Overview
Attribution attempts to explain the difference in a function evaluated at different points. For example, suppose you a function of {% n %} variables as such.
{% value_1 = f(x_{1}, x_{2} , ... ,x_{n}) %}
Now, if the function is evaluated using different parameters, a different value results.
{% value_2 = f(x_{1}', x_{2}' , ... ,x_{n}') %}
In general the difference between the two values is not zero.
{% value_2 - value_1 \not= 0 %}
Attribution seeks to break the difference in {% f %} due to the influence of the underlying variables such that
{% value_2 - value_1 = \Delta f = \Delta f_{x1} + \Delta f_{x2} + ... + \Delta f_{xn} %}
where {% f_{xi} %} is the amount of the difference that has been attributed to the change in {% x_i %}.
Example Usage
Attribution is used heavily in finance. Many instruments, such as fixed income securities and derivatives, can be expressed as a function of a set of underlying factors, usually market factors such as the discount rate at various points of the curve, asset volatilties and time.
Every day that the market value of an instrument or portfolio changes, the manager typically will want to understand what caused the value to change, and how much each factor contributed to the change.
Topics
- Allocation - allocation is similar to attribution.
- Examples