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How to Calculate Expected Rate of Return

March 30, 2020 · 6 minute read

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How to Calculate Expected Rate of Return

The basic idea behind investing is finding ways for your money to earn you even more money. Getting your money to do work for you? Yes, please.

But how do you figure out how much your investment is going to make you?

The money that you earn on an investment is known as your return. The rate of return on an investment is the money that is earned (or lost) on an investment.

If you’re going to invest in something, you may want to consider how much money that investment is likely to earn you. Though it’s not possible to predict the future—no one has a crystal ball—having some idea of what to expect is critical in setting expectations.

Therefore, the expected rate of return is the profit (or loss) that an investor may earn on an investment.

To determine an investment’s expected rate of return, you’ll use the expected return formula.

It’s possible to use the formula with either historical or expected values (of earnings or losses).

Here’s how to calculate an investment’s expected return, along with a discussion around the uses of such a calculation. The expected rate of return formula is useful for investors looking to build out a model portfolio but does have its limitations.

To understand the expected rate of return formula, it helps to start with a base knowledge of a simple rate of return calculation.

A rate of return is typically expressed as a percentage of the investment’s initial cost. For example, an investment that grew from $100 to $110 has a 10% rate of return. Here’s the rate of return formula:

Rate of return = [(Current value − Initial value) ÷ Initial Value ] × 100

In our example, the calculation would be [($110 – $100) ÷ $100] x 100 = 10

So this investment had a 10% rate of return (RoR) during this period.

Next, consider the expected rate of return. This is the return an investor expects from an investment, given either historical rates of return or probable rates of return under different scenarios. The expected return formula projects potential future returns.

To determine the expected rate of return based on historical data, it can be helpful by starting with calculating the average of the historical return for that investment.

This strategy may be useful when there is a robust pool of historical data on the returns of that particular asset type, but remember that past performance is far from a guarantee of future performance.

To calculate an expected return based on probable returns under different scenarios, you’ll need to give each potential return outcome a probability.

For example, you might say that there is a 50% chance the investment will return 20% and a 50% chance that an investment will return 10%. (Note: All the probabilities must add up to 100%.) Next, multiply each scenario’s probability percentage by the investment’s expected return for that period. Then, add those numbers together (hint: 15% is the answer).

How to Calculate Expected Return

To calculate the expected return using historical data, you’ll want to take an average of each outcome. Here’s an example of what that would look like.

Year

Return

2000 14%
2001 2%
2002 22%
2003 34%
2004 5%
2005 -18%
2006 -21%
2007 29%
2008 6%
2009 16%
2010 22%
2011 1%
2012 -4%
2013 8%
2014 -11%
2015 31%
2016 7%
2017 13%
2018 22%
Average 9%

In this example, the average rate of return is 9%. When using historical data, you may want to consider your pool of data. Are you using all of the data available? Or only data from a select period? If you are only using some data and not others, why?

When using probable rates of return, you’ll need the additional data point of the expected probability of each outcome. Remember, the probability column must add up to 100%. Multiply the return by the probability and add the outcomes together to get the expected rate of return. Here’s an example of how this would look.

Scenario

Return

Probability

Outcome

1 14% 30% 0.042
2 2% 10% 0.0028
3 22% 30% 0.066
4 -18% 10% -0.018
5 -21% 10% 0.00441
100% 0.09721

In this hypothetical example, the expected rate of return is 9.7%.

The expected rate of return looks like this:

Expected Return = SUM (Returni x Probabilityi)

(Where “i” indicates each known return and its respective probability in the series.)

Limitations of the Expected Returns Formula

Whether you use historical rates of return or probable rates of return, outcomes are never guaranteed. All the historical data in the world can’t predict the future.

Having historical data can be a good place to start in your journey of understanding how an investment behaves. That said, investors may want to be leery of extrapolating past returns for the future. Historical data is a guide, it’s not necessarily predictive.

Another limitation to the expected returns formula is that it does not take into account the risk involved by investing in a particular asset class. After all, investing can be inherently risky.

And risk and return are often two sides of the same coin. In order to achieve a higher rate of return, you’ll most likely have to take more risk. The risk involved in an investment is not represented by its expected rate of return.

Look at the first example. In this example, which uses historical returns, 9% is the expected rate of return. What that number doesn’t reveal is the risk taken in order to achieve that rate of return. The investment experienced negative returns in the years 2005, 2006, 2012, and 2014. The variability of returns is often called volatility.

Sometimes, investment risk comes with the possibility of losing money in that investment. Knowing this, it might be misguided to assume that 9% annual returns were going to show up as positive 9% returns each and every year. To achieve 9% average returns, there must be some risk involved.

All investments are subject to pressures in the market. These pressures, or sources of risk, can come in the form of systematic and unsystematic risk. Systematic risk affects an entire investment type. Within that investment category, it probably can’t be “diversified” away.

For example, a sweeping stock market crash could affect all or most stocks and is, therefore, a systematic risk.

Because of systematic risk, you may want to consider building an investment strategy that includes different asset types.

In the stock market, unsystematic risk is risk that’s specific to one company, country, or industry.

For example, technology companies will face different risks than healthcare companies and energy companies.

This type of risk can be mitigated with diversification, the process of purchasing different types of investments.
Both systematic and unsystematic risks are difficult, if not impossible, to time.

To be a savvy investor, it’s helpful to understand the risks involved with each asset class you’re looking to invest in. One way is to consider the standard deviation of an investment.

Need a quick throwback to Statistics 101? Standard deviation measures volatility by calculating the dispersion (values’ range) of a dataset relative to its mean. The larger the standard deviation, the larger the range of returns.

Consider two different investments. Investment A has an annual return of 9%, and Investment B has an annual return of 6%. But when you look at the year by year performance, you’ll notice that Investment A experienced significantly more volatility. There are years where returns are much higher and lower than with Investment B.

Year

Investment A

Investment B

2000 14% 11%
2001 2% 12%
2002 22% 12%
2003 34% 3%
2004 5% 8%
2005 -18% -1%
2006 -21% -5%
2007 29% 11%
2008 6% 1%
2009 16% 8%
2010 22% 4%
2011 1% 3%
2012 -4% 0%
2013 8% 7%
2014 -11% -4%
2015 31% 9%
2016 7% 5%
2017 13% 15%
2018 22% 14%
Average 9% 6%
ST. DEV. 16% 6%

On Investment A, the standard deviation is 16%. On Investment B, the standard deviation is 6%. Although Investment A has a higher rate of return, there is more risk. Investment B has a lower rate of return, but there is less risk. Investment B is not nearly as volatile as Investment A.

Building an Investment Portfolio

Once you’ve done your research on the risk and return characteristics of the different asset classes, you may feel ready to start investing.

If your goal is to build an investment portfolio, you may want to consider diversifying. Diversification is the process of buying assets that are hopefully non-correlated; the performance of one is not necessarily related to the performance of the other.

For example, you could build a portfolio of stocks and bonds, two non-correlated asset classes.

To do this, you can buy stocks and bonds directly, or you can buy them within funds. Funds can provide a way to achieve a diversified portfolio because they bundle many different investments together.

One fund could hold hundreds or even thousands of stocks, bonds, or other investments. For example, an S&P 500 index fund invests in the 500 leading companies in the United States. But the variety of funds doesn’t stop there. There are funds that invest in countries and industries all over the globe.

When building a portfolio, you may also want to keep costs as low as possible. Any trading fees, transaction costs, or account fees may come directly out of your potential returns. With SoFi Invest®, you’ll pay no fees to build out your portfolio—whether you want to buy stocks or exchange-traded funds (ETFs).

If you would like help creating an investment portfolio, SoFi Automated Investing might be right for you. SoFi Automated Investing uses a portfolio of ETFs based on your goals, risk tolerance, and projected timeline.

A diversified portfolio is built and maintained for you. With SoFi Invest®, there are no management fees, and you’ll have access to multiple member benefits like financial advisors, career services, and exclusive events and offers.

Ready to start investing? Download the SoFi app to get started.


Investment Risk: Diversification can help reduce some investment risk. It cannot guarantee profit, or fully protect in a down market.
External Websites: The information and analysis provided through hyperlinks to third party websites, while believed to be accurate, cannot be guaranteed by SoFi. Links are provided for informational purposes and should not be viewed as an endorsement.
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