Investing > Portfolio Expected Return: How it Works

Portfolio Expected Return: How it Works

No one knows how much a stock will grow in the future—but statistics can show us what portfolio returns to expect.

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Updated April 04, 2022

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Nothing beats the feeling you get when you predict something and it comes true—especially when it results in profit.

In investing, there’s no formula that will let you see the future but there are quite a few that will help make your predictions more probable—and expected returns is one of them. Over the long term, the markets move in cycles, and if looking back far enough, we start to see patterns that tend to repeat. 🔁

The expected return formula looks at the past performance of an asset and calculates the average growth based on the performance in that period from the past. This tells investors what a likely return for the current year is, and is a helpful tool for comparing stocks and choosing long-term investments.

Of course, we can’t consider this calculation as set in stone, considering how quickly the markets can change as a result of one event. No one could have anticipated that Russia would be hit with a wave of sanctions, in the midst of strained relations with the West—and no math equation can account for such macroeconomic events of that scale.

As the present times become more unpredictable with each day, many investors fear that traditional investing methodology like the 60/40 portfolio is losing steam—and that means that we need to be more careful with our stock picks.

In this article, we will discuss how to quickly calculate expected returns, how to adjust those predictions for risk, and how this formula can be used in investing. Let’s see how this simple method of making a portfolio just a bit more well-optimized works. 👷‍♂️

What you’ll learn
  • What is the Expected Return of a Portfolio?
  • How to Calculate a Single Investment Return
  • How to Calculate Expected Return of a Portfolio
  • Uses of the Expected Return Formula
  • Importance of Risk Tolerance
  • Limitations of Expected Return
  • Conclusion
  • Get Started with a Stock Broker

What is the Expected Return of a Portfolio?

In short, an expected return is a number—it tells us how an asset might perform in the future based on its past performance. There are multiple formulae for calculating expected returns and different time frames can be used, but most commonly, investors simply get expected returns for the current year by calculating the average annual performance of an asset for the past 10 years.

Why would a new investor need to know about formulae? After one has done their due diligence – setting aside finances to trade, selecting an ideal stock broker for their investment needs, and creating their account – the next step is to identify stocks to invest in. The expected return formula is one of the simpler ones that can give investors an idea of which direction to go in.

Investors can use the expected return formula to get an idea of how long it will take to hit their investment goal, based on the performance of their stocks in the last decade. It’s good to note that these returns are predictions, so they won’t give you a 100% clear indication of how much an investment will be worth a year from now.

Instead, calculating the deviation of the expected return will give you a price range, and the asset you’re looking at will likely grow (or fall) into that predicted range in the future. Many businesses use this formula to make projections of their stock’s future value in order to attract investors and creditors.

So, we can use expected returns to analyze several stocks, pick out the most promising ones, and build a portfolio around them. Pretty straightforward, right? Let’s take a look at a simple way of calculating expected returns.

How to Calculate a Single Investment’s Expected Return 🧮

The expected return formula is easy to use once you understand how to apply it. So, if math isn’t your strong suit, don’t worry, you’ll get the hang of it.

Let’s start with an example: After months of contemplation, Mike has decided to start investing. He’s narrowed down his options and signed up with one of the top apps for stock trading which aligns with his needs. Now, he needs to find the right stocks to invest in.

He comes across a stock that looks like it’s been performing well – let’s call it STONK. Based on the average annual growth of STONK in the past decade, Mike can guess how the current year might look for the stock. Moreover, he can determine how likely it is for the stock to match its best and worst performance.

Mike can do this simply by summing up all the gains for each year separately as percentage values and dividing the whole sum by 10 (which is the number of years). And voila— he has a 10-year average that can give him an idea of where STONK will be in a year from now.

Expected Return for a Single Investment Calculated 📙

Here’s how it works: Say STONK had 2 very good years where it grew by 20%, 3 solid years by 15%, 3 years by 10%, and it decreased by 5% in the last 2 years. It would look like this in the table below: 

StonkReturns
2 Years20%
3 Years15%
3 Years10%
2 Years-5%

When Mike plugs these numbers into the expected return formula, it looks like this:

Expected return of STONK = [(2/10).(20%) + (3/10).(15%) + (3/10).(10%) + (2/10).(-5%)]

=  0.2(20%) + 0.3(15%) + 0.3(10%) + 0.2(-5%)  

= 10.5% per year

Alternatively, he can calculate the expected return like this:

[(2).(20%) + (3).(15%) + (3).(10%)+(2).(*5%)]/10

(40% + 45% + 30% – 10%) / 10

= 105% over 10 years

= 10.5% per year

So, this equation shows us that, based on STONK’s performance in the last ten years, the expected return for the next year would be 10,5%.

Yet, “expected” doesn’t mean the outcome is set in stone. From the table, we can see that STONK grew by 20% for 2 years, dropped by 5% for the next 3 years, and experienced a -5% drop in the last 2 years.

A stock’s performance can be unpredictable, so the best an investor can do is use their predictions to make a calculated guess and continually monitor both internal and external market conditions that can affect the performance of the stock.

How to Calculate Expected Return of a Portfolio 👨‍🏫

You can use the same formula to calculate the expected rate of return for an entire portfolio, too. Once we’ve calculated the expected return of each of our assets, we add them together to get our total result.

To do this, we need to note how much each security is weighed in a portfolio—this basically means what percentage of the portfolio it takes up. OK, this was a bunch of dull-sounding words, so here is a simple example to illustrate how everything works.

Expected Return of a Portfolio – Example 📝

To make this easier to follow, let’s use a fun example. Say we have a portfolio with 3 stocks: Apple (AAPL), Tesla (TSLA), and Disney (DIS). Let’s look at the 10-year period from 2011 to 2021 and see what the expected return for the next year is.

Yearly ReturnsAAPL (A)TSLA (B)DIS (C)
2011+24.8%+5.5%-1.7%
2012+33.5%+26%+33.4%
2013+5%+324.5%+49.2%
2014+38.3%+46.1%+23.5%
2015-3.6%+1.9%+12.1%
2016+13.1%-2.9%+1.2%
2017+48.3%+47.7%+5.4%
2018-8.3%-2.3%-2.5%
2019+90.2%+38.7%+32.7%
2020+72.3%+748%+22.5%
2021 (Expected Return)+31.3%+123.3%+35.1%

We calculated the expected return of each stock by finding its average growth rate over 10 years. Now, let’s see how each stock is weighed.

Say 50% of our portfolio is devoted to Disney because it is a company with good, steady growth and only a few poorly-performing years. Then let’s allocate 30% to Apple as our reliable growth stock and another 20% to Tesla because it’s a pure play stock that focuses on a single industry, but tends to explode every time they make a technological breakthrough.

Let’s use this formula to calculate what our hypothetical portfolio will do in 2021, using this formula:

Expected Portfolio Return formula.

Here is what this means:

  • ☑ WA = Weight of stock A 
  • ☑ RA = Average return of stock A
  • ☑ WB = Weight of stock B
  • ☑ RB = Average return of stock B
  • ☑ WC= Weight return of stock C
  • ☑ RB =  Average return of stock C

The average returns are in the final row of the table above. 

In this case, A is for Apple, B is for Tesla, and C is for Disney, so the formula for our imaginary portfolio would look like this:

Expected return = (30% x 31.3) + (20% x 123.3) + (50% x 35.1) 

= (0.3 x 31.3) + (0.2 x 123.3) + (0.5 x 35.1) =

9.4 +  24.7 + 17.5 = 51.6

So, if the past were to repeat itself in a quite literal sense, our imaginary portfolio should be up 51.6% in the year 2021. Needless to say, that’s pretty great—but let’s see how accurate this prediction would have been if we had made it in 2021.

Incidentally, this article is a bit more recent than the period from our example, so we know that in real life this portfolio actually would have grown by 18.9%. Namely, Apple actually performed above its average in 2021, Tesla had a good, but not crazy good year for its standards, and Disney actually lost over 11% of its value, in part because Disneyland’s attendance suffered due to Covid restrictions that were only lifted in early 2022.

Uses and Relevance of the Expected Return Formula 🌟

As we can see from the example above, the expected return formula would have given us a prediction that is pretty far off from what actually happened. But, expected returns can be precise too—stocks are far more volatile and are sensitive to economic and political events among other things, but stable assets like Treasury bonds are much more predictable.

Moreover, calculating expected returns has more than one benefit for the investor. For one, it can show the investor that some assets simply performed better than others, and that perhaps they should weigh their portfolio more heavily towards securities that yield more profits.

Also, it can help the investor rank their assets. Now, you don’t necessarily want to compare stocks and bonds in this manner, but if you’re choosing between 5 growth stocks and don’t know which one to pick, their expected returns might help you find the one with the most potential. 

A stock chart showing apple's growth over the course of 10 years
Investors can also look at whether the average growth of a stock is accelerating or slowing down year after year, which can help them spot a trend.

And finally, it pays to be aware of how expected returns work because companies and funds use this formula to convince investors to buy their stock. Even though past performance isn’t really an indicator of future performance since there are just too many variables involved—for example, no one could have predicted the Suez Canal blockage in 2020 that disrupted trade and impacted countless companies.

Importance of Risk Tolerance and Other Factors 🎯

How much risk can you tolerate? In other words, how risky a stock would you invest in? This is a very important question, and expected returns can’t really tell you the whole answer.

The only info that the expected returns formula uses is the past performance of an asset—which means it doesn’t account for anything that can happen now but hasn’t happened in the past. Sometimes, when the markets are slow and unexciting this can be a good indicator of the future.

However, at other times, relying on the past for guidance can completely mislead you. Here’s a clear example—when COVID-19 lockdowns first began, the S&P 500 crashed by over 30%, but a few industries rallied and then exploded as a result of the whole situation.

Among these were healthcare stocks that had seen temporary impressive growth. This is completely logical—you have a pandemic situation and the health industry suddenly becomes more important than ever. In this case, expected returns couldn’t have told us absolutely anything—health stocks grew because of something that happened over the course of a few months, and not because of something that had been happening over the past decade.

Stock chart illustrating moderna's bull run in 2020 and it's correction in 2022
Moderna’s bull run in 2020 couldn’t have been predicted with expected returns, but its correction in 2022 was a likely long-term outcome.

We can’t account for this using expected returns, which is why experienced investors trade news events as well as use statistical predictions. All in all, just using the expected return formula won’t really tell you how much risk you’re assuming—a stock might seem safe, but be vulnerable to major policy changes, geopolitical events, or new disruptive technologies.

So, when using expected returns, it is important to watch the news and conduct fundamental analysis to see if there’s something that might indicate that a stock’s performance will be better or worse than it was in the past decade.

Then, in order to further cushion ourselves from unforeseen consequences, we can use the expected return number to get an expected return range—this standard deviation makes statistical predictions much more reliable, so let’s see how it works.

Analyzing Risk of Investments 🔍

Even though seasoned cyclists rarely crash their bicycles, the wisest among them have a habit of wearing a helmet, and maybe even elbow pads. In the same way, to protect our money, we can measure how risky our portfolio is—this means, how much our portfolio is likely to deviate from the performance predicted by our expected return calculations.

Analyzing risk in this sense is simple—we just need to look at an asset and see how much (on average) its yearly returns in the past 10-year period deviate from its expected returns. We can return to our Tesla example:

Elon Musk’s favorite stock is well-known for huge price changes, and when we factor that in, we can conclude that even though TSLA has an expected return of 123.3% for 2021, it is likely to be far off from that target. Let’s see just how far off using this standard deviation formula:

Standard deviation formula

Let’s break this down:

  • ☑ σ = Standard deviation
  • ☑ N = Size of population
  • ☑ Xi = Each value from the population
  • ☑ μ = Population mean

In this case, the size of the population (N) is 10 because we are looking at a 10-year period. We can take a look at the chart with Tesla’s past returns to find each of the values of the population (Xi)—the return for each year. And finally, the mean (μ) is the expected return of 123.3%.

Once we’ve reminded ourselves of how algebra works, we can solve this formula to find the standard deviation and find the answer, which is in this case 228%.

So, our average deviation is 228% (this is huge but TSLA is an extremely volatile stock) which means that for 2021, TSLA is likely to be 2.28 times higher or lower than the projected 123.3% expected return—the range is therefore between 54% and 281%. We know that in real life TSLA grew by about 60% in 2021, so that’s within the range we’ve determined.

What Are the Limitations of Expected Return?

Is there a mathematical formula that can tell you who’s going to win the next Superbowl ? No, there isn’t—and even if there was and we knew it, we would probably keep it a secret for the safety of the world. 🛡

But, what you can do with math is look at the past performance of each football team and determine how likely they are to win this time according to statistics. However, using that logic is obviously flawed because players change teams, running backs get injured, and many random things happen—there’s no way to account for any of these variables by simply looking at past performance.

In the same way, when it comes to more volatile risk assets like stocks and cryptos, the expected returns can be useful, but also misleading. For example, if this year has the same economic climate as the past decade and there haven’t been any significant changes to the company we’re looking to invest in, the expected return will likely be pretty close to the mark.

💡 Pro tip: Investment analysis can be approached from many angles. A simple way to make sure you’re covered on all fronts is to use stock analysis software.

However, if something unexpected like a war breaks out and causes economic calamity, that means that the current year will be vastly different, making a stock’s past performance a very poor indicator of future results.

Something similar can happen if a company changes in a significant way—for instance, when Microsoft acquired Activision-Blizzard, insider trading accusations followed, affecting the stock. We can’t expect the company to keep working like before when it had a different owner, management, and business goals.

On the other hand, fixed-income securities like bonds are very likely to match their historic performance barring any very major change in fiscal policy like changes in interest rates. Therefore, expected returns are much more precise for assets that are characterized by slow, steady growth. 📈

All in all, whether expected returns will give you an accurate idea about the future heavily depends on the surrounding context—something that this formula disregards completely. For instance, the stock of the communications software company Zoom went parabolic after COVID-19 lockdowns started in 2020 and everyone realized they’ll be doing a lot of video calls—and that is why expected returns should ideally be used for comparing stocks and in combination with thorough fundamental analysis.

Conclusion 🏁

Like any investment analysis method, expected returns will not give you some amazing insight into the future—but it can help you pick investments that are more statistically likely to succeed. In and of itself, this small edge doesn’t mean much, but these small advantages add up.

Pro traders and seasoned investors are always looking to increase their odds of success even a little bit and expected returns certainly help with that. It is only important to keep in mind that expected returns are based solely on fairly superficial historical data, which might be enough sometimes—but when it comes to researching stocks and other volatile assets, expected returns should just be one more tool in an investor’s toolbox.

Expected Portfolio Return: FAQs

  • What is a Good Expected Return for a Portfolio?

    Usually, anything more than 10% is considered a good expected return. This is because, looking at the past century, the average annual stock market return is 10%—and since most passive investors expect their portfolios to grow at the average stock market rate, anything above that is considered a bonus.

  • What Type of Risk is Relevant for Determining the Expected Return?

    Systematic risk is most relevant for calculating expected returns. As systematic risk impacts the entire market, it cannot be managed by diversification, and that makes it the most relevant factor when determining the expected return—which is entirely based on past average returns of an asset without considering the rest of the context surrounding the asset’s performance. 

  • What Does the Expected Return Tell Me?

    The expected return formula can tell you what a possible future return of an asset is likely to be based on its past performance. Essentially, the expected return formula disregards the surrounding context and assumes that past performance is an indicator of future performance—which is not categorically true—and can therefore give the investor an approximation of a likely future return.

  • What is Meant by Portfolio Return?

    Portfolio return means portfolio growth expressed in percentages. For example, a 20% annual return means that a portfolio has grown by 20% over the course of a year.

  • How Do You Measure Portfolio Risk?

    There are dozens of ways of measuring portfolio risk, but most of them revolve around something called standard deviation. In the context of expected returns, standard deviation only looks at historical returns and measures how much a future return is likely to deviate from the 10-year average. A greater standard deviation means that the real future return is more likely to be further off from the predicted value.

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