Investing is all about realizing a positive return. But, how do you calculate returns? In this post, we teach you the fundamentals of return calculations. The principles we teach apply to any asset including stocks, bonds, real estate, cryptocurrencies, and so on.

__Learning objectives:__

- Learn how to perform basic return calculations.
- Understand the concepts of net return, total return, dividend yield, and capital gains.

**Jump to:**

- Performing return calculations in 3 easy steps
- Net returns and gross returns
- Stock return calculations: Dividend yields and capital gains

## Performing return calculations in 3 easy steps

Let’s begin our discussion with a fundamental question: Why do we need to make return calculations? To understand that, let’s imagine that Amy invested in stock A, and Ben invested in stock B. Ben tells Amy that his profit last year was $3,000. Amy is upset to hear that as her profit was only $800 over the same period. But, such a comparison might be misleading if Ben invested a much larger amount in stock B than the amount Amy invested in stock A.

It is more appropriate to compare investment returns than investment profits as the former takes into account the original amount of investment. Therefore, return calculations is all about scaling the profits (or losses) made at the end of an investment period to the principal invested at the start of that period.

A key point is to ensure all relevant cash-flows are accounted for. For example, in the case of a stock, we need to consider any **dividends** paid as well as the change in the stock price. For bonds, any **coupon** payments made have to be taken into account. If we are talking about letting out a property, we have to look at both the amount of **rent** earned and any running expenses such as property management fees.

So, here are the 3 steps we should take when calculating returns on our investments:

- Determine the total amount of investment made at the start of the period.
- Add all the relevant cash flows (both incoming and outgoing) during the investment period.
- Divide the sum of cash flows by the total investment made to obtain the return figure.

To illustrate this approach, let’s go back to our example with Amy and Ben. Amy’s profit was $800. Let’s say, her total investment in stock A was $2,000. Then, Amy’s return on investment is $800 / $2,000 = 40%. Let’s imagine, Ben invested $10,000 in stock B. In that case, his return on investment is $3,000 / $10,000 = 30% as his profit was $3,000. So, even though Ben made a greater profit than Amy ($3,000 vs $800), actually Amy’s investment in stock A paid off much better than Ben’s investment in stock B: 40% > 30%.

## Net returns and gross returns

Now that we understand the steps involved in return calculations, we can move on to discussing relevant details. Suppose you bought shares of a stock for $10 last month and the stock is currently trading at $11 per share. If you sold your shares now, your return would be:

*R = ($11 — $10) / $10 = 10%*

In general, when you buy shares for *P _{t-1}*, and sell them for

*P*, the

_{t}**net return**you realize over the period

*t*is:

*R _{t}* = (

*P*

_{t}*—*

*P*) /

_{t-1}*P*

_{t-1}Moreover, we can rewrite this formula as:

*R _{t}* =

*P*/

_{t}*P*

_{t-1}*—*1

If we didn’t subtract one at the end, we would end up with the **gross return** formula:

*R _{t}* =

*P*/

_{t}*P*

_{t-1}So, in our example, the gross return is

*R = $11 / $10 = 110%*

In general, gross return refers to the return including the original investment, and net return gives the return net of the original investment.

## Stock return calculations: Dividend yields and capital gains

In this section, we delve deeper into stock return calculations. As we have already mentioned, if a stock pays a dividend during the investment period, you need to take that into account when calculating your return. Let’s assume the stock you bought last month just paid a dividend of $1 per share. Then, if you sold your shares now, your **total return** would be:

*R = ($11 — $10 + $1) / $10 = 20%*

The total return has two parts: The one due to the dividend payment is called the **dividend yield**, and the one due to the change in price is called the **capital gains** (or capital loss if the price goes down). The formula for the total return is:

*R _{t}* = (

*P*

_{t}*—*

*P*+

_{t-1}*D*) /

_{t}*P*

_{t-1}where *D _{t}* is the dividend paid in period

*t*. We can rewrite this formula as follows:

*R _{t}* = (

*P*

_{t}*—*

*P*) /

_{t-1}*P*+

_{t-1}*D*/

_{t}*P*

_{t-1}Then, *(P _{t} — P_{t-1}) / P_{t-1}* is the capital gains, and

*D*is the dividend yield.

_{t}/ P_{t-1}### A solved example

__Example:__ An investor bought shares of a stock at $10/share at the end of December. The share price was worth $8, $10, and $11 at the end of January, February, and March, respectively. Moreover, the stock paid a dividend of $2/share in February. Calculate the investor’s return for each month.

__Solution:__ The January return was *($8 — $10) / $10 = —20%*. The February return was

*($10*. Finally, the investor’s return in March was

*—*$8 + $2) / $8 = 50%*($11*.

*—*$10) / $10 = 10%##### Summary

It is crucial for investors to make accurate return calculations. In this post, we offer a step-by-step guide to calculating returns on assets such as stocks. We also make a distinction between gross returns and net returns. Finally, we explain the details of stock return calculations by highlighting the two components of stock returns: dividend yield and capital gains. If you would like to learn more about the type of firms that pay dividends and firms’ propensity to pay dividends, we recommend the paper by Fama and French below.

Further reading:

Fama and French (2001) ‘Disappearing dividends: changing firm characteristics or lower propensity to pay?‘ Journal of Financial Economics, Vol. 60 (1), pp. 3-43.

##### What is next?

This post is the first post in our course on investments. The next post in the series explains the distinction between nominal returns and real returns.

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