Why do we invest in real estate, financial products like stocks, bonds, mutual funds and many more? The simple answer is that we support our money to earn more money! But if you are going to invest, you will want an idea of how much you will likely earn from an investment. The money you earn on an investment is known as your return. In finance, a return is a profit made from an investment.
How do you figure out how much you are going to make on an investment? What is the difference between the rate of return (ROR) and return on investment (ROI)? How do you differentiate the expected rate of return from the required rate of return? Where can you find a reliable expected rate of return calculator?
What Is Rate Of Return (ROR)?
Return is defined as the profit made from an investment. It includes any changes in the value of the investment, and/or cash flows (or securities, or other investments) which an investor receives from that investment. These receipts include interest payments, coupons, cash dividends, stock dividends or the payoff from a derivative or structured product. It may be measured either in absolute terms (e.g., dollars) or as a percentage of the amount invested. A loss instead of a profit is described as a negative return, assuming the amount invested was greater than zero.
To compare returns over periods of different lengths, it is helpful to convert each return into a return over a period of time of a standard length. The result of the conversion is called the rate of return. Typically, the period is in a year, in which case the rate of return is also called the annualized return and the conversion process called annualization. The resulting value is called the internal rate of return (IRR). Rate of return can be further expressed as expected rate of return (ERR), which is the profit or loss that an investor anticipates on investment with known historical rates of return (ROR). We will delve deeper into the expected rate of return and its calculation below.
The Difference Between Rate Of Return (ROR) And Return On Investment (ROI)?
Before we go into the details of calculating the expected rate of return, let us first look into another investment metric which is often used synonymously with the rate of return (ROR). This metric is the return on investment (ROI). Investopedia defines ROI as is a performance measure used to evaluate the efficiency or profitability of an investment or compare the efficiency of several different investments. ROI tries to directly measure the return on a particular investment relative to the investment’s cost.
ROI is a measurement of how well an investment performs in relation to its cost. It is expressed as a ratio.
ROI, IRR, and ROR are three measurements that analyze the performance of an investment over time. The ROI looks at investment’s growth from beginning to end. The internal rate of return or IRR looks at the investment’s annual growth rate. The rate of return or ROR is the net value of discounted cash flows on an investment after inflation.
The Rate Of Return Formula
Now that we have defined ROR, IRR and ROI and the difference between them, let’s take a look at the basic ROR formula, which is similar to the ROI formula:
Rate of return = [(Current value − Initial value) ÷ Initial Value ] × 100
A rate of return is expressed as a percentage of the investment’s initial cost. For example, an investment that grew from $100 to $130 has a 30% rate of return over the time period in consideration.
In our example, the calculation would be [($130 – $100) ÷ $100] x 100 = 30
The investment had a 30% rate of return (RoR) during this period.
The Expected Rate Of Return Calculator
To illustrate how to calculate the expected rate of return, let us consider an investment made on the stock. As you probably know, stocks can be volatile. There are many scenarios in which the stock could see a gain or loss. These different gain or loss scenarios are taken into consideration in calculating the expected rate of return.
For each scenario, multiply that amount of gain or loss (return) by the probability of it happening. Finally, add up the numbers you get from each scenario after multiplying the returns by the probabilities.
The formula for the expected rate of return looks like this:
Expected Return = (Return A X Probability A) + (Return B X Probability B)
(Where A and B indicate a different scenario of return and probability of that return.)
For example, you might say that there is a 70% chance the investment will return 30% and a 30% 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 to return for that period.
Expected Return = (70% X 30%) + (30% X 10%)
Then, add those numbers together.
Expected Return = 21% + 3% = 24%
As you can see, the expected rate of return is calculated here, given probable rates of returns under different scenarios. It can also be calculated using historical rates of return.
Calculating Expected Rate Of Return Using Historical Data
To determine the expected rate of return based on historical data, it is helpful to calculate the average of the historical return for that investment. This strategy is useful if there is a robust pool of historical data on the returns of that particular asset type. Do remember that past performance does not guarantee future performance. Below is an example from Social Finance, Inc. (SoFi) of calculating the ERR from historical data:
| 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, it is best to consider a pool of data.
Calculating Expected Rate Of Return Based On Probable Returns
We already mentioned calculating ERR based on probable returns earlier. Here is a further elucidation of this calculation from Social Finance, Inc. (SoFi):
| 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 |
The most important thing to remember is that the probabilities of each scenario must add up to a total of 100%. Using the formula earlier cited with an example, the expected rate of return is 9.7%.
Limitations Of The Expected Rate Of Return
The expected rate of return is always used in conjunction with other investment metrics. To make investment decisions solely on expected return calculations without considering the risk characteristics of investment opportunities can be pretty dangerous. Although the risk is inherent in investments, managing it and making investments with the risk aligned with your investment portfolio is wise. Here is an example from Corporate Finance Institute of two investment scenarios where the expected rate of returns are similar, but the risk characteristics differ:
For example, assume two hypothetical investments exist. Their annual performance results for the last five years are:
Investment A: 12%, 2%, 25%, -9%, and 10%
Investment B: 7%, 6%, 9%, 12%, and 6%
Both of these investments have expected returns of exactly 8%. However, as defined by the standard deviation, investment A is approximately five times riskier than investment B when analyzing each risk. Investment A has a standard deviation of 12.6%, and investment B has a standard deviation of 2.6%. Standard deviation is a common statistical metric used by analysts to measure an investment’s historical volatility or risk.
In addition to expected returns, investors should also consider the likelihood of that return. Certain lotteries, for example, offer a positive expected return, despite the meager chances of realizing that return.
Expected Rate Of Return Versus Required Rate Of Return
The required rate of return (RROR) is a concept in corporate finance. It’s the amount of money, or the proportion of money received back from money invested, that a project needs to generate to be worth the investment. This is important to investors because it tells the relationship between the risk of an investment and the potential profitability or return from it. There are different ways to calculate the RROR; let us briefly discuss two methods here.
The Dividend-Discount Model
The dividend-discount model can be used for stocks that pay out high dividends and have a steady growth. In this model, you get the stock’s value by dividing expected annual dividends by the required rate of return minus the dividend growth rate. By moving around the terms, you can find the required rate of return by dividing the dividend payments by the stock price and adding the growth of dividends.
For example, if you have a stock paying $2 in dividends per year and is worth $30 and the dividends are growing at 5% a year, you have a required rate of return of:
$2/30 + .05,
.066 + .05
For a required rate of return of 11.67%
Capital Asset Pricing Model
A more complex way of calculating the required rate of return is known as the capital asset pricing model.
In this model, the required rate of return is equal to the “risk-free rate” plus what’s known as “beta” (the stock’s volatility, or its price change, compared to the market), which is then multiplied by the market rate of return minus the risk-free rate.
Here is a sample calculation from Social Finance Inc. (SoFi). We can take the yield on 10-year Treasuries for the risk-free rate, which is about 1% or .01, a beta of 1.5, and the market rate of return of 5% or .05.
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%
Risk And Return Characteristics
Risk and return characteristics go hand in hand in assessing a potential investment. Return on investment, rate of return, expected rate of return and the real rate of return are the most common metrics used in assessing potential investments. Once you have done your research on these, you will hopefully feel more confident investing or building your investment portfolio. Another essential technique that investors use to mitigate risk is diversification. The adage of not putting all your eggs in one basket is true in investments.
Diversification is the process of buying assets that are hopefully non-correlated. The performance of one is not necessarily related to the understanding 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. Whatever combination of investment vehicles, always bear in mind the risks associated with them.
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