The Mathematics of Portfolio Return
Mathematics is the gate and key of the sciences.... Neglect of mathematics works injury to all knowledge, since he who is ignorant of it cannot know the other sciences or the things of this world.
Roger Bacon, Doctor Mirabilis, Opus Majus (1214-1294)
Mathematics has given economics rigour, alas also mortis.
Robert Helibroner (1919-2005)
In measuring the performance of a “portfolio” or collection of investment assets we are concerned with the increase or decrease in the value of those assets over a specific time period, in other words the change in “wealth”.
This change in wealth can be expressed either as a “wealth ratio” or a “rate of return”.
The wealth ratio describes the ratio of the end value of the portfolio relative to the start value, mathematically:
VE = the end value of the portfolio VS = the start value of the portfolio.
A wealth ratio greater than 1.0 indicates an increase in value, a ratio less than 1.0 a decrease in value.
Starting with a simple example, take a portfolio valued at £100m initially and valued at £112m at the end of the period. The wealth ratio is calculated as follows:
Exhibit 2.1 Wealth ratio
The value of a portfolio of assets is not always easy to obtain, but should represent a ...