# How to calculate annualized portfolio return

Last Updated: December 19, 2020 References

This article was co-authored by Jonathan DeYoe, CPWA®, AIF®. Jonathan DeYoe is a Financial Advisor and the CEO of Mindful Money, a comprehensive financial planning and retirement income planning service based in Berkeley, California. With over 25 years of financial advising experience, Jonathan is a speaker and the best-selling author of “Mindful Money: Simple Practices for Reaching Your Financial Goals and Increasing Your Happiness Dividend.” Jonathan holds a BA in Philosophy and Religious Studies from Montana State University-Bozeman. He studied Financial Analysis at the CFA Institute and earned his Certified Private Wealth Advisor (CPWA®) designation from The Investments & Wealth Institute. He also earned his Accredited Investment Fiduciary (AIF®) credential from Fi360. Jonathan has been featured in the New York Times, the Wall Street Journal, Money Tips, Mindful Magazine, and Business Insider among others.

There are 14 references cited in this article, which can be found at the bottom of the page.

If you want to find out how much you’re earning on your investments, you likely know that you can subtract the starting value from the ending value. If you then divide that number by the starting value and multiply by 100, you have the basic rate of return. But what if you’ve had your portfolio for several years? Your portfolio is (hopefully) growing every year, compounding your returns. If you want to compare your portfolio’s performance with someone else’s, the annualized portfolio return gives you the best way to do this. There are 2 different ways to calculate your annualized portfolio return. Your choice depends on whether you want to control for the effect that your contributions and withdrawals have on your portfolio’s performance. [1] X Research source

## What Is The Yearly Rate Of Return Method?

The yearly rate of return method, commonly referred to as the annual percentage rate, is the amount earned on a fund throughout an entire year. The yearly rate of return is calculated by taking the amount of money gained or lost at the end of the year and dividing it by the initial investment at the beginning of the year. This method is also referred to as the annual rate of return or the nominal annual rate.

### Key Takeaways

• Yearly rate of return is computed by looking at the value of an investment at the end of one year and comparing it to the value to the beginning of the year.
• The rate of return for a stock includes capital appreciation and any dividends paid.
• A disadvantage of the yearly rate of return is that it only includes one year and does not consider the potential for compounding over many years.

## Example of Yearly Rate of Return Method Calculation

If a stock begins the year at $25.00 per share and ends the year with a market price of$45.00 a share, this stock would have an annual, or yearly, rate of return of 80.00%. First, we subtract the end of year price from the beginning price, which equals 45 – 25, or 20. Next, we divide by the beginning price, or 20/25 equals .80. Lastly, to arrive at a percentage, .80 is multiplied by 100 in order to arrive at a percentage and the rate of return 80.00%.

It should be noted that this would technically be called capital appreciation, which is only one source of an equity security’s return. The other component would be any dividend yield. For instance, if the stock in the earlier example paid $2 in dividends, the rate of return would be$2 greater or, using the same calculation, roughly 88.00% over the one-year period.

As a measure of return, the yearly rate of return is rather limiting because it delivers only a percentage increase over a single, one-year period. By not taking into consideration the potential effects of compounding over many years, it’s limited by not including a growth component. But as a single period rate, it does serve its purpose.

## Other Return Measures

Other common return measures, which may be an extension of the basic return method, include adjusting for discrete or continuous time periods, which is helpful for more accurate compounding calculations over longer time periods and in certain financial market applications.

Asset managers commonly use money-weighted and time-weighted rates of return to measure performance or the rate of return on an investment portfolio. While money-weighted rates of return focus on cash flows, the time-weighted rate of return looks at the compound rate of growth of the portfolio.

In an effort to be more transparent with investors, particularly retail, measuring and disseminating investment performance has become its niche within capital markets. The CFA Institute, a worldwide leader in the advancement of financial analysis, now offers a professional Certificate in Investment Performance Measurement (CIPM) designation.

According to the CIPM Association, the CIPM program was developed by the CFA Institute as a specialty credentialing program that develops and recognizes the performance evaluation and presentation expertise of investment professionals who “pursue excellence with a passion.”

This Stock Investment Calculator will calculate the expected rate of return given a stock’s current dividend, the current price per share, and the expected growth rate.

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### What ERR is, how it’s calculated, and what it’s useful for.

#### What is ERR?

In the case of stocks, expected rate of return (ERR) is a formula used to forecast the future return on investment from a stock purchase — which includes income from both equity and dividend growth.

#### How to Calculate Expected Return of a Stock

To calculate the ERR, you first add 1 to the decimal equivalent of the expected growth rate (R) and then multiply that result by the current dividend per share (DPS) to arrive at the future dividend per share. You then divide the future dividend by the current price per share (PPS) and then add the decimal equivalent of the expected growth rate to get the ERR.

For example, if a stock had a dividend of $1.50, a price per share of$60.00, and an expected growth rate of 10%, then the expected rate of return would be 12.75%, computed as follows:

Please note that the ERR formula is based on the dividend growth model, which assumes that dividends will be paid and that both the dividends and the company will grow at a constant rate. Of course, neither of these assumptions will likely hold true in the real world.

#### What is Expected Rate of Return Useful For?

Since ERR is based on assumptions that rarely hold true, most investors use ERR to compare the potential returns of one stock investment with another. After all, the growth rate figure used in the ERR formula does account for the actual historical growth of a company’s earnings per share. Therefore, using ERR to compare potential returns of investing in one company over another makes more sense (at least to me) than using a high expected rate of return as the sole reason for buying shares in a particular stock.

The bottom line is, all methods of forecasting the potential return on investing in stocks are simply methods of making educated guesses. Sure, the better your educated guesses, the more you increase the odds that you will achieve a fair return for the risks you are taking. But there is no way to guarantee that some unforeseen event won’t cause you to lose your principal in a short period of time.

Measuring the return you receive from an investment over the course of a year can help you make strategic and educated investment decisions both in your business and personal life. In this article, we explain how to calculate an annualized return with examples, and how it differs from average return.

## What is annualized return?

Annualized return, also called annual return or annualized total return, is the geometric average of an investment’s earnings in a year. This formula determines the return rate on the principle that has been invested and does not account for any available cash or committed cash. The annualized return can also show an investor what they would earn if the annual return was compounded over a period of time. It’s important to note that this calculation will not show an investor any potential price fluctuations or negative change or volatility of an investment.

Because analyzing an investment’s return rate over a single year isn’t always the best indicator of its value, many investors calculate an investment’s annualized return over several years. This can be done by calculating each year’s return rate or by grouping longer periods of time when calculating the annualized return of an investment. Using the information derived from the annualized return formula, an investor can then determine how effective an investment has been by comparing their return to that of similar investments.

## How to calculate annualized return

The following is the formula for calculating the annualized return of an investment:

(1 + Return) ^ (1 / N) – 1 = Annualized Return

N = number of periods measured

To accurately calculate the annualized return, you will first have to determine the overall return of an investment. The formula for the overall return is (ending value – beginning value) / beginning value. In this formula, the beginning value is what your portfolio was worth when you invested, or how much you put into an investment. The ending value is how much your portfolio is worth at the end of the period that you are trying to calculate the annualized return for.

Once you have the overall return, you can then calculate the annualized return. In the annualized return formula, the “1” that is divided by “N” in the exponent represents the unit that is being measured, e.g. one year. You can also use “365” instead of “1” to calculate the daily return of an investment. The “N” in this formula represents the number of periods that are being measured. For example, if you want to calculate the annualized return of an investment over a period of five years, you would use “5” for the “N” value.

An example calculation of an annualized return is as follows:

(1 + 2.5) ^ 1/5 – 1 = 0.28
In this case, the annualized return for this investment would be 28% over a period of five years.

## Annualized return vs. average return

While an annualized return and an average return may seem similar at first, there are key differences between these two calculations. Understanding these differences and the benefits of these two calculations can help you decide which formula to use when analyzing your investments.

An annualized return, which may also be referred to as the “geometric average,” is the annual rate of return on an investment that analyzes how much is lost or gained in a time period with consideration of compounding. This calculation is beneficial because it accounts for the interdependency of the return rate of a year on previous years’ return rates. It can also provide a better idea of various stocks that have been traded over several periods of time and assist in making investment-related decisions.

On the other hand, average returns, which may also be referred to as simple average returns or mean return, is the process of adding all of the annual returns together and then dividing the total by the number of years that the investment is being analyzed for. This formula does not take into account compounding or allow for the comparison of mutual funds or stocks.

## How to report annualized return

When reporting the annualized return of a particular investment, there are a few principles that must be adhered to as set forth by the Global Investment Performance Standards (GIPS). The primary principle that must be abided by is that an investment cannot report its performance to be annualized if it has not been in existence for less than one year.

So, for example, if a fund has been in operation for only two months and has earned 6%, it cannot report an annualized performance of 48%. This principle is meant to keep funds from reporting a predicted performance instead of reporting facts.

## Example of calculating annualized return

The following is an example of calculating the annualized return of an investment:

An investor has a portfolio with a beginning value of $2,000 and an ending value of$5,000 over a five-year time period. To calculate the total return rate (which is needed to calculate the annualized return), the investor will perform the following formula: (ending value – beginning value) / beginning value, or (5000 – 2000) / 2000 = 1.5. This gives the investor a total return rate of 1.5.

Next, the investor will perform the annualized return formula: (1 + Return) ^ (1 / N) – 1. Using the information given, this gives the investor the following formula to calculate: (1 + 1.5) ^ (1 / 5) – 1. The following are the calculations used to get the answer to this formula:

2.5 ^ (1 / 5 or .2) = 1.2

1.2 – 1 = .20 or 20%

Conclusion: The investor’s portfolio has an annualized return of 20% over a period of five years in which the beginning value was $2,000 and the ending value is$5,000.

The main point of investing is to make money. Although you can’t predict how your investment portfolio will do, there are different metrics that can help you determine how far your money may go. One of those is called the return on investment (ROI), which can measure an investment’s success. This is an important metric for any investor because It directly measures the return on that investment relative to its cost.

To calculate the ROI, divide the cost of the investment by its return. Although it’s not a perfect science, this is a crude gauge of how effective an investment performs relative to an entire portfolio. But what if you want to know how well your that portfolio will do? Read on to learn how you can calculate its returns.

### Key Takeaways

• To calculate your investment returns, gather the total cost of your investments and the average historical return, and define the time period for which you want to calculate your returns.
• You can use the holding period return to compare returns on investments held for different periods of time.
• You’ll have to adjust for cash flows if money was deposited or withdrawn from your portfolio(s).
• Annualizing returns can make multi-period returns more comparable across other portfolios or potential investments.

## Calculating Returns for an Entire Portfolio

As mentioned above, there are uncertainties that come with investing, so you won’t necessarily be able to predict how much money you’ll make—or whether you’ll make any at all. After all, there are market forces at play that can impact the performance of any asset, including economic factors, political forces, market sentiment, and even corporate actions. But that doesn’t mean you shouldn’t work out the figures.

Working out the returns on individual investments can be a very exhaustive feat especially if you have your money spread across different investment vehicles that are maintained by a variety of different firms and institutions.

But before you calculate your investment returns, identify and gather the requisite data. You’ll need to know the following:

• The total cost of your investments including any fees and commissions
• The average return for all your investments

Once you have the data prepared, you’ll want to take a few things into consideration. The first thing is to define the time period over which you want to calculate returns—daily, weekly, monthly, quarterly, or annually. You need to strike a net asset value (NAV) of each position in each portfolio for the time periods and note any cash flows, if applicable.

Remember to define the time period for which you want to calculate your returns.

## Holding Period Return

Once you define your time periods and sum up the portfolio NAV, you can start making your calculations. The simplest way to calculate a basic return is called the holding period return.

Here’s the formula to calculate the holding period return:

• HPR = Income + (End of Period Value – Initial Value) ÷ Initial Value

This return/yield is a useful tool to compare returns on investments held for different periods of time. It simply calculates the percentage difference from period to period of the total portfolio NAV and includes income from dividends or interest. In essence, it’s the total return from holding a portfolio of assets—or a singular asset—over a specific period of time.

You will need to adjust for the timing and amount of cash flows if money was deposited or withdrawn from your portfolio(s). So if you deposited $100 in your account mid-month, the portfolio end-of-month NAV has an additional$100 that was not due to investment returns when you calculate a monthly return. This can be adjusted using various calculations, depending on the circumstances.

The modified Dietz method is a popular formula to adjust for cash flows. Using an internal rate of return (IRR) calculation with a financial calculator is also an effective way to adjust returns for cash flows. IRR is a discount rate that makes the net present value zero. It is used to measure the potential profitability of an investment.

## Annualizing Returns

A common practice is to annualize returns for multi-period returns. This is done to make the returns more comparable across other portfolios or potential investments. It allows for a common denominator when comparing returns.

An annualized return is a geometric average of the amount of money an investment earns each year. It shows what could have been earned over a period of time if the returns had been compounded. The annualized return does not give an indication of volatility experienced during the corresponding time period. That volatility can be better measured using standard deviation, which measures how data is dispersed relative to its mean.

## An Example of Calculating Portfolio Returns

The sum total of the positions in a brokerage account is $1,000 at the beginning of the year and$1,350 at the end of the year. There was a dividend paid on June 30. The account owner deposited $100 on March 31. The return for the year is 16.3% after adjusting for the$100 cash flow into the portfolio one-quarter of the way through the year.

James Chen, CMT, is the former director of investing and trading content at Investopedia. He is an expert trader, investment adviser, and global market strategist.

Gordon Scott has been an active investor and technical analyst of securities, futures, forex, and penny stocks for 20+ years. He is a member of the Investopedia Financial Review Board and the co-author of Investing to Win. Gordon is a Chartered Market Technician (CMT). He is also a member of ASTD, ISPI, STC, and MTA.

## What Is Annualized Total Return?

An annualized total return is the geometric average amount of money earned by an investment each year over a given time period. The annualized return formula is calculated as a geometric average to show what an investor would earn over a period of time if the annual return was compounded. An annualized total return provides only a snapshot of an investment’s performance and does not give investors any indication of its volatility or price fluctuations.

## Understanding Annualized Total Return

To understand annualized total return, we’ll compare the hypothetical performances of two mutual funds. Below is the annualized rate of return over a five-year period for the two funds:

Mutual Fund A Returns: 3%, 7%, 5%, 12% and 1%

Mutual Fund B Returns: 4%, 6%, 5%, 6%, and 6.7%

Both mutual funds have an annualized rate of return of 5.5%, but Mutual Fund A is much more volatile. Its standard deviation is 4.2%, while Mutual Fund B’s standard deviation is only 1%. Even when analyzing an investment’s annualized return, it is important to review risk statistics.

## Annualized Return Formula and Calculation

The formula to calculate annualized rate of return needs only two variables: the returns for a given period of time and the time the investment was held. The formula is:

For example, take the annual rates of returns of Mutual Fund A above. An analyst substitutes each of the “r” variables with the appropriate return, and “n” with the number of years the investment was held. In this case, five years. The annualized return of Mutual Fund A is calculated as:

An annualized return does not have to be limited to yearly returns. If an investor has a cumulative return for a given period, even if it is a specific number of days, an annualized performance figure can be calculated; however, the annual return formula must be slightly adjusted to:

For example, assume a mutual fund was held by an investor for 575 days and earned a cumulative return of 23.74%. The annualized rate of return would be:

### Key Takeaways

• An annualized total return is the geometric average amount of money earned by an investment each year over a given time period.
• The annualized return formula shows what an investor would earn over a period of time if the annual return was compounded.
• Calculating annualized rate of return needs only two variables: the returns for a given period and the time the investment was held.

## Difference Between Annualized Return and Average Return

Calculations of simple averages only work when numbers are independent of each other. The annualized return is used because the amount of investment lost or gained in a given year is interdependent with the amount from the other years under consideration because of compounding. For example, if a mutual fund manager loses half of her client’s money, she has to make a 100% return to break even. Using the more accurate annualized return also gives a clearer picture when comparing various mutual funds or the return of stocks that have traded over different time periods.

## Reporting Annualized Return

According to the Global Investment Performance Standards (GIPS), a set of standardized, industry-wide principles that guide the ethics of performance reporting, any investment that does not have a track record of at least 365 days cannot “ratchet up” its performance to be annualized. Thus, if a fund has been operating for only six months and earned 5%, it is not allowed to say its annualized performance is approximately 10% since that is predicting future performance instead of stating facts from the past. In other words, calculating an annualized rate of return must be based on historical numbers.

### What is an Annualized Total Return?

An annualized total return is a metric that captures the average annual performance of an investment or portfolio of investments. It is calculated as a geometric average, meaning that it captures the effects of compounding over time. The annualized total return is sometimes referred to as the Compound Annual Growth Rate (CAGR).

### What is the difference between an Annualized Total Return and an Average Return?

The key difference between the Annualized Total Return and the Average Return is that the Annualized Total Return captures the effects of compounding, whereas the Average Return does not. For example, consider the case of an investment that loses 50% of its value in year 1, but has a 100% return in year 2. Simply averaging these two percentages would give you an Average Return of 25% per year. However, common sense would tell you that the investor in this scenario has actually broken even on their money (losing half its value in year one, then regaining that loss in year 2). This fact would be better captured by the Annualized Total Return, which would be 0.00% in this instance.

### What is the difference between the Annualized Total Return and the Compound Annual Growth Rate (CAGR)

The Annualized Total Return is conceptually the same as the CAGR, in that both formulas seek to capture the geometric return of an investment over time. The main difference between them is that the CAGR is often presented using only the beginning and ending values, whereas the Annualized Total Return is typically calculated using the returns from several years. This, however, is more a matter of convention. In substance, the two measures are the same.

I understand how to calculate the Annualized return on a stock when I have single purchase ie

but how is it calculated when I have multiple buys and sells over a time period?

Treat each transaction as separate, with its own principal, its own gain, and its own number of days. Then the total annualized return is just a weighted average of each annualized return, with the weighting related to the number of shares in that transaction.

The best way to do this is to use IRR. It’s a complicated calculation, but will take into account multiple in/out cash flows over time along with “idle periods” where your money may not have been doing anything. Excel can calculate it for you using the XIRR function

Since Brad answered with a great reply, I’d like to offer another comment: Be careful with the results. Annualized returns of short term trading can produce some crazy results. For example, a 10% gain in a week isn’t unheard of for individual stocks, but (1.1)^52 = 142. or a 14,100% return. This may be obvious, but may help those who aren’t so familiar with the numbers to understand that data running less than a year isn’t going to provide as much useful conclusion as longer term. Note: Even a year doesn’t really reflect success in a given strategy.

## Friday, January 29, 2021

### How to Calculate Annualized Portfolio Return

If you want to find out how much you’re earning on your investments, you likely know that you can subtract the starting value from the ending value. If you then divide that number by the starting value and multiply by 100, you have the basic rate of return. But what if you’ve had your portfolio for several years? Your portfolio is (hopefully) growing every year, compounding your returns. If you want to compare your portfolio’s performance with someone else’s, the annualized portfolio return gives you the best way to do this. There are 2 different ways to calculate your annualized portfolio return. Your choice depends on whether you want to control for the effect that your contributions and withdrawals have on your portfolio’s performance. [1]

## [ Edit ] Steps

### [ Edit ] Time-Weighted Rate of Return

This calculation shows you a rate of return that ignores investor behavior (deposits and withdrawals), making it the best way to compare the performance of investment managers and brokers.

Find the difference between the beginning and ending values for each year. Subtract the value of the portfolio at the end of the year from the value of the portfolio at the beginning of the year, then divide that number by the value at the beginning of the year. This is your simple, or basic, rate of return. Multiply by 100 to find the percentage. [2]

• For example, if the beginning value of your portfolio was $100,000 and your ending value was$105,000, your simple rate of return for that year would be 5%: ( 105 , 000 − 100 , 000 ) 100 , 000 = 0.05 x 100 = 5 % <\displaystyle <\frac <(105,000-100,000)><100,000>>=0.05×100=5\%>
• If you earned any dividends, include those in your ending value. In the previous example, if you’d also earned $50 in dividends, your ending value would be$105,050.
• Add 1 to each rate and multiply them together. Start by adding 1 to each basic rate of return you’ve calculated for each year. Then, multiply those figures together to calculate the return for the entire time frame. This incorporates the way the value of your portfolio builds on itself, or compounds over time. [3]

• For example, suppose you’ve had your portfolio for 4 years and your simple rates of return are 5% (0.05), 7% (0.07), 2% (0.02), and 4% (0.04). Your total return would be 1.19 (rounded): ( 1 + 0.05 ) x ( 1 + 0.07 ) x ( 1 + 0.02 ) x ( 1 + 0.04 ) = 1.1918 <\displaystyle (1+0.05)x(1+0.07)x(1+0.02)x(1+0.04)=1.1918>
• Raise the total rate by an exponent of 1/n. In the exponent position, “n” represents the number of years you included in your calculations. You’re trying to find the average for any 1 of those years, so the exponent is represented as a fraction of 1 over the number of years. [4]

• Continuing with the previous example, plug 1.1918 into your calculator and multiply by the exponent 1/4. Your answer should be 1.044.
• This calculation gets you a geometric average, which is simply an average of all the simple rates of return that also takes into account the compounding that occurs year after year. [5]
• Subtract 1 and multiply by 100 to get the annualized rate of return. Now that you have your geometric average, you need to turn it into a percentage. Subtract 1 (this takes care of the 1s you previously added to each yearly return) to get your decimal. Then, multiply 100 to get your percentage. [6]

• To continue with the example, your annualized rate would be 4.4%: ( 1.044 − 1 ) x 100 = 4.4 % <\displaystyle (1.044-1)x100=4.4\%>
• The full formula is ( ( ( 1 + R 1 ) x ( 1 + R 2 ) x ( 1 + R 3 ) x ( 1 + R 4 ) ) 1 n − 1 ) x 100 <\displaystyle (((1+R_<1>)x(1+R_<2>)x(1+R_<3>)x(1+R_<4>))^<\frac <1>>-1)x100>, where “R” is the rate of return for each investment period and “n” is the number of years.
• Use a different formula if you only have the initial and final values. To calculate the annualized portfolio return, divide the final value by the initial value, then raise that number by 1/n, where “n” is the number of years you held the investments. Then, subtract 1 and multiply by 100. [7]

• For example, suppose your portfolio’s initial value was $100,000 and the final value after 10 years is$150,000. Divide 150,000 by 100,000 to get 1.5. Then multiply 1.5 by the exponent of 1/10 to get 1.04. Subtract 1 to get 0.04, then multiply by 100. Your annualized rate of return is 4%: ( ( 150 , 000 / 100 , 000 ) 1 10 − 1 ) x 100 = 4 % <\displaystyle ((150,000/100,000)^<\frac <1><10>>-1)x100=4\%>
• The full formula is ( ( f i n a l v a l u e o f i n v e s t m e n t i n i t i a l v a l u e o f i n v e s t m e n t ) 1 n − 1 ) x 100 <\displaystyle ((<\frac >)^<\frac <1>>-1)x100>
• ### [ Edit ] Dollar-Weighted Rate of Return (IRR)

This calculation shows the impact your deposits and withdrawals have on your portfolio’s performance and is best used to compare your portfolio’s returns to another individual investor’s returns.

Enter your contributions or withdrawals in column A of a spreadsheet. Open a spreadsheet, then use column A to list each of your contributions or withdrawals to your portfolio, with your first value on row 1 (cell A1). Express withdrawals as negative numbers with a ( – ) in front of them. [8]

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