The path based attribtuion approach is a simple method of attribution that can be applied to fixed income securities.
The algorithm requires the specification of a function which takes the relevant attribution factors as inputs and returns the value of the security.
{% value = f(x_1, x_2, ..., x_n) %}
where {% (x_1, x_2, ..., x_n) %}
are the underlying factors.
Factors
There are often a common set of factors that used in a fixed income attribution.
- Fixed Income Discount Curve - the current interest rate environment.
- Interest Rate Volatility - for securities with embedded optionality
- Credit Quality - for obligors who might possibly default.
- Time - the passage of time will cause the value of the security to change, in particular, the holder will accrue interest every day. (carry)
Attributing Market Observed Prices
Many securities have market observed prices, that is, the portfolio manager is not using a model (function) to value the securities, but still wants to obtain an attribution of the price changes.
In this case, it is often necessary to create a function that values the security, but then to use market observed prices to infer the value of one of the inputs. For example, it is common for managers to have a computed discount curve and a computed value of interest rate volatility, and then to back out the value of the credit spread that makes the computed value of security match the market price.
Once this is done, the manager then has a value for all the inputs in the value function which is calibrated to market prices., and can then proceed to run an attribution from two such sets of inputs.