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, if Maria bought stock for $100 at the beginning of the month and it is worth $110 at the end of month, her P&L for the month would be $10 (calculated as the $110 ending value – $100 purchase amount).
A company whose primary business it is to oversee investments, such as Goldman Sachs, Vanguard, or a hedge fund, typically measure their P&L at least every day and sometimes minute by minute. On the other hand, individuals like you and me, typically log into our investment or 401K accounts and check how much our portfolio of investments went up or down less frequently. However, technology has now made this information available to us almost on a real-time basis.
As an example of what I am referring to, take a look at the “Total Gain/Loss” column below. This is a snapshot of an investment portfolio on one of the major investment sites.
While at first glance this may seem like a straightforward calculations, it’s not always simple to do.
7 Concepts You Should Know In Order to Calculate P&L
Concept #1: Price changes of holdings
When you own a security, such as an equity or bond, the value of the security will change simply due to price fluctuations.
Example: You hold 100 shares of Apple. At the end of the day yesterday, Apple’s closing price is $150. Apple closes today at $151. What is your P&L for the day today?
The value of your investment went from $15,000 (100 shares * $150) to $15,100 (100 shares * $151). Your overall profit in this case is $100.
Practice: Look up the closing price of a company as of last trading day and the day before that. If you hold 1,000 shares of that company’s stock, what would the beginning and ending values be? What would be the P&L?
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 simply hold a security, its simple to determine what its value was at the beginning of the period and what its value was at the end of the period (like we saw with the Apple example above).
With transactions, it is more complicated. The values are not always based on a price you can find on the internet.
Similar to when you buy any item, a purchase of a security will have a transaction that shows how much you paid for it, including transaction costs. This is typically called the “net amount” of the purchase.
Net Amount = (Price You Traded At * Shares) – Transaction Costs
Once you have the net amount, the P&L is calculated as:
P&L = Ending Value – Net Amount
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.
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
Class actions are actually a type of corporate action, but deserve their own category when it comes to P&L calculations.
Class actions occur when a company does something illegal, and as a result the people who held the stock of the company were financially hurt. For example, Enron hid debt on their accounting statements and ultimately went bankrupt. Their shareholders were significantly hurt from the companies wrong doings.
The shareholders can sue to get cash proceeds from whats left of the company to try to make up for their loss. If proceeds are awarded, this usually occurs years after the loss.
From a P&L standpoint, you will see a large sum of cash come into the portfolio for a security that may not even be in the account.
For example, lets say in 1990 you bought Enron and when the company went bankrupt in 2001 you lost your $50,000 investment. In 2008, after the litigation was settled, $45,000 of class action proceeds were awarded to you. Should this be reflected as a $45,000 profit in 2008? Well, yes, if you were the one picking the stock then it makes sense that it is obviously a profit since its making up for an earlier loss.
The only time it may not be considered a profit is when someone selected to hold Enron in your account on your behalf.
Imagine a scenario where you hire a manager in the 90s who buys Enron in your account. Unfortunately, you lost your money in 2001 when Enron collapsed. In 2005, you decide to hire a different money manager, and moved your portfolio to another firm. In 2009, the new firm you hired receives notice that your portfolio is owed $45,000. They take those cash proceeds in. Was it a profit?
If you want to measure how well they are doing as a manager, you should not count the $45,000 profit. That is because those proceeds were not due to one of their investment decisions. The $45,000 will simply be counted as an additional cash deposit from you instead.
If you want to measure how your portfolio is doing regardless of who was managing your account, then you can count the $45,000 as a profit.
Concept #6: External Flows
When you hold a portfolio of investments, many times you will be adding or taking money out from the account. These deposits and withdrawals will increase or decrease in the value of your portfolio. However, they are not due to profit or losses – they are simply due to the fact that you added or took away money.
For example, your portfolio at the start of the day is valued at $100. During the day, you contribute $10, and at the end of the day your portfolio is worth $112. Your portfolio went up by $12. However, only $2 of that is profit since $10 of the increase is due to you putting more money in.
In the investment world, these are referred to as flows or “external cash flows.” The word external is used because the funds are coming into the account from an “external” source – you. Compare that to increases or decreases that are due to the investments themselves – those are “internal.”
Concept #7: Gross and Net P&L
Sometimes P&L will be quoted as “gross” or “net.” This usually refers to whether fees and/or taxes are taken out.
In regards to fees, gross would be before fees and net would be after fees. For example, if you are letting someone else oversee your investments, you will probably have to pay a fee. Let’s say your investments started at $100,000 and end at $120,000, but you have to pay an investment manager $1,000. What is your gross and net P&L?
Your gross P&L is before fees, so it is the $20,000 ($120,000 – $100,000).
Your net P&L is after fees, so it is $19,000 ($20,000 – $1,000)
The same principle would apply to taxes which are typically paid by individuals to the government during tax season.
Please note that any fees or taxes that are specific to a transaction, such as an brokerage fee on a trade or a tax on a foreign dividend are always netted out at the time of the transaction. Very rarely would P&L be gross of those types of fees or taxes.
Why Should You Learn How To Calculate P&L?
Most people think that they don’t need to understand how a P&L is calculated – the computers are doing it just fine. But here are some reasons investment management professionals should know how P&L is derived:
1) P&L is the dollar amount behind an investment return. If you understand P&L, you can confidently answer questions on what is driving returns.
2) In the investment industry, there are professionals who work on inputting security trades and handling client requests to add or take money out of their account. Sometimes, there are mistakes made in that process and found when the P&L or investment return doesn’t look right. In order to figure out where the mistake happened, you need to have an understanding of how P&L is calculated.
3) Computer programmers who work in the investment industry will look for expertise from investment professionals when enhancements are needed. There needs to be a human who knows how these programs should work.
A Call For Your Input
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