Returns. Probably the most fundamental and focal concept within investment analysis & portfolio management. How to calculate stock returns then? Perhaps more importantly, why should you calculate it that way?
If you haven’t seen our post on Investment Fundamentals: Price, Risk & Return, stop right now and read that post first.
If you have read it, here’s a quick recap.
Recall that ‘Return’ refers to the amount of money that you make from your investment, expressed in percentage terms.
Let’s see how we go about calculating the Return.
Profits vs. Return
Imagine that you buy stock in Facebook for $160 and sell it for $192.73.
What is your profit and what is your return?
If you think about profit – profit shows you the amount of money that you earn from an investment. And it’s expressed in dollars or pounds or whichever currency you’re working with.
The return shows you exactly the same information, except that it’s expressed in percentage terms.
So in this example to get the profits we would start by the selling price (the amount or the price at which we sold the stock for) and take away the purchase price (the price of which we bought the stock for).
And that gives you the profit. We can annotate the Selling Price as and the Purchase Price is .
So means this is the price at time plus one. And means that is the price of the stock at time .
And could be whatever you like. So it could be the date of purchase, or it could be the month of purchase, or it could be the quarter of purchase. It really depends on the frequencies that you are working with.
in our case was $192.73 and was $160. Take the difference between the two and you end up with a profit of $32.73.
To get the return, all we need to do is express the same $32.73 in percentage terms. And we do that by expressing it relative to the original investment of $160.
What does that look like? Well, the return of a stock is calculated as:
Remember again the is the Selling Price. is the Purchase Price. And then we’re scaling the difference between the two by the original price (i.e., the Purchase Price) to get the amount of money that you make, expressed in percentage terms.
In this example, is $192.73 and is $160. Take the difference between the two and divide it by (which is $160).
Now, because of the way the equation is written out, we can actually split it into two parts.
So I can take $192.73 and divide that by $160. And then subtract $160 divided by $160. So I can rewrite this equation like so:
And this then simplifies to $192.73 divided by $160, minus one (because anything divided by itself is always equal to 1).
When you solve for this, you’ll find that the return is 20.46%.
Generalised return of a stock
Let’s just look at calculating returns again. But this time, we’ll work with notations instead of numbers.
The return on a stock is:
This can be rewritten as:
Anything divided by itself is always equal to 1. And so this equation here can be rewritten like this:
And that’s pretty much it!
So when you want to calculate the return on the stock, the general equation can look like this:
Notice the subscript in .
could be anything – it could be Facebook or Alphabet (formerly Google) or Amazon or Netflix – whatever you like.
is just a generic term or generic notation for any stock.
So refers to the return on the stock .
You can calculate the return on a stock using either formula and you’ll end up at exactly the same result.
All right. Hopefully this makes sense. If it’s not quite clear, please reread this article up until here before continuing on.
Incorporating Dividends
Let’s step it up now, and consider an example with dividends.
Imagine you buy 67 shares of Apple Incorporated at $149.04; you earn dividends of 63 cents per share for 4 quarters, and then sell your shares for $191.03 each.
What is your profit and what is your return?
Before we crunch the numbers, there’s a fair bit of information here. So let’s just declutter make sure we understand what we’re working with.
We have the number of shares, which is not really relevant to calculate the return. But it is relevant to calculate the total profit for instance. That’s because your total profit is impacted by the number of shares that you own as well as the difference in the purchase price and selling price.
Then we have the purchase price which is $149.04.
And then we have information about dividends.
Now in case you’re not familiar with what dividends, they’re just a share of the profit that investors can get.
When you buy shares in a company, you technically own part of that company. And that entitles you to earn this ‘dividend’, which is just a part of the profit that the company can pay out for you to keep.
This is just one of the rewards that you get for owning shares.
So in this example you’re going to earn a dividend of 63 cents for every share that you own. And remember, you own 67 shares.
So you’re going to get 67 times sixty three cents as your total dividends. And you’re earning this dividend every quarter, for four quarters. So you’re earning the sixty three cents four times in a year.
And then we’re saying that you sell your shares for $191.03. So that’s your selling price.
Let’s see how we can split the profit.
The profit now would be the selling price plus the dividends (because this is the total amount of money that you’re earning); and then you would subtract the purchase price (which is how much it’s cost you).
Using annotations again can make life easier. So the profit can be expressed as:
Strictly speaking, the notations should be more clear.
The notation implies that you get all of the dividends at time . But in reality that’s not true. Because you’re getting dividends every quarter.
And so really, you would want to have:
But that just makes it unnecessarily complicated. And so to simplify things, and make life easier, we’ve just called it .
Plugging in our numbers then:
Note that the dividends are 63 cents per share for four quarters. Multiplying $0.63 by 4 gives us the total dividends for 1 share for 1 year.
Solve for that, and you’ll find that the profit is $44.51. That’s for 1 share though. If you want the total profit, you’ll want to incorporate the fact that you own 67 shares.
The total profit is therefore:
Let’s now look at how to calculate stock returns when we’re dealing with dividends.
It’s actually quite straightforward. We just change the equation for return a little bit, and include this ‘dividend’ aspect. Our ‘modified’ equation looks like this:
Plugging in our numbers looks like so:
Again, as before, if you were to split this into three parts like so:
Or even two parts, like so:
Which then simplifies to this:
Note that .
And the 1 represents .
And finally, when you solve for this you’ll find that the return on Apple is 29.86%.
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Generalised return of a stock with dividends
Let’s just quickly look at how this equation works (using only notations this time).
The return of a dividend paying stock is:
This can be rewritten as:
Which can then be simplified to:
Now that this is hopefully clear, we can come up with a general equation for the return of a stock :
Importantly, if you know this equation, then you don’t really need to know the previous equation that we looked.
That’s because we can just modify this new equation that we know and we’ll end up with a previous one anyway.
Say for instance you’re trying to calculate the return for a stock that doesn’t pay any dividends.
Well then the will just be equal to zero.
And so the equation with then simplify to:
Just a quick note. I know it’s tempting to call the dividends instead of , but I would strongly encourage you to write it out as and not .
That’s because we tend to use to refer to debt.
And as you progress on in your journey to mastering finance, you’ll end up using the notation a lot more frequently (and you’ll use it to refer to the debt of a company).
To make your life easier then, and to avoid any confusion, I would strongly recommend that you work with as your own notation for dividends, instead of .
All right so hopefully this makes sense. If any part of this article is not clear, please read it again before moving on any further.
How to calculate stock returns on Excel®
Alright. Now that you know how to calculate stock returns manually, let’s look at how we can implement this on Excel®, using some real world data.
Accessing Financial Data
Getting access to financial data can be an expensive affair. But thankfully, we have free alternatives as well.
If you pop into Yahoo! Finance, let’s say we’re looking at Facebook. You just put in the ticker over here.
We want to get some data right, so you can go into historical data right here and then set the time period.
I’m just going to go with 1st of January 2012. Importantly, Facebook was not listed as a public company on the 1st of January 2012. They were listed later on in 2012, but it doesn’t matter because Yahoo! Finance will pull the data from the first day of trading.
So we don’t need to know the exact date and when they started trading. I’m just going to arbitrarily set the last date of data as the 31st of December 2017.
You can choose any other time frame that you like. But if you want to work with me in this then maybe work with the same dates just to make life easier.
Go ahead and click done then and then make sure to hit ‘Apply’.
And then you want to download your data which will come out as a CSV file.
Extracting Relevant Data
Here’s the data that we’re looking at. There’s quite a lot of things going on here but let’s just see what the information is.
We’ve got the Date, which is the date of trading. Then we’ve got the Open, which is the price at which the stock opened. Next, the High, which is the high point of the day – so that’s the highest price at which the stock traded at on the day.
Low is the lowest point of the stock – so it’s the lowest price at which the stock traded at on the day. Close is what the stock closed at. And Adjusted Close is pretty much the same thing, except that it will also adjust for dividends. When companies pay out dividends, the stock price actually decreases. And so the Adjusted Closing Price will factor in that change in price as a result of the dividends. It will also incorporate effects for things like stock splits, and stock bonuses, for example.
Volume is just the number of trades that took place on the day.
For the purpose of what we’re trying to do here – to calculate returns – we don’t actually need all of this information.
We only really need the Date and Adjusted Close columns so we’re going to keep just those 2. And rename “Adjusted Close” to “Price” (see below).
Calculating Stock Returns on Excel
Now we can calculate returns, daily.
Recall that return is:
In this case, is the price on the 21st of May 2012. And is the price on the 18th of May 2012. Apply the formula on Excel® like this:
We can see that the return there is 10.99\% or approximately 11 percent (see pic below).
And then you want to do exactly the same thing for all of these prices.
All you need to do is double click the corner of the cell (where you see the little green square in the bottom right corner of cell C3) and Excel® will magically calculate all of your daily returns.
And that’s pretty much it!
You know know how to calculate stock returns. Actually, you know more than that including:
 The different ways of expressing the return formula, both with and without dividends.
 How to calculate stock returns manually.
 Accessing data for free from Yahoo! Finance
 Extracting relevant data for calculating returns with real world data.
 Using Excel® to make your life easier by quickly calculating daily returns in one go.
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