Appendix: Intra- and interday P&L

For the purposes of backtesting, P&L from positions held from one day to the next
must be separated from P&L due to trading during the day. This is because market
risk measures only measure risk arising from the fluctuations of market prices and
rates with a static portfolio. To make a meaningful comparison of P&L with risk, the
P&L in question should likewise be the change in value of a static portfolio from close
of trading one day to close of trading the next. This P&L will be called interday P&L.
Contributions from trades during the day will be classified as intraday P&L. This
appendix aims to give unambiguous definitions for inter- and intraday P&L, and
show how they could be calculated for a portfolio. The basic information required for
this calculation is as follows:
Ω Prices of all instruments in the portfolio at the close of the previous business day.
This includes the prices of all OTC instruments, and the price and number held
of all securities or exchange traded contracts.
Ω Prices of all instruments in the portfolio at the close of the current business day.
This also includes the prices of all OTC instruments, and the price and number
held of all securities or exchange traded contracts.
Ω Prices of all OTC contracts entered into during the day. Price and amount of security
traded for all securities trades (including exchange traded contract trades).
The definitions shown are for single-security positions. They can easily be extended
by summing together P&L for each security to form values for a whole portfolio. OTC
contracts can be treated similarly to securities, except that they only have one
intraday event. This is the difference between the value when the contract is entered
into and its value at the end of that business day.
Inter- and intraday P&L for a single-security position can be defined as follows:
Interday P&LóN(t0)(P(t1)ñP(t0))
where
N(t)ónumber of units of security held at time t
P(t)óPrice of security at time t
t0óClose of yesterday
t1óClose of today
This is also the definition of synthetic P&L.
Intraday P&L is the total value of the day’s transactions marked to market at the
end of the day. For a position in one security, this could be written:
Intraday P&Ló(N(t1)ñN(t0))P(t1))ñ ;
No. of trades
ió1
*NiPi
where
*Niónumber of units of security bought in trade i
Pióprice paid per unit of security in trade i
The first term is the value of net amount of the security bought during the day
valued at the end of the day. The second term can be interpreted as the cost of
purchase of this net amount, plus any profit or loss made on trades during the day. 290