Overview
The rate that is charged on a loan is generally attributable to four different factors.
{% rate = risk\;free \; rate + optionality + credit + liquidity %}
- Risk Free Rate - the rate that is charged on debt that is free of any risks, typically government debt
- Optionality - a charge to cover the cost of any embedded options in the bond
- Credit Risk - charge for the credit risk of the borrower
- Liquidity - a charge for loans or bonds that cannot easily be sold in secondary markets
Calculating the Rates
- Risk Free Rate - is an observable quantity that can be read from the markets
- Optionality - generally requires a model to compute. A common method is to use a binomial tree to model the short rate and then the value of the bond. Once the value of the embedded option is computed, a rate is computed that when applied to the bond would yield the option value.
- Credit Risk - the creidt risk for the borrower is typically calculated as a hazard rate, i.e. from a calculated probability of default (see poisson credit risk model)
- Liquidity - the liquidity charge is typically bank specific. That is, the liquidity risk is often dependent on the banks portfolio. If the instrument can be actively traded, then its liquidity risk is zero.
Any remainder that is present after calculating the above rates is attributable as pure profit, or alpha. Alternatively, an analyst may compute the values of three of the above risks, and take the remainder to be the (market) value of the fourth. For example, one could impute a market credit risk (and hence probability of default) but taking the risk free, computing an option value, assigning the liquidty risk to zero (market traded instruments) and then taking the remainder to be the makret assigned credit risk.
PnL after an Event
There are two events that can occur to a bond that will alter the standard calculation of PnL given above.