Algorithmic Trading Strategies

Algorithmic Trading

• Also known as automated trading, black-box trading, or systematic trading.
• Computer programs follow a set of instructions (algorithm) to place trades.
• The trader provides the algorithm and the program executes trades based on stipulated conditions.

Advantages of Algorithmic Trading

• Trades can be executed at optimal prices.
• Trade order placement is instant and accurate.
• Trading reduces the likelihood of manual errors.
• Back-testing is possible using historical and real-time data.

Common Algorithmic Trading Strategies

Trend Following Strategies

• Capitalize on securities moving in a clear direction.
• Uses moving averages, channel breakouts, and technical indicators like MACD.

Arbitrage Strategies

• Exploit pricing inefficiencies of identical securities on different exchanges.
• Risk-free profits are attainable when the same security trades at different prices.

Mathematical Model-Based Strategies

• Uses quantitative models involving cross-market relationships and statistical arbitrage.
• Identifies trading opportunities through mathematical calculations.
• The pairs trading strategy serves as a classic example.

Trading Range Strategies

• Involves trading within a defined range based on support and resistance levels.
• Traders buy at the support level and sell at the resistance level.

Index Fund Rebalancing

• Index funds deploy algorithmic trading to mirroring the index.

Time Weighted Average Price (TWAP) strategy

• Large orders are divided into smaller chunks over evenly divided time intervals.
• This seeks to execute orders near the average price to minimize market impact.

Volume Weighted Average Price (VWAP) strategy

• Large orders are distributed based on historical volume profiles.
• This seeks to have the order executed close to the volume-weighted average price.

Percentage of Volume (POV) strategy

• Orders are proportional to traded volume
• Employs percentage of market volume until completion.

High-Frequency Trading (HFT)

• A subset of algorithmic trading.

Characteristics of HFT

• High-speed data processing.
• Co-location.
• Very short-term investment horizons.
• Uses algorithms to exploit small or short-term market inefficiencies.
• Aims to be risk-neutral by avoiding overnight positions.

HFT Strategies

Market Making

• Involves placing buy and sell orders to profit from the bid-ask spread.
• Provides liquidity to the market.

Event Arbitrage

• Capitalizes on opportunities surrounding specific events.
• For example, acquisition announcements can cause discrepancies in stock prices.

Latency Arbitrage

• Exploits time differences in receiving market data from different exchanges.
• Employs co-location and advanced tech for a speed advantage.

Quote Stuffing

• Flooding the market with a large number of orders and cancelling them quickly.
• Creates confusion in the market and allows firms to profit from temporary distortions.
• This practice is manipulative and outlawed by exchanges.

Recursive Definitions

• Defining something in terms of itself.
• Consists of:
  • Base case(s): non-recursive part.
  • Recursive case(s): definition in terms of itself.

Example 1:

• $\sum_{i=1}^{n}i = 1 + 2 + 3 +... + n$

Recursive definition:

• $\sum_{i=1}^{1}i = 1$
• $\sum_{i=1}^{n}i = n + \sum_{i=1}^{n-1}i$, for $n > 1$

Example 2:

• $n! = n \cdot (n-1) \cdot (n-2) \cdot... \cdot 2 \cdot 1$

Recursive definition:

• $0! = 1$
• $n! = n \cdot (n-1)!$, for $n > 0$

General Form of a Recursive Function

returnType functionName(parameterList) {
 if (stoppingCase) { // base case
 return baseValue;
 } else { // recursive case
 return recursiveExpression;
 }
}

Designing Recursive Functions

1. Understand the problem requirements.
2. Determine the stopping condition(s).
3. Develop the recursive step(s).

Algèbre Linéaire et Analyse Matricielle

Vecteurs

• Un vecteur est une liste ordonnée de nombres.
• Ex: $\begin{bmatrix} 1 \ 2 \end{bmatrix}$

Matrices

• Une matrice est un tableau rectangulaire de nombres.
• Ex: $\begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}$

Opérations sur les vecteurs et les matrices

Addition

• L'addition de vecteurs et de matrices se fait élément par élément.
• Ex. Vecteurs: $\begin{bmatrix} 1 \ 2 \end{bmatrix} + \begin{bmatrix} 3 \ 4 \end{bmatrix} = \begin{bmatrix} 1+3 \ 2+4 \end{bmatrix} = \begin{bmatrix} 4 \ 6 \end{bmatrix}$
• Ex. Matrices: $\begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} + \begin{bmatrix} 5 & 6 \ 7 & 8 \end{bmatrix} = \begin{bmatrix} 1+5 & 2+6 \ 3+7 & 4+8 \end{bmatrix} = \begin{bmatrix} 6 & 8 \ 10 & 12 \end{bmatrix}$

Multiplication scalaire

• La multiplication scalaire consiste à multiplier chaque élément du vecteur ou de la matrice par un scalaire.
• Ex. Vecteurs: $2 \cdot \begin{bmatrix} 1 \ 2 \end{bmatrix} = \begin{bmatrix} 2 \cdot 1 \ 2 \cdot 2 \end{bmatrix} = \begin{bmatrix} 2 \ 4 \end{bmatrix}$
• Ex. Matrices: $2 \cdot \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} = \begin{bmatrix} 2 \cdot 1 & 2 \cdot 2 \ 2 \cdot 3 & 2 \cdot 4 \end{bmatrix} = \begin{bmatrix} 2 & 4 \ 6 & 8 \end{bmatrix}$

Multiplication matricielle

• La multiplication matricielle est une opération plus complexe. Si A est une matrice $m \times n$ et B est une matrice $n \times p$, alors le produit AB est une matrice $m \times p$.
• L'élément (i, j) de AB est donné par: $(AB){ij} = \sum{k=1}^{n} A_{ik}B_{kj}$
• Ex: $\begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \cdot \begin{bmatrix} 5 & 6 \ 7 & 8 \end{bmatrix} = \begin{bmatrix} 1 \cdot 5 + 2 \cdot 7 & 1 \cdot 6 + 2 \cdot 8 \ 3 \cdot 5 + 4 \cdot 7 & 3 \cdot 6 + 4 \cdot 8 \end{bmatrix} = \begin{bmatrix} 19 & 22 \ 43 & 50 \end{bmatrix}$

Explore algorithmic trading: automated strategies using computer programs to execute trades, minimizing manual errors and ensuring optimal pricing. Learn about trend-following, arbitrage, and mathematical model-based strategies.