Course description
Linear Algebra for Investment Management
This course is designed to demonstrate the usefulness and practical relevance of working with vectors and matrices in various applications in investment management, ranging from simple portfolio calculations with assets and factors to non-parametric time series models for extracting trends and scenarios.
Upcoming start dates
Suitability - Who should attend?
The Linear Algebra for Investment Management course was designed for:
- Investment Managers, Both Traditional and Alternative
- Risk Managers
- Financial Economists
- Quantitative Investment Analysts
- Data Scientists
Prior Knowledge
- Basic understanding of economics and financial markets, instruments and quantitative concepts like CAPM, mean-variance portfolio selection, time series analysis
Outcome / Qualification etc.
Learning Objectives
- Overcome the terminology and notation barriers of Linear Algebra
- Learn how to execute calculations involving vectors and matrices to solve practical problems in investment analytics
- Develop common sense intuition for seemingly abstract mathematical concepts
- Increase awareness for numerical issues in Linear Algebra applications
This programme is eligible for CE/CPD credit hours from CFA and GARP Institutes.
Training Course Content
Day One
Introduction
- What is Linear Algebra
- Why is Linear Algebra interesting for investment analysis?
Scalars, Vectors and Matrices
- One and Zero Objects
- Symmetrical Matrices
- Diagonals (minor/major/nth), Triangulars (upper/lower)
- Geometrical, Statistical & Analytical Interpretations of Vectors and Matrices
Transformations
- Transpose
- Vectorisations
- Hankel, Toeplitz
- Sort, Centre, Standardize
- Circular Shift
- Matrices from Lagged Data
Applications (discussed and calculated in Excel):
- Covariance Matrix Decomposition and Construction from Correlations and Volatilities
- Building Inputs for Vector Autoregressive Models
- Transition Probability Matrices in Markov Regime Switching & Credit Risk Analysis
Basic Operations with Vectors and Matrices
- Addition & Subtraction
- Multiplication: Matrix Products
- Division: Inverse of a Matrix, Pseudoinverse
- Elementwise Operations
Applications (discussed and calculated in Excel):
- Portfolio Risk and Return Calculations
- Interpreting the Inverse of a Correlation Matrix In Regression Analysis
Day Two
Matrix Properties
- Unitary, Zero
- Symmetry
- Square
- Rank
- Determinant
- Definiteness: positive/negative, semi
- Singular
- Norms
Applications (discussed and calculated in Excel):
- Factor Model Analytics: Portfolio Decomposition, Asset Risk and Return from Factors
- Validity of a Correlation Matrix
Advanced Operations
- Introduction to Matrix Factorizations
- Cholesky Decomposition
- PCA, SVD
- QR, LU
- Matrix Derivatives
Applications (discussed and calculated in Excel):
- Regression Analysis: Least Square Problems in Matrix Form
- Simulating Correlated Time Series Data
- Linear Model Identification: Principal Component Analysis (PCA) for S&P 500 Constituents
- Dimensionality Reduction: PCA versus SVD
- Singular Spectral Analysis: Non-Parametric Decomposition of Time Series Data
Linear Algebra in Microsoft Excel
- Built-in Functionality
- VBA Functions
- Add-Ins
Course delivery details
Courses are delivered in the London classroom and live online via LFS Live in London, New York, and Singapore time zones.
Please contact LFS for more details.
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