What Is an Abnormal Return?

An abnormal return describes the unusually large profits or losses generated by a given investment or portfolio over a specified period. The performance diverges from the investments’ expected, or anticipated, rate of return (RoR)—the estimated risk-adjusted return based on an asset pricing model, or using a long-run historical average or multiple valuation techniques.

Returns that are abnormal may simply be anomalous or they may point to something more nefarious such as fraud or manipulation. Abnormal returns should not be confused with “alpha” or excess returns earned by actively managed investments.

Understanding Abnormal Returns

Abnormal returns are essential in determining a security or portfolio’s risk-adjusted performance when compared to the overall market or a benchmark index. Abnormal returns could help to identify a portfolio manager’s skill on a risk-adjusted basis. It will also illustrate whether investors received adequate compensation for the amount of investment risk assumed.

An abnormal return can be either positive or negative. The figure is merely a summary of how the actual returns differ from the predicted yield. For example, earning 30% in a mutual fund that is expected to average 10% per year would create a positive abnormal return of 20%. If, on the other hand, in this same example, the actual return was 5%, this would generate a negative abnormal return of 5%.

Cumulative Abnormal Return (CAR)

Cumulative abnormal return (CAR) is the total of all abnormal returns. Usually, the calculation of cumulative abnormal return happens over a small window of time, often only days. This short duration is because evidence has shown that compounding daily abnormal returns can create bias in the results.

Cumulative abnormal return (CAR) is used to measure the effect lawsuits, buyouts, and other events have on stock prices and is also useful for determining the accuracy of asset pricing models in predicting the expected performance.

The capital asset pricing model (CAPM) is a framework used to calculate a security or portfolio’s expected return based on the risk-free rate of return, beta, and the expected market return. After the calculation of a security or portfolio’s expected return, the estimate for the abnormal return is calculated by subtracting the expected return from the realized return.

Example of Abnormal Returns

An investor holds a portfolio of securities and wishes to calculate the portfolio’s abnormal return during the previous year. Assume that the risk-free rate of return is 2% and the benchmark index has an expected return of 15%.

The investor’s portfolio returned 25% and had a beta of 1.25 when measured against the benchmark index. Therefore, given the amount of risk assumed, the portfolio should have returned 18.25%, or (2% + 1.25 x (15% – 2%)). Consequently, the abnormal return during the previous year was 6.75% or 25 – 18.25%.

The same calculations can be helpful for a stock holding. For example, stock ABC returned 9% and had a beta of 2, when measured against its benchmark index. Consider that the risk-free rate of return is 5% and the benchmark index has an expected return of 12%. Based on the CAPM, stock ABC has an expected return of 19%. Therefore, stock ABC had an abnormal return of -10% and underperformed the market during this period.

What Is the Average Annual Return (AAR)?

The average annual return (AAR) is a percentage used when reporting the historical return, such as the three-, five-, and 10-year average returns of a mutual fund. The average annual return is stated net of a fund’s operating expense ratio. Additionally, it does not include sales charges, if applicable, or portfolio transaction brokerage commissions.

In its simplest terms, the average annual return (AAR) measures the money made or lost by a mutual fund over a given period. Investors considering a mutual fund investment will often review the AAR and compare it with other similar mutual funds as part of their mutual fund investment strategy.

Understanding the Average Annual Return (AAR)

When you are selecting a mutual fund, the average annual return is a helpful guide for measuring a fund’s long-term performance. However, investors should also look at a fund’s yearly performance to fully appreciate the consistency of its annual total returns.

For example, a five-year average annual return of 10% looks attractive. However, if the yearly returns (those that produced the average annual return) were +40%, +30%, -10%, +5% and -15% (50 / 5 = 10%), performance over the past three years warrants examination of the fund’s management and investment strategy.

Components of an Average Annual Return (AAR)

There are three components that contribute to the average annual return (AAR) of an equity mutual fund: share price appreciation, capital gains, and dividends.

Share Price Appreciation

Share price appreciation results from unrealized gains or losses in the underlying stocks held in a portfolio. As the share price of a stock fluctuates over a year, it proportionately contributes to or detracts from the AAR of the fund that maintains a holding in the issue.

For example, the American Funds AMCAP Fund’s top holding is Netflix (NFLX), which represents 3.7% of the portfolio’s net assets as of Feb. 29, 2020. Netflix is one of 199 equities in the AMCAP fund. Fund managers can add or subtract assets from the fund or change the proportions of each holding as needed to meet the fund’s performance objectives. The fund’s combined assets have contributed to the portfolio’s 10-year AAR of 11.58% through Feb. 29, 2020.

Capital Gains Distributions

Capital gains distributions paid from a mutual fund result from the generation of income or sale of stocks from which a manager realizes a profit in a growth portfolio. Shareholders can opt to receive the distributions in cash or reinvest them in the fund. Capital gains are the realized portion of AAR. The distribution, which reduces share price by the dollar amount paid out, represents a taxable gain for shareholders.

A fund can have a negative AAR and still make taxable distributions. The Wells Fargo Discovery Fund paid a capital gain of $2.59 on Dec. 11, 2015, despite the fund having an AAR of negative 1.48%.

Dividends

Quarterly dividends paid from company earnings contribute to a mutual fund’s AAR and also reduce the value of a portfolio’s net asset value (NAV). Like capital gains, dividend income received from the portfolio can be reinvested or taken in cash.

Large-cap stock funds with positive earnings typically pay dividends to individual and institutional shareholders. These quarterly distributions comprise the dividend yield component of a mutual fund’s AAR. The T. Rowe Price Dividend Growth Fund has a trailing 12-month yield of 1.36%, a contributing factor to the fund’s three-year AAR of 15.65% through Feb. 29, 2020.

Special Considerations

Calculating an average annual return is much simpler than the average annual rate of return, which uses a geometric average instead of a regular mean. The formula is: [(1+r₁) x (1+r₂) x (1+r₃) x … x (1+r_i)] ^(1/n) – 1, where r is the annual rate of return and n is the number of years in the period.

The average annual return is sometimes considered less useful for giving a picture of the performance of a fund because returns compound rather than combine. Investors must pay attention when looking at mutual funds to compare the same types of returns for each fund. 

What Is Average Annual Growth Rate (AAGR)?

The average annual growth rate (AAGR) reports the mean increase in the value of an individual investment, portfolio, asset, or cash flow on an annualized basis. It doesn’t take compounding into account.

Formula for Average Annual Growth Rate (AAGR)

$\begin{aligned} &AAGR = \frac{GR_A + GR_B + \dotso + GR_n}{N} \\ &\textbf{where:}\\ &GR_A=\text{Growth rate in period A}\\ &GR_B=\text{Growth rate in period B}\\ &GR_n=\text{Growth rate in period }n\\ &N=\text{Number of payments}\\ \end{aligned}$​AAGR=NGRA​+GRB​+…+GRn​​where:GRA​=Growth rate in period AGRB​=Growth rate in period BGRn​=Growth rate in period nN=Number of payments​

Understanding the Average Annual Growth Rate (AAGR)

The average annual growth rate helps determine long-term trends. It applies to almost any kind of financial measure including growth rates of profits, revenue, cash flow, expenses, etc. to provide the investors with an idea about the direction wherein the company is headed. The ratio tells you your average annual return.

The average annual growth rate is a calculation of the arithmetic mean of a series of growth rates. AAGR can be calculated for any investment, but it will not include any measure of the investment’s overall risk, as measured by its price volatility. Furthermore, the AAGR does not account for periodic compounding.

AAGR is a standard for measuring average returns of investments over several time periods on an annualized basis. You’ll find this figure on brokerage statements and in a mutual fund’s prospectus. It is essentially the simple average of a series of periodic return growth rates.

One thing to keep in mind is that the periods used should all be of equal length—for instance, years, months, or weeks—and not to mix periods of different duration.

AAGR Example

The AAGR measures the average rate of return or growth over a series of equally spaced time periods. As an example, assume an investment has the following values over the course of four years:

• Beginning value = $100,000
• End of year 1 value = $120,000
• End of year 2 value = $135,000
• End of year 3 value = $160,000
• End of year 4 value = $200,000

The formula to determine the percentage growth for each year is:

$\text{Simple percentage growth or return} = \frac{\text{ending value}}{\text{beginning value}} – 1$Simple percentage growth or return=beginning valueending value​−1

Thus, the growth rates for each of the years are as follows:

• Year 1 growth = $120,000 / $100,000 – 1 = 20%
• Year 2 growth = $135,000 / $120,000 – 1 = 12.5%
• Year 3 growth = $160,000 / $135,000 – 1 = 18.5%
• Year 4 growth = $200,000 / $160,000 – 1 = 25%

The AAGR is calculated as the sum of each year’s growth rate divided by the number of years:

$AAGR = \frac{20 \% + 12.5 \% + 18.5 \% + 25 \%}{4} = 19\%$AAGR=420%+12.5%+18.5%+25%​=19%

In financial and accounting settings, the beginning and ending prices are usually used. Some analysts may prefer to use average prices when calculating the AAGR depending on what is being analyzed.

As another example, consider the five-year real gross domestic product (GDP) growth for the United States over the last five years. The U.S. real GDP growth rates for 2017 through 2021 were 2.3%, 2.9%, 2.3%, -3.4%, and 5.7%, respectively. Thus, the AAGR of U.S. real GDP over the last five years has been 1.96%, or (2.3% + 2.9% + 2.3% + -3.4% + 5.7%) / 5.

AAGR vs. Compound Annual Growth Rate

AAGR is a linear measure that does not account for the effects of compounding. The above example shows that the investment grew an average of 19% per year. The average annual growth rate is useful for showing trends; however, it can be misleading to analysts because it does not accurately depict changing financials. In some instances, it can overestimate the growth of an investment.

For example, consider an end-of-year value for year 5 of $100,000 for the AAGR example above. The percentage growth rate for year 5 is -50%. The resulting AAGR would be 5.2%; however, it is evident from the beginning value of year 1 and the ending value of year 5, the performance yields a 0% return. Depending on the situation, it may be more useful to calculate the compound annual growth rate (CAGR).

The CAGR smooths out an investment’s returns or diminishes the effect of the volatility of periodic returns. 

Formula for CAGR

$CAGR = \frac{\text{Ending Balance}}{\text{Beginning Balance}}^{\frac{1}{\text{\# Years}}} – 1$CAGR=Beginning BalanceEnding Balance​# Years1​−1

Using the above example for years 1 through 4, the CAGR equals:

$CAGR = \frac{\$200,000}{\$100,000}^{\frac{1}{4}}- 1 = 18.92\%$CAGR=$100,000$200,000​41​−1=18.92%

For the first four years, the AAGR and CAGR are close to one another. However, if year 5 were to be factored into the CAGR equation (-50%), the result would end up being 0%, which sharply contrasts the result from the AAGR of 5.2%.

Limitations of the AAGR

Because AAGR is a simple average of periodic annual returns, the measure does not include any measure of the overall risk involved in the investment, as calculated by the volatility of its price. For instance, if a portfolio grows by a net of 15% one year and 25% in the next year, the average annual growth rate would be calculated to be 20%.

To this end, the fluctuations occurring in the investment’s return rate between the beginning of the first year and the end of the year are not counted in the calculations thus leading to some errors in the measurement.

A second issue is that as a simple average it does not care about the timing of returns. For instance, in our example above, a stark 50% decline in year 5 only has a modest impact on total average annual growth. However, timing is important, and so CAGR may be more useful in understanding how time-chained rates of growth matter.

What is Activity-Based Budgeting (ABB)?

Activity-based budgeting (ABB) is a system that records, researches, and analyzes activities that lead to costs for a company. Every activity in an organization that incurs a cost is scrutinized for potential ways to create efficiencies. Budgets are then developed based on these results.

Activity-based budgeting (ABB) is more rigorous than traditional budgeting processes, which tend to merely adjust previous budgets to account for inflation or business development.

How Activity-Based Budgeting (ABB) Works

Keeping costs to a minimum is a crucial part of business management. When done effectively and not too excessively, companies should be able to maintain and keep growing their revenues, while squeezing out higher profits from them.

Using activity-based budgeting (ABB) can help companies to reduce the activity levels required to generate sales. Eliminating unnecessary costs should boost profitability.

The activity-based budgeting (ABB) process is broken down into three steps.

1. Identify relevant activities. These cost drivers are the items responsible for incurring revenue or expenses for the company.
2. Determine the number of units related to each activity. This number is the baseline for calculations.
3. Delineate the cost per unit of activity and multiply that result by the activity level.

Activity-Based Budgeting (ABB) Vs. Traditional Budgeting Processes

Activity-based budgeting (ABB) is an alternative budgeting practice. Traditional methods are more simplistic, adjusting prior period budgets to account for inflation or revenue growth. Rather than using past budgets to calculate how much a firm will spend in the current year, activity-based budgeting (ABB) digs deeper.

Activity-based budgeting (ABB) is not necessary for all companies. For example, established firms that experience minimal change typically find that applying a flat rate to data from the previous year to reflect business growth and inflation is sufficient.

In contrast, newer companies without access to historical budgeting information cannot consider this an option. Activity-based budgeting (ABB) is also likely to be implemented by firms undergoing material changes, such as those with new subsidiaries, significant customers, business locations, or products. In these types of cases, historical information may no longer be a useful basis for future budgeting.

Example of Activity-Based Budgeting

Company A anticipates receiving 50,000 sales orders in the upcoming year, with each single order costing $2 to process. Therefore, the activity-based budget (ABB) for the expenses relating to processing sales orders for the upcoming year is $100,000 ($50,000 * $2). 

This figure may be compared to a traditional approach to budgeting. If last year’s budget called for $80,000 of sales order processing expenses and sales were expected to grow 10%, only $88,000 ($80,000 + ($80,000 * 10%)) is budgeted.

Advantages and Disadvantages of Activity-Based Budgeting

Activity-based budgeting (ABB) systems allow for more control over the budgeting process. Revenue and expense planning occurs at a precise level that provides useful details regarding projections. ABB allows for management to have increased control over the budgeting process and to align the budget with overall company goals.

Unfortunately, these benefits come at a cost. Activity-based budgeting (ABB) is more expensive to implement and maintain than traditional budgeting techniques and more time consuming as well. Moreover, ABB systems need additional assumptions and insight from management, which can, on occasion, result in potential budgeting inaccuracies.