is 75
• At a price of $100.03 the size of the ask is 100
• Shares the sellers will sell for an ask price

Dynamics of Order Book

• Order Placement: Traders place order
• Order Cancellation: Traders can cancel their existing orders
• Order Matching: Trading happens when buy orders match sell orders
• Price Discovery: Price discovery is finding out the correct price

The definition and description of further Order Book jargon

• Market Impact: Affected because change in price affected by trading
• Slippage: Not the intended result

Thermodynamics

• Study of energy, its transformations, and its relation to matter.

Basic Concepts

• A System is part of the universe under study
• The Surroundings are everything outside of the system
• The Boundary Separates system from surroundings.

Types of Systems

• An Isolated System does not exchange matter or energy
• A Closed System exchanges energy but not matter
• An Open System exchanges both energy and matter

Thermodynamic Properties

• Intensive Properties: Temperature, Pressure, Density
• Extensive Properties: Volume, Mass, Energy

Intensive Properties

• Are independent of the amount of substance ex. Temperature, Pressure and Density

Extensive Properties

• Are dependent on the amount of substance ex. Volume, Mass and Energy

Thermodynamic Process Types

• Isothermal: Constant temperature.
• Adiabatic: No heat exchange.
• Isobaric: Constant pressure.
• Isochoric: Constant volume.

Process Types Based on Equilibrium

• Reversible System is in equilibrium, is infinitesimally slow.
• Irreversible Occurs spontaneously, is not in equilibrium.

Laws of Thermodynamics

• Zeroth Law States: If two systems are each in thermal equilibrium, they are in thermal equilibrium with each other.
• First Law States: Energy cannot be created or destroyed, only transformed. With $\Delta U = Q - W$
• Second Law States: The entropy of an isolated system always increases or remains constant. $\Delta S \geq 0$
• Third Law States: The entropy of a perfect crystal at absolute zero temperature is zero.

Thermodynamic Functions

• Enthalpy: H = U + PV U is internal energy, P is pressure, and V is volume
• Entropy: Measure of randomness

Gibbs Free Energy

• G = H - TS where T is Temperature

Thermodynamic Applications

• Heat Engines: Convert energy to work
• Refrigerators: Transfer heat
• Chemical Reactions: Predict equilibrium

Fourier Transform Properties

Linearity

• The Fourier transform is a linear combination defined as: $F{af(t) + bg(t)} = aF(f(t)) + bF(g(t))$

Time Scaling

$F{f(at)} = \frac{1}{|a|}F(\frac{\omega}{a})$

• Proof:*

$F{f(at)} = \int_{-\infty}^{\infty} f(at)e^{-j\omega t} dt$

Let $\tau = at$, $dt = \frac{1}{a}d\tau$

$F{f(at)} = \int_{-\infty}^{\infty} f(\tau)e^{-j\omega \frac{\tau}{a}} \frac{1}{a} d\tau = \frac{1}{a} \int_{-\infty}^{\infty} f(\tau) e^{-j\frac{\omega}{a} \tau} d\tau$

$F{f(at)} = \frac{1}{a}F(\frac{\omega}{a})$ if a > 0

$F{f(at)} = \frac{1}{|a|}F(\frac{\omega}{a})$

Other Identities

$F{f(t - t_0)} = e^{-j\omega t_0}F(\omega)$ $F{e^{j\omega_0 t}f(t)} = F(\omega - \omega_0)$ $F{\frac{df(t)}{dt}} = j\omega F(\omega)$ $F{\frac{d^n f(t)}{dt^n}} = (j\omega)^n F(\omega)$ $F{tf(t)} = j\frac{dF(\omega)}{d\omega}$ $F{t^n f(t)} = j^n \frac{d^n F(\omega)}{d\omega^n}$ $F{\int_{-\infty}^{t} f(\tau) d\tau} = \frac{1}{j\omega}F(\omega) + \pi F(0)\delta(\omega)$ $F{f(t) * g(t)} = F(\omega)G(\omega)$ $F{f(t)g(t)} = \frac{1}{2\pi}F(\omega) * G(\omega)$

More identities

• Duality If $f(t) \leftrightarrow F(\omega)$, then $F(t) \leftrightarrow 2\pi f(-\omega)$
• Parseval's Theorem: $\int_{-\infty}^{\infty} |f(t)|^2 dt = \frac{1}{2\pi} \int_{-\infty}^{\infty} |F(\omega)|^2 d\omega$

Organic Chemistry

Alkanes

Nomenclature Rules

• Localizar la cadena continua más larga de átomos de carbono;
• Numerar la cadena principal comenzando por el extremo más cercano.Localizar la cadena continua más larga de átomos de carbono.

Naming Example

• Prefix "met" if 1 carbon
• Prefix "et" if 2 carbon
• Prefix "prop" if 3 carbon
• Prefix "but" if 4 carbon
• Prefix "pent" if 5 carbon
• Prefix "hex" if 6 carbon
• Prefix "hept" if 7 carbon
• Prefix "oct" if 8 carbon
• Prefix "non" if 9 carbon
• Prefix "dec" if 10 carbon

Organic Chemistry Group

Alkyl Group

• Has 1 Alkane removed
• Methyl (CH3)
• Ethyl (CH2CH3)
• Propyl (CH2CH2CH3)
• Isopropyl

Alkyl Halides

• An alkyl halide contains a halogen attached to sp3 ex

Halogenuros de alquilo

• Chloride(CH3Cl)
• Bromide(CH3CH2Br)

Alcohols contains Hydroxyl(OH)

• Metanol
• Ethanol

Ethers Contains (O)

• Dimethyl ether
• Diethyl ether

Amines Contains Nitrogen(N)

• Methylamine
• Dimethylamine
• Trimethylamine

Aldehydes Conatin Carbonyl

• Aldehyde has hydrogen attached to carbonly carbon

Ketones Contains Carbonly

• Has 2 carbon connected to the carbons in carbonyl

Caboxylic Acids Has Caronyl(C=O)w/ Hydroxyl Group(OH)

Esters Has C=O Attached w/ oxygen attached

Chapter 5: The Nucleus of the Cell

Genetic info exists inside of the Nucleus

• The Nucleus is the largest organelle in eukaryotic cells
• It has all the cell's DNA composed in the form of chromosomes
• The Nucleus is involved in gene expression and cell activities

Nuclear Structure and Function

• Is composed of the nuclear envelope which is a double membrane
• Contains nuclear powers that control molecules between the nucleus and cytoplasm
• The Nucleolus is involved in production of protiens
• Composed of DNA and protein which compose the nucleus

Chromosomes

• Has chromatin
• Each chromosome is composed of DNA
• The Chromosomes become condensed which allows them to become visible with machines

Chromatin Structure

• DNA is wrapped around nucleosomes.
• Nucleosomes form higher-order configurations
• Chromatin compaction changes based on the cell cycle and the level of expression

Nuclear Envelope

• Is a double membrane that surrounds the nucleus
• Is composed of an inner and outer membrane with a perinucleal region
• Contains Nuclear powers that modulate molecules from the outside and inside

Nuclear Powers

• Are complexes
• Modulate transfer of molecules

Nucleolus

• Is involved in protiens using ribosomal RNA also knows as rRNA

Nuclear Matrix

• Has protein fibres throughout and functions by -Providing structural support -Organizing chromatin

Replication and repair

Polymerase

• Synthesizes DNA

Ligase

• Joins Fragments

Origin of replication

DNA repair

• corrects DNA damage

Types of DNA Repair

• Mismatch repair
• Nucleotide excision repair
• Base excision repair

The Cell Cycle Overview

• The cell cycle is essential for growth, development, and repair in multicellular organisms.
• In unicellular organisms, the cell cycle is essential for reproduction

Cell Death

• Cell cycle is divided to interphase and m phase

Necrosis

• Cell Death caused by injury

Apoptosis

• Cell Death which is part of devolopment

Interphase

• Preparation for dividing, gathering nutrient $G_1$: Growth and Function S: DNA copies $G_2$: Further growth and prep

M Phase

• Division consists mitosis and cytokinesis

Mitosis:

• Nuclear division has stages such as -Prophase -Prometaphase -Metaphase -Anaphase -Telophase

Key Regulators:

1. Cyclins: proteins that fluctuate in concentration cyclically.
2. Cyclin-Dependent Kinases (CDKs): Enzymes

Cell Cycle Checkpoints

• 1. $G_1$ Checkpoint is at DNA damage

2. $G_2$ Checkpoint is for problems via for complete replication
3. M checkpoint is an error preventer in mitosis