In
investment banking
Investment banking pertains to certain activities of a financial services company or a corporate division that consist in advisory-based financial transactions on behalf of individuals, corporations, and governments. Traditionally associated with ...
, PnL Explained (also called P&L Explain, P&L Attribution or Profit and Loss Explained) is an
income statement
An income statement or profit and loss accountProfessional English in Use - Finance, Cambridge University Press, p. 10 (also referred to as a ''profit and loss statement'' (P&L), ''statement of profit or loss'', ''revenue statement'', ''stateme ...
with commentary that attributes or ''explains'' the daily fluctuation in the value of a portfolio of trades to the root causes of the changes.
The report is produced by
product control; and is used by
traders – especially
desks
A desk or bureau is a piece of furniture with a flat table-style work surface used in a school, office, home or the like for academic, professional or domestic activities such as reading, writing, or using equipment such as a computer. Desks of ...
dealing in
derivatives (
swaps and
options
Option or Options may refer to:
Computing
*Option key, a key on Apple computer keyboards
*Option type, a polymorphic data type in programming languages
*Command-line option, an optional parameter to a command
*OPTIONS, an HTTP request method
...
) and
interest rate products.
P&L is the day-over-day change in the value of a portfolio of trades typically calculated using the following formula:
PnL = Value today - Value from Prior Day
Report
A PnL Explained Report will usually contain one row per trade or group of trades and will have at a minimum these columns:200
* Column 1: PnL - This is the PnL as calculated outside of the PnL Explained report
* Column 2: PnL Explained - This is the sum of the explanatory columns
* Column 3: PnL Unexplained - This is calculated as PnL minus PnL Explained (i.e., Column 1 - Column 2)
* Column 4: Impact of Time - This is the PnL due to the change in time.
* Column 5: Impact of Prices - This is the change in the value of a portfolio due to changes in commodity or equity/stock prices
* Column 6: Impact of Interest Rates - This is the PnL due to changes in interest rates
* Column 7: Impact of Volatility - This is the PnL due to changes in volatilities. Volatilities are used to value
Option (finance)
In finance, an option is a contract which conveys to its owner, the ''holder'', the right, but not the obligation, to buy or sell a specific quantity of an underlying asset or financial instrument, instrument at a specified strike price on or be ...
(i.e., calls and puts)
* Column 8: Impact of New Trades - PnL from trades done on the current day
* Column 9: Impact of Cancellation / Amendment - PnL from trades cancelled or changed on the current day
Methodologies
There are two methodologies for calculating Pnl Explained, the 'sensitivities' method and the 'revaluation' method.
Sensitivities method
The Sensitivities Method involves first calculating option sensitivities known as the
Greeks
The Greeks or Hellenes (; el, Έλληνες, ''Éllines'' ) are an ethnic group and nation indigenous to the Eastern Mediterranean and the Black Sea regions, namely Greece, Cyprus, Albania, Italy, Turkey, Egypt, and, to a lesser extent, ot ...
because of the common practice of representing the sensitivities using Greek letters. For example, the delta of an option is the value an option changes due to a $1 move in the underlying commodity or equity/stock.
See .
To calculate 'Impact of Prices' the formula is: Impact of Prices = Option Delta * Price Move; so if the price moves $100 and the option's delta is 0.05% then the 'Impact of Prices' is $0.05. To generalize, then, for example to yield curves:
: Impact of Prices = Position Sensitivity × Move in the variable in question
Revaluation method
This method calculates the value of a trade based on the current and the prior day's prices. The formula for price impact using the revaluation method is
* Impact of Prices = (Trade Value using Today's Prices) - (Trade Value using Prior Day's Prices)
for some small-value assets such as "loose tools".
* Depreciation = value at the beginning of the year (opening balance) + purchases in the year - value at the end of the year (closing balance)
PnL unexplained
''PnL unexplained'' is a critical metric that regulators and product control within a bank alike pay attention to.
''PnL attribution'' is used to test the hypothesis that the risk factors identified for a risky position are sufficient to materially explain the value change expected from the risky position;. Such that if position sensitivities to those risk factors are calculated, then the value change observed over a day can be attributed to the market price change of those risk factors, with the magnitude of the estimated as a sum product of the risk factor sensitivities and the corresponding daily risk factor price change.
Any residual P&L left unexplained (PnL unexplained) would be expected to be small IF the identified risk factors are indeed sufficient to materially explain the expected value change of the position AND if the models used to calculate sensitivities to these risk factors are correct. ''PnL unexplained'' is thus a critical metric that when large may highlight instances where the risk factors classified for a risky position are incomplete or the models used for sensitivities calculations are incorrect or inconsistent.
External links
PnL Explained ProfessionalsInformation and examples from PnL Explained Professionals Association's home page
Pantz, Julien 2013 PnL prediction under extreme scenarios
References
{{DEFAULTSORT:Pnl Explained
Financial statements
Financial markets
Financial risk
Derivatives (finance)