Financial Toolbox

Using Matrix Functions for Finance

Many financial analysis procedures involve sets of numbers; for example, a portfolio of securities at various prices and yields. Matrices, matrix functions, and matrix algebra are the most efficient ways to analyze sets of numbers and their relationships. Spreadsheets focus on individual cells and the relationships between cells. While you can think of a set of spreadsheet cells (a range of rows and columns) as a matrix, a matrix-oriented tool like MATLAB manipulates sets of numbers more quickly, easily, and naturally.

Key Definitions

Matrix.   A rectangular array of numeric or algebraic quantities subject to mathematical operations; the regular formation of elements into rows and columns. Described as an "m-by-n" matrix, with m the number of rows and n the number of columns. The description is always "row-by-column." For example, here is a 2-by-3 matrix of two bonds (the rows) with different par values, coupon rates, and coupon payment frequencies per year (the columns) entered using MATLAB notation.

• Bonds = [1000   0.06   2
            500   0.055  4]
  

Vector.   A matrix with only one row or column. Described as a "1-by-n" or "m-by-1" matrix. The description is always "row-by-column." Here is a 1-by-4 vector of cash flows in MATLAB notation.

• Cash = [1500   4470   5280   -1299]
  

Scalar.   A 1-by-1 matrix; i.e., a single number.

Overview

Referencing Matrix Elements