# Expected Return

Expected return represents the anticipated profit or loss on an investment. It's computed by multiplying potential outcomes by their probabilities and summing these products.
Expected Return
3 min
26-August-2024
The amount of profit or loss an investor might expect to get on an investment is known as the expected return. Multiplying possible possibilities by their likelihood of occurring and adding up the findings yields an expected return. Anticipated profits are not assured.

This article will explore the concept of expected return on investment, including expected return meaning, how it is calculated, its limitations, and how it is used in finance.

## What is the expected return?

The profit or loss that an investor expects from an investment with known historical rates of return (RoR) is known as the expected return. It is computed by adding up all of the possible outcomes after multiplying them by the likelihood that they will occur.

## Example of expected return

It is impossible to predict with certainty whether you will make money when you invest. A given investment's performance is influenced by numerous factors. An instrument for estimating the possible rate of return on a specific asset is expected return.

Calculating the probability of different probable outcomes based on previous rates of return is the process of determining the expected return of an asset. Put differently, what are your chances of making that investment profit if history repeats itself?

To obtain the overall expected return, add the probabilities of the various return scenarios that you have determined.

Assume, for instance, if a fund had a 25% chance of returning -3%, a 50% probability of returning 3%, and a 25% chance of returning 9%. Your expected return is 3% when the probabilities of each scenario are added together.

## Key takeaways

• The amount of profit or loss an investor might expect to get on an investment is known as the expected return.
• Multiplying possible possibilities by their likelihood of occurring and adding up the findings yields an expected return.
• Anticipated profits are not assured.
• The weighted average of each investment's expected return determines the expected return for a portfolio with several investments.

## Formula of expected return

The projected return of a financial investment can be expressed more formally as follows when examining individual investments or portfolios:

 ra = rf + βa (rm - rf )

where:

• ra = expected return
• rf = the risk-free rate of return
• β = the investment's beta
• rm =the expected market return
This formula basically says that the investment's beta, or relative volatility to the overall market, determines the expected return that is higher than the risk-free rate of return.

A portfolio can be examined using two statistical measures: the standard deviation and the expected return. The mean (average) of a portfolio's potential return distribution is its expected return, which is the amount of returns that the portfolio is predicted to earn. On the other hand, a portfolio's standard deviation serves as a stand-in for the risk of the portfolio by indicating how far the returns depart from the mean.

## How to calculate expected return?

### Step-by-step calculation

• Identify the Risk-Free Rate (rf): This is the return on a risk-free investment, such as a government bond.
• Determine the Investment's Beta (β): Beta measures the volatility of the investment relative to the market. A higher beta indicates higher volatility.
• Estimate the Expected Market Return (rm): This is the anticipated return of the overall market.
• Calculate the Expected Return (ra): Use the formula:
• ra = rf + βa (rm - rf )

### Example calculation

Suppose:

• rf = 2%
• β = 1.2
• rm = 8%
Using the formula:

ra=2%+1.2×(8%−2%)

ra=2%+1.2×(8%−2%)

ra=2%+1.2×6%

ra=2%+1.2×6%

ra=2%+7.2%

ra=2%+7.2%

ra=9.2%

ra=9.2%

In this example, the expected return of the investment is 9.2%.

## Benefits of expected return

• Aids in estimating the return on an investor's portfolio: Based on past performance, expected return on investment can be a helpful tool in estimating how much you can anticipate to make from your current investments.
• Can aid in directing the asset allocation of an investor: Expected return can be used not only to calculate a portfolio's future return but also to direct your investment choices. When selecting their investments, investors frequently take return into account. Making investment decisions may be made easier if you are aware of the predicted return for each asset.

## How is expected return used in finance?

A crucial component of financial theory and company operations, expected return computations are found in the well-known Black-Scholes options pricing model and modern portfolio theory (MPT) models. It's a tool for figuring out if the average net outcome of an investment is positive or negative. Though it might create fair expectations, the computation is typically based on historical data and cannot be guaranteed for future results.

## Alternatives to expected return

Though it's not the only tool available, you can use expected return on investment to assess a possible investment or your portfolio. Some of the holes left by the expected-return calculation can be filled in with the use of other tools.

• It's critical that investors utilising the expected-return calculation understand that it is not a guarantee of actual returns. The expected return on investment is predicated on past returns; however, past performance may not imply future results. When choosing an asset or portfolio to invest in, you should consider other factors outside just the predicted return.
• The predicted return of a specific investment does not take the degree of risk associated with it into account. Returns on high-risk investments are frequently extraordinary, ranging from extremely good to extremely terrible. It is not clear from examining the predicted return. If you were to compare two investments with significantly different risk profiles, the difference in risk would not be noticeable.

## Expected return vs. standard deviation

The standard deviation, which gauges how much the return deviates from the average, is a useful tool for assessing the riskiness of an investment. A stock with a low standard deviation typically exhibits reasonably stable prices and returns that are in line with the average. A stock with a high standard deviation is likely to be very volatile. This implies that your returns could differ considerably from the average, either way.

The advantage of standard deviation is that it takes into account the risk involved in any investment, in contrast to expected return. The standard deviation quantifies the chance of obtaining the expected return, whereas the expected return is predicated on the mean average return for a certain asset.

Explore these related articles to deepen your understanding and make informed investment decisions:

## Expected return vs. Required rate of return

The lowest return you would accept for an investment to be worthwhile is known as the necessary rate of return. An investment's needed rate of return often rises as the amount of risk involved does. For instance, since bonds often carry less risk than stocks, investors are frequently willing to accept a lower return on their investment.

## Summary

The average return that an investment or portfolio of investments should provide over a specific time period is estimated by the term "expected return." Higher predicted returns are typically required of riskier assets or securities in order to offset the increased risk. The expected return is a projection based on past performance and other pertinent variables; it is not a promise. It is an essential component of many financial models, including the capital asset pricing model (CAPM) and modern portfolio theory (MPT), and it may be utilised by investors to evaluate various investment possibilities and make knowledgeable decisions about their portfolios.

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## Essential tools for all mutual fund investors

What is the mean of expected returns?
The mean return (also known as the expected return) represents the anticipated average or typical value of all the possible returns from an investment or portfolio. It is calculated by summing the products of each possible return and its corresponding probability, and then dividing by the total number of possible outcomes.

What is the expected return also known as?
The expected return is also known as the mean return. It is the anticipated average or typical value of all the possible returns from an investment or portfolio.

What is expected return used for?
Expected return is used to quantify the relationship between a portfolio's risk and its potential return. It helps investors understand how individual securities can impact the overall portfolio and make informed investment decisions.

Why is expected return important?
Expected return is important because it allows investors to estimate the potential profit or loss from an investment based on its historical performance. It helps them assess the risk-reward tradeoff and make informed investment decisions.

What is expected return formula with examples?
The expected return formula is: E(R) = ∑(Ri × Pi), where E(R) is the expected return, Ri is the possible return, and Pi is the probability of that return occurring.

Is expected return a risk?
No, expected return is not a risk. It is a measure of the average or typical return an investment or portfolio is expected to generate. Risk, on the other hand, is the uncertainty or variability of returns around the expected return.

What is present value of expected return?
The present value of expected return is the current value of the future expected returns from an investment, discounted at an appropriate rate to account for the time value of money. It is used to evaluate the attractiveness of an investment opportunity.

What are the different types of expected returns?
The main types of expected returns are:

• Historical expected return: based on an investment's past performance
• Forward-looking expected return: based on projected future performance
• Required return: the minimum return an investor demands to invest in an asset
• Market expected return: the expected return of the overall market or a specific asset class.

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