How to Calculate Expected Rate of Return
When investing, you often want to know how much money an investment is likely to earn you. That’s where the expected rate of return comes in; expected rate of return is calculated using the probabilities of investment returns for various potential outcomes. Investors can utilize the expected return formula to help project future returns.
Though it’s impossible to predict the future, having some idea of what to expect can be critical in setting expectations for a good return on investment.
Key Points
• The expected rate of return is the profit or loss an investor expects from an investment based on historical rates of return and the probability of different outcomes.
• The formula for calculating the expected rate of return involves multiplying the potential returns by their probabilities and summing them.
• Historical data can be used to estimate the probability of different returns, but past performance is not a guarantee of future results.
• The expected rate of return does not consider the risk involved in an investment and should be used in conjunction with other factors when making investment decisions.
What Is the Expected Rate of Return?
The expected rate of return — also known as expected return — is the profit or loss an investor expects from an investment, given historical rates of return and the probability of certain returns under different scenarios. The expected return formula projects potential future returns.
Expected return is a speculative financial metric investors can use to determine where to invest their money. By calculating the expected rate of return on an investment, investors get an idea of how that investment may perform in the future.
This financial concept can be useful when there is a robust pool of historical data on the returns of a particular investment. Investors can use the historical data to determine the probability that an investment will perform similarly in the future.
However, it’s important to remember that past performance is far from a guarantee of future performance. Investors should be careful not to rely on expected returns alone when making investment decisions.
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How To Calculate Expected Return
To calculate the expected rate of return on a stock or other security, you need to think about the different scenarios in which the asset could see a gain or loss. For each scenario, multiply that amount of gain or loss (return) by its probability. Finally, add up the numbers you get from each scenario.
The formula for expected rate of return looks like this:
Expected Return = (R1 * P1) + (R2 * P2) + … + (Rn * Pn)
In this formula, R is the rate of return in a given scenario, P is the probability of that return, and n is the number of scenarios an investor may consider.
For example, say there is a 40% chance an investment will see a 20% return, a 50% chance that the investment will return 10%, and a 10% chance the investment will decline 10%. (Note: all the probabilities must add up to 100%)
The expected return on this investment would be calculated using the formula above:
Expected Return = (40% x 20%) + (50% x 10%) + (10% x -10%)
Expected Return = 8% + 5% – 1%
Expected Return = 12%
What Is Rate of Return?
The expected rate of return mentioned above looks at an investment’s potential profit and loss. In contrast, the rate of return looks at the past performance of an asset.
A rate of return is the percentage change in value of an investment from its initial cost. When calculating the rate of return, you look at the net gain or loss in an investment over a particular time period. The simple rate of return is also known as the return on investment (ROI).
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How to Calculate Rate of Return
The formula to calculate the rate of return is:
Rate of return = [(Current value − Initial value) ÷ Initial Value ] × 100
Let’s say you own a share that started at $100 in value and rose to $110 in value. Now, you want to find its rate of return.
In our example, the calculation would be [($110 – $100) ÷ $100] x 100 = 10
A rate of return is typically expressed as a percentage of the investment’s initial cost. So, if you were to sell your share, this investment would have a 10% rate of return.
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Different Ways to Calculate Expected Rate of Return
How to Calculate Expected Return Using Historical Data
To calculate the expected return of a single investment using historical data, you’ll want to take an average rate of returns in certain years to determine the probability of those returns. Here’s an example of what that would look like:
|
Annual Returns of a Share of Company XYZ | |
|---|---|
| Year | Return |
| 2011 | 16% |
| 2012 | 22% |
| 2013 | 1% |
| 2014 | -4% |
| 2015 | 8% |
| 2016 | -11% |
| 2017 | 31% |
| 2018 | 7% |
| 2019 | 13% |
| 2020 | 22% |
For Company XYZ, the stock generated a 21% average rate of return in five of the ten years (2011, 2012, 2017, 2019, and 2020), a 5% average return in three of the years (2013, 2015, 2018), and a -8% average return in two of the years (2014 and 2016).
Using this data, you may assume there is a 50% probability that the stock will have a 21% rate of return, a 30% probability of a 5% return, and a 20% probability of a -8% return.
The expected return on a share of Company XYZ would then be calculated as follows:
Expected return = (50% x 21%) + (30% x 5%) + (20% x -8%)
Expected return = 10% + 2% – 2%
Expected return = 10%
Based on the historical data, the expected rate of return for this investment would be 10%.
However, when using historical data to determine expected returns, you may want to consider if you are using all of the data available or only data from a select period. The sample size of the historical data could skew the results of the expected rate of return on the investment.
How to Calculate Expected Return Based on Probable Returns
When using probable rates of return, you’ll need the data point of the expected probability of an outcome in a given scenario. This probability can be calculated, or you can make assumptions for the probability of a return. Remember, the probability column must add up to 100%. Here’s an example of how this would look.
|
Expected Rate of Return for a Stock of Company ABC | |||
|---|---|---|---|
| Scenario | Return | Probability | Outcome (Return * Probability) |
| 1 | 14% | 30% | 4.2% |
| 2 | 2% | 10% | 0.2% |
| 3 | 22% | 30% | 6.6% |
| 4 | -18% | 10% | -1.8% |
| 5 | -21% | 10% | -2.1% |
| Total | 100% | 7.1% | |
Using the expected return formula above, in this hypothetical example, the expected rate of return is 7.1%.
Calculate Expected Rate of Return on a Stock in Excel
Follow these steps to calculate a stock’s expected rate of return in Excel (or another spreadsheet software):
1. In the first row, enter column labels:
• A1: Investment
• B1: Gain A
• C1: Probability of Gain A
• D1: Gain B
• E1: Probability of Gain B
• F1: Expected Rate of Return
2. In the second row, enter your investment name in B2, followed by its potential gains and the probability of each gain in columns C2 – E2
• Note that the probabilities in C2 and E2 must add up to 100%
3. In F2, enter the formula = (B2*C2)+(D2*E2)
4. Press enter, and your expected rate of return should now be in F2
If you’re working with more than two probabilities, extend your columns to include Gain C, Probability of Gain C, Gain D, Probability of Gain D, etc.
If there’s a possibility for loss, that would be negative gain, represented as a negative number in cells B2 or D2.
Limitations of the Expected Rate of Return Formula
Historical data can be a good place to start in 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 consider the risk involved by investing in a particular stock or other asset class. The risk involved in an investment is not represented by its expected rate of return.
In this historical return example above, 10% 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 2014 and 2016. The variability of returns is often called volatility.
Standard Deviation
To understand the volatility of an investment, you may consider looking at its standard deviation. Standard deviation measures volatility by calculating a dataset’s dispersion (values’ range) relative to its mean. The larger the standard deviation, the larger the range of returns.
Consider two different investments: Investment A has an average annual return of 10%, and Investment B has an average 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 when returns are much higher and lower than with Investment B.
| Year | Annual Return of Investment A | Annual Return of Investment B |
|---|---|---|
| 2011 | 16% | 8% |
| 2012 | 22% | 4% |
| 2013 | 1% | 3% |
| 2014 | -6% | 0% |
| 2015 | 8% | 6% |
| 2016 | -11% | -2% |
| 2017 | 31% | 9% |
| 2018 | 7% | 5% |
| 2019 | 13% | 15% |
| 2020 | 22% | 14% |
| Average Annual Return | 10% | 6% |
| Standard Deviation | 13% | 5% |
Investment A has a standard deviation of 13%, while Investment B has a standard deviation of 5%. 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.
Recommended: A Guide to Historical Volatility
Systematic and Unsystematic Risk
All investments are subject to pressures in the market. These pressures, or sources of risk, can come from systematic and unsystematic risks. Systematic risk affects an entire investment type. Investors may struggle to reduce the risk through diversification within that asset class.
Because of systematic risk, you may consider building an investment strategy that includes different asset types. For example, a sweeping stock market crash could affect all or most stocks and is, therefore, a systematic risk. However, if your portfolio includes different types of bonds, commodities, and real estate, you may limit the impact of the equities crash.
In the stock market, unsystematic risk is specific to one company, country, or industry. For example, technology companies will face different risks than healthcare and energy companies. This type of risk can be mitigated with portfolio diversification, the process of purchasing different types of investments.
Expected Rate of Return vs Required Rate of Return
Expected return is just one financial metric that investors can use to make investment decisions. Similarly, investors may use the required rate of return (RRR) to determine the amount of money an investment needs to generate to be worth it for the investor. The required rate of return incorporates the risk of an investment.
What Is the Dividend Discount Model?
Investors may use the dividend discount model to determine an investment’s required rate of return. The dividend discount model can be used for stocks with high dividends and steady growth. Investors use a stock’s price, dividend payment per share, and projected dividend growth rate to calculate the required rate of return.
The formula for the required rate of return using the dividend discount model is:
RRR = (Expected dividend payment / Share price) + Projected dividend growth rate
So, if you have a stock paying $2 in dividends per year and is worth $20 and the dividends are growing at 5% a year, you have a required rate of return of:
RRR = ($2 / $20) + 0.5
RRR = .10 + .05
RRR = .15, or 15%
What is the Capital Asset Pricing Model?
The other way of calculating the required rate of return is using a more complex model known as the capital asset pricing model.
In this model, the required rate of return is equal to the risk-free rate of return, plus what’s known as beta (the stock’s volatility compared to the market), which is then multiplied by the market rate of return minus the risk-free rate. For the risk-free rate, investors usually use the yield of a short-term U.S. Treasury.
The formula is:
RRR = Risk-free rate of return + Beta x (Market rate of return – Risk-free rate of return)
For example, let’s say an investment has a beta of 1.5, the market rate of return is 5%, and a risk-free rate of 1%. Using the formula, the required rate of return would be:
RRR = .01 + 1.5 x (.05 – .01)
RRR = .01 + 1.5 x (.04)
RRR = .01 + .06
RRR = .07, or 7%
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The Takeaway
There’s no way to predict the future performance of an investment or portfolio. However, by looking at historical data and using the expected rate of return formula, investors can get a better sense of an investment’s potential profit or loss.
There’s no guarantee that the actual performance of a stock, fund, or other assets will match the expected return. Nor does expected return consider the risk and volatility of assets. It’s just one factor an investor should consider when deciding on investments and building a portfolio.
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FAQ
How do you find the expected rate of return?
An investment’s expected rate of return is the average rate of return that an investor can expect to receive over the life of the investment. Investors can calculate the expected return by multiplying the potential return of an investment by the chances of it occurring and then totaling the results.
How do you calculate the expected rate of return on a portfolio?
The expected rate of return on a portfolio is the weighted average of the expected rates of return on the individual assets in the portfolio. You first need to calculate the expected return for each investment in a portfolio, then weigh those returns by how much each investment makes up in the portfolio.
What is a good rate of return?
A good rate of return varies from person to person. Some investors may be satisfied with a lower rate of return if its performance is consistent, while others may be more aggressive and aim for a higher rate of return even if it is more volatile. Ultimately, it is up to the individual to decide what is considered a good rate of return.
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