#### P&L

Profit and Loss (P&L) is a finance and risk reporting term to describe the profitability of an individual trade, a book, a desk, or a company. Whilst the P&L of a company includes all activity, and costs (offices, staff etc.) the trading P&L is a measure of the profitability of a single, or a set of, trade(s)

Detail

P&L is a change in the value of something, or a set of things between two points in time

You will often hear people refer to the P&L of the trade in terms of its value - the value at any point in time is effectively the difference between the value at that point in time, and the value before the trade was executed. We usually refer to this as the Lifetime to Date P&L or LTD P&L

Often we are interested in the change in value, the P&L, from the start of the year, from the start of the month, or from the last valuation. These are respectively known as:

• Year to Date P&L (YtD)
• Month to Date P&L (MtD)
• Change on day P&L (CoD or DtD)

As an example, let's say we bought some shares in a company for £60, and a year later we sold them for £100, then it seems obvious that we made £40 profit, assuming there were no cost of buying the shares, or selling them, nor indeed any other costs directly associated with the buying or selling

From the trading point of view we have executed two deals, or trades. Let's now think a bit more about these two trades, and ask some further questions:

We know the P&L after both trades have been executed (£40) but:

• What was the P&L after the first trade?
• What was the P&L of each individual trade?
Before continuing we will align our example with a more normal energy trading example.

In general traders don't buy a commodity, and then sell it later because of the difficulty and cost of storing energy commodities - see Storage

In general traders enter into a Forward contract, that is to buy the shares at  fixed time in the future, at a fixed price

The other advantage of Forward contracts is that the trader can enter a Forward contract to sell, as well as buy, at some time in the future. This is known as taking a short - i.e. negative - position

We enter into a Forward contract to buy an amount of shares for £60 in March 2018

In March 2018 we will give £60 to the seller of the shares. This is called the financial side or leg of the trade. It has a known cash value: £60

The seller will give us (he will deliver) the shares. We don't know what they will be worth then, but we can look up the current expected market value of the shares in March 2018, and see what they're worth - see MtM for the details. We call this marking to market, or MtM. Let's say we go online and the market value is £58, then at that time the P&L of the trade is minus £2, we have made a loss. Each day a new price is published we should revalue our trade, and this should continue until the shares are delivered. We have a long position in this share until we sell it. We say the trade has an unrealized P&L of minus £2. We say it is unrealized, because we still have the contract to buy the shares and their value (to us) will continue to vary until we receive them

We call this the physical side or leg (it's physical because it's not cash, even though the share certificates are electronic, we still call this physical)

After ten months we note that the market price has risen to £110, the trade has a P&L of £50, the current physical side value of £110 less the cash or financial side of £60. We say the trade has an unrealized P&L of £50

In March 2018, our seller delivers the trades, and we give the seller £60. We note that the market price has dropped to £100, the trade has a P&L of £40, the current physical side value of £100 less the cash or financial side of £60. We say the trade has an unrealized P&L of £40

We decide to immediately execute the second trade and sell the shares for £100, by then the spot price, and execute a sell transaction

Between the two trades we can say that the P&L is £40 and that it is now realized. We can say the P&L is realized based on three criteria:
In general, with derivatives, these criteria are usually not met simultaneously, and realization may be defined according to one or more of these criteria, and may be dependent on other criteria as well

We have said the P&L of the two trades is £40, but what is the P&L of each individual trade? There are two general ways to define this:

1. Ignore the physical side of each trade, so the first trade has a P&L of minus £60, the second trade has a p&l of £100, between them the P&L is £40. We can use this method when we are sure that the position of both trades has been closed out (which is another way of saying that the two trades' net position is zero). This method is sometimes called realized cash flow because it only considers the value of the cash elements of the trades
2. Retain the physical side of each trade, and continue to mark it to market for each trade. By this method the realized P&L on the day the second trade was executed was £40, and the P&L of the second trade is zero. If we use this method the P&L of each individual trade will continue to fluctuate for as long as we use it. This method is sometimes called Realized MtM
In general the first method is preferred because it is simpler, we may have to use the second method when we are not sure the position is entirely closed out, or we know some is, and some isn't.

if the first method sounds odd, think about buying and selling a house, once you've bought a house you're very interested in how much you paid for it, and how much it's currently worth. Once you sell it however, you're only really interested in the price you paid and the price you sold it. You have little real interest in the current price

P&L that may result in a cash flow in the future is often discounted back to present day value

We may refer to undiscounted, and discounted P&L