What Is the After-Tax Real Rate of Return?

The after-tax real rate of return is the actual financial benefit of an investment after accounting for the effects of inflation and taxes. It is a more accurate measure of an investor’s net earnings after income taxes have been paid and the rate of inflation has been adjusted for. Both of these factors must be accounted for because they impact the gains an investor receives. This can be contrasted with the gross rate of return and the nominal rate of return of an investment.

Understanding the After-Tax Real Rate of Return

Over the course of a year, an investor might earn a nominal rate of return of 12% on his stock investment, but the real rate of return, the money he gets to put in his pocket at the end of the day, will be less than 12%. Inflation might have been 3% for the year, knocking his real rate of return down to 9%. And since he sold his stock at a profit, he will have to pay taxes on those profits, taking another, say 2%, off his return, for an after-tax real rate of return of 7%.

The commission he paid to buy and sell the stock also diminishes his return. Thus, in order to truly grow their nest eggs over time, investors must focus on the after-tax real rate of return, not the nominal return.

The after-tax real rate of return is a more accurate measure of investment earnings and usually differs significantly from an investment’s nominal (gross) rate of return, or its return before fees, inflation, and taxes. However, investments in tax-advantaged securities, such as municipal bonds and inflation-protected securities, such as Treasury inflation protected securities (TIPS), as well as investments held in tax-advantaged accounts, such as Roth IRAs, will show less discrepancy between nominal returns and after-tax real rates of return.

Example of the After-Tax Real Rate of Return

Let’s be more specific about how the after-tax real rate of return is determined. The return is calculated first of all by determining the after-tax return before inflation, which is calculated as Nominal Return x (1 – tax rate). For example, consider an investor whose nominal return on his equity investment is 17% and his applicable tax rate is 15%. His after-tax return is, therefore:
$0.17 \times (1 – 0.15) = 0.1445 = 14.45\%$0.17×(1−0.15)=0.1445=14.45%

Let’s assume that the inflation rate during this period is 2.5%. To calculate the real rate of return after tax, divide 1 plus the after-tax return by 1 plus the inflation rate, then subtract 1. Dividing by inflation reflects the fact that a dollar in hand today is worth more than a dollar in hand tomorrow. In other words, future dollars have less purchasing power than today’s dollars.

Following our example, the after-tax real rate of return is:

$\frac{(1 + 0.1445)}{(1 + 0.025)} – 1 = 1.1166 – 1 = 0.1166 = 11.66\%$(1+0.025)(1+0.1445)​−1=1.1166−1=0.1166=11.66%

That figure is quite a bit lower than the 17% gross return received on the investment. As long as the real rate of return after taxes is positive, however, an investor will be ahead of inflation. If it’s negative, the return will not be sufficient to sustain an investor’s standard of living in the future.

The Bottom Line

When you are assessing the value of your investments, it’s important to look at not just your nominal rate of return but also the after-tax real rate of return, which takes into account the taxes you’ll owe and inflation’s effect. The after-tax real rate of return can tell you if your nest egg investments will allow you to maintain your standard of living in the future.

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:


$\begin{aligned} \text{Annualized Return} = &\big ( (1 + r_1 ) \times (1 + r_2) \times (1 + r_3) \times \\ &\dots \times (1 + r_n) \big ) ^ \frac{1}{n} – 1 \\ \end{aligned}$Annualized Return=​((1+r1​)×(1+r2​)×(1+r3​)×⋯×(1+rn​))n1​−1​

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:


$\begin{aligned} \text{Annualized Return} &= \big ( (1 + .03) \times (1 + .07) \times (1 + .05) \times \\ &\quad \quad (1 + .12) \times (1 + .01) \big ) ^ \frac{1}{5} -1 \\ &= 1.309 ^ {0.20} – 1 \\ &= 1.0553 – 1 \\ &= .0553, \text{or } 5.53\% \\ \end{aligned}$Annualized Return​=((1+.03)×(1+.07)×(1+.05)×(1+.12)×(1+.01))51​−1=1.3090.20−1=1.0553−1=.0553,or 5.53%​

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:


$\begin{aligned} &\text{Annualized Return} = ( 1 + \text{Cumulative Return} ) ^ \frac {365}{ \text{Days Held} } – 1 \\ \end{aligned}$​Annualized Return=(1+Cumulative Return)Days Held365​−1​

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:


$\begin{aligned} \text{Annualized Return} &= ( 1 + .2374) ^ \frac{365}{575} – 1 \\ &= 1.145 – 1 \\ &= .145, \text{or } 14.5\% \\ \end{aligned}$Annualized Return​=(1+.2374)575365​−1=1.145−1=.145,or 14.5%​

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.

The Bottom Line

Annualized total return represents the geometric average amount that an investment has earned each year over a specific period. By calculating a geometric average, the annualized total return formula accounts for compounding when depicting the yearly earnings that the investment would generate over the holding period. While the metric provides a useful snapshot of an investment’s performance, it does not reveal volatility and price fluctuations.

What Is an Annual Return?

The annual return is the return that an investment provides over a period of time, expressed as a time-weighted annual percentage. Sources of returns can include dividends, returns of capital and capital appreciation. The rate of annual return is measured against the initial amount of the investment and represents a geometric mean rather than a simple arithmetic mean.

Understanding Annual Return

The de facto method for comparing the performance of investments with liquidity, an annual return can be calculated for various assets, which include stocks, bonds, funds, commodities and some types of derivatives. This process is a preferred method, considered to be more accurate than a simple return, as it includes adjustments for compounding interest. Different asset classes are considered to have different strata of annual returns.

Annual Returns on Stocks

Also known as an annualized return, the annual return expresses the stock’s increase in value over a designated period of time. In order to calculate an annual return, information regarding the current price of the stock and the price at which it was purchased are required. If any splits have occurred, the purchase price needs to be adjusted accordingly. Once the prices are determined, the simple return percentage is calculated first, with that figure ultimately being annualized. The simple return is just the current price minus the purchase price, divided by the purchase price.

Example Annual Return Calculation


$\begin{aligned} &\text{CAGR} = \left ( \left ( \frac{ \text{Ending Value} }{ \text{Beginning Value } } \right ) ^ \frac{ 1 }{ \text{Years} } \right ) – 1 \\ &\textbf{where:} \\ &\text{CAGR} = \text{compound annual growth rate} \\ &\text{Years} = \text{holding period, in years} \\ \end{aligned}$​CAGR=((Beginning Value Ending Value​)Years1​)−1where:CAGR=compound annual growth rateYears=holding period, in years​

Consider an investor that purchases a stock on Jan. 1, 2000, for $20. The investor then sells it on Jan. 1, 2005, for $35 – a $15 profit. The investor also receives a total of $2 in dividends over the five-year holding period. In this example, the investor’s total return over five years is $17, or (17/20) 85% of the initial investment. The annual return required to achieve 85% over five years follows the formula for the compound annual growth rate (CAGR):


$\begin{aligned} &\left ( \left ( \frac { 37 }{ 20 } \right ) ^ \frac{ 1 }{ 5 } \right ) – 1 = 13.1\% \text{ annual return} \\ \end{aligned}$​((2037​)51​)−1=13.1% annual return​

The annualized return varies from the typical average and shows the real gain or loss on an investment, as well as the difficulty in recouping losses. For instance, losing 50% on an initial investment requires a 100% gain the next year in order to make up the difference. Because of the sizable difference in gains and losses that can occur, annualized returns help even out investment results for better comparison. 

Annual Returns on a 401K

The calculation differs when determining the annual return of a 401K during a specified year. First, the total return must be calculated. The starting value for the time period being examined is needed, along with the final value. Before performing the calculations, any contributions to the account during the time period in question must be subtracted from the final value.

Once the adjusted final value is determined, it is divided by the starting balance. Finally, subtract 1 from the result and multiply that amount by 100 to determine the percentage total return.