P&L Calculation – What Is It?
Before I jump into the 7 concepts, let’s first define what I mean by P&L. A P&L calculation (aka Profit and Loss, or Gain/Loss calculation) measures how much money someone made on their investments, such as stocks, bonds, real estate, over a certain time period.
For example, the “Total Gain/Loss” columns blow shows how much you made in profits and/or losses due to market changes and dividends and interest.
7 Concepts You Should Know
In the rest of the post, I will provide you with detailed examples of how each of these affect your Profits & Losses:
1) Market Fluctuations: the value of your holding will fluctuate based on how much it is trading or being sold at in the market, which will affect your profits and losses
2) Transactions such as Purchases and Sales: when you buy or sell a security in your portfolio, you will generate a profit or a loss based on the price and cost of that transaction
3) Dividends and Coupons: depending on the type of security you hold, it can generate income which is part of your profits
4) Other Types of Corporate Actions, such as mergers, spin-offs or tender offers: when you own a security such as a bond or a stock, the company may merge or make a change that will affect your profits or losses
5) Class Actions: if you hold shares in a company that is found to have harmed you as an investor (e.g., created a loss in your investment due to an illegal action of the company), you can earn money back if there is a litigation and proceeds are awarded
6) External Flows: when you add or take away money from your investment account, these have to be removed or excluded to calculate a correct P&L
7) Fees and Taxes: if you have hired someone to manage your investments or invest in an ETF or fund, fees will be taken out and negatively affect your P&L. Taxes will also negatively affect your P&L.
Concept #1: Market Fluctuations
Securities, such as equities or bonds, will change in value based on what they are trading at.
Example: You hold 100 shares of Apple. Yesterday, Apple’s closing price was $150 and today Apple closes at $151. What is your P&L for the day?
Value Yesterday (“Beginning Value”): 100 shares * $150 = $15,000
Value Today (“Ending Value”): 100 shares * $151 = $15,100
P&L = Ending Value – Beginning Value = $15,100 – $15,000 = $100
If you had multiple holdings, you would do this for each security in the portfolio that was held over the entire time period, and sum the results.
Concept #2: Transactions such as Purchases and Sales
When you purchase a security, you create what is called a “transaction.” The transaction will have lots of information associated to it (e.g., how many units you bought, who you bought it from, when you bought it, etc.).
For P&L calculation purposes, what is important is what is called the “Net Amount” of the transaction. The “Net Amount” is how much you bought the security for minus any costs, and is calculated as follows:
Net Amount = (Price You Bought The Security At * Shares) – Transaction Costs
The Profit & Loss is then calculated using the Net Amount:
P&L = Ending Value – Net Amount
The Ending Value is how much it is worth on the date you are calculating your P&L as of.
Example: You buy 1,000 shares of IBM for $125,000 and the ending price of IBM that day is $124. What is the P&L for the day?
First, the ending value of 1,000 shares valued at $124 is $124,000. The net amount was $125,000. Therefore, your loss in this case is -$1,000.
Some systems will just show you that you lost $1,000 on IBM. However, if you look behind the scenes, you will see that what actually happened is that your cash went down by $125,000 (you spent the cash to buy the security) and your security value went up by $124,000.
Let’s use the same example as before and assume you have $200,000 in cash. You spend $125,000 on IBM, so cash is decreased to $75,000. But you don’t want to reflect a $125,000 loss on cash since it wasnt a loss – you chose to spend it. Therefore, what a P&L system would do is that it would treat the $125,000 as a “withdrawal” or “flow” from cash. You will see that on the first line below.
On the second line, you are putting that $125,000 into IBM so it is reflected as a “deposit” or “flow” into IBM. Since the ending value of IBM is $124,000 then you have a $1,000 loss appropriately attributed to IBM. If you sum the cash and IBM positions, you get the correct total account values with the same $1,000 loss.
Note: It actually gets more complicated then this when you factor in that the cash doesn’t actually leave the account until settlement date. If you are interested in seeing how cash is treated in this scenario for purposes of trade date vs. settlement date accounting please look at the Purchases page.
2) Sales are very similar to purchases. Please take a look at the dedicated page to sales if you want more details.
Concept 3: Dividends and Coupons
Dividends and coupons are classified as “income,” meaning the are a different source of return when talking about profits and losses. They are typically regular scheduled events which an investor can depend upon receiving a lump sum of cash on a quarterly, semi-annual or annual basis.
Technically, dividends and coupons are actually a type of “corporate action.” However, I have separated them from the other types of corporate actions because they are regularly scheduled income events while other corporate actions are not.
For example, Sue is a 70 year investor who holds 1,000 shares of Verizon stock. She likes Verizon because the company usually gives a cash dividend every quarter, and she can rely on this additional income in her retirement.
So, how do you calculate the P&L with a dividend? There are a few moving pieces:
• The dividend amount will first be announced and it will be quoted as a dollar amount per share. For example, a .75 dividend that is paid in US dollars means that for each share you hold you will receive 75 cents.
• The stock price will drop by the dividend amount on the date it goes “ex.” For more information on what “ex” means and why the price of the stock drops, please read this post on cash dividends.
Example: Today a a $.75 dividend is going “ex” for Verizon. Yesterday it closed at $50 and today it closes at $49.25 (for simplicity I assume there was no other market movement beside the change in price for the dividend going ex). Sue owns 1,000 shares. What is her P&L on this day?
Since Sue owns 1,000 shares of Verizon, the value of her holding as of yesterday is $50,000 ($50 * 1,000), her dividend will be $750 ($.75 * 1,000), and the ending value of the stock will be $49,250 ($49.25 * 1,000).
P&L = Ending Value – Beginning Value + Income*
P&L = $50,000 – $49,250 + $750*
P&L = $0
*Note that this income is actually being accrued, meaning that it is owed to Sue but hasn’t been paid yet. For P&L purposes, we want to reflect that Sue does have this economic benefit when she is owed it, not when it is paid.
Alternatively, you can calculate the beginning and ending values with accrued income. Accrued income would be $0 in the beginning and $750 at the end:
P&L = Ending Value with Accrued Income – Beginning Value with Accrued Income
P&L = ($49,250 + $750) – ($50,000 + $0)
P&L = $50,000 – $50,000
P&L = $0
So, there is technically no profit from the dividend. The dividend simply gives you cash now versus the money being invested in the stock.
What we can do to distinguish this in the P&L calculation is to separate the capital gain/loss (P&L derived from stock price) vs the income, it would look like this:
For bonds, an investor receives income via what are called “coupon” or “interest” payments. The P&L calculation for bonds actually has to account for this coupon or interest on a daily basis.
For example, Michael holds a 4% bond that pays semi-annually (twice a year). This means it will pay a total of 4% interest per year but it will be broken up into two payments, approx 2% every 6 months.
How do you reflect this in P&L? Well, you actually have to figure out what the interest is on a monthly and daily basis and put that into the profit each day. Why? Because if Michael sells the bond at any time in between now and the next coupon payment, the person buying the bond needs to pay Michael for the interest he earned through the day he sells it. Since you will be paid for the interest each day you hold it, it needs to be reflected in the P&L.
Let’s say Michael also owns a $100,000 4% corporate bond that is priced at 99.375 as of yesterday. Today the bond closes at 99.50. What is the daily P&L?
Step 1: Calculate the interest. Using the correct day count convention for corporate bonds, we first calculate the monthly interest which is (30/360) * 4% * 100,000 = $333.33. We then convert that to the daily interest by dividing by 30, which is $11.11. That is the income for that day.
Step 2: We calculate the price change. The price went from 99.375 to 99.50, which is an increase of $.125. Bond prices are quoted as a percent of 100, so we take the price change divided by 100 and multiply that by the principal of the bond which was $100,000. So, the P&L for the price change is calculated as ($.125/100)* $100,000 = $125
Step 3: Add the price change P&L to the interest P&L to get the total P&L.
Total P&L = $125 + $11.11 = $136.11
Concept #4: Other Types of Corporate Actions, such as mergers, spin-offs or tender offers
Corporate actions are events that can cause the number of shares you hold in a security to change or to even cause the security you hold to no longer exist and be replaced with another security and/or cash. For example, lets say you hold wireless company small and it gets bought by wireless company big. Since wireless company small will no longer exist as a separate company, your shares of wireless small might automatically be exchanged for shares of wireless company big.
For other corporate actions, you may receive cash in exchange for your shares or a combination of shares or cash. It all depends on the terms of the corporate action.
From a P&L standpoint, all you need to do is look at the value of the shares you hold before the corporate action and then look at the value of the the new shares and/or cash after the corporate action. The change in the value will be your P&L.
For example, lets say you own 100 shares of stock A. Stock B is buying stock A and agreed to a cash and stock merger. The “terms” of the merger are that for each share of stock A you own, you will receive .25 shares of B and $5. In order to see what you will own after the merger, you multiply the .25 and $5 by the 100 shares. So after the merger you will own 25 shares of B (100 shares of A * .25) and $500 ($5 * 100 shares of A).
If stock A closed at $6 the day before the corporate action, and stock B closed at $8 the day of the corporate action, what is the P&L on the day of the corporate action?
Value you hold the day before the corporate action = 100 shares of stock A * $6 = $600
Value you hold at the end of the day of the corporate action = (25 shares of stock B * $8) + $500 = $200 + $500 = $700
P&L of the corporate action = $700 – $600 = $100