How do you annualize a 9 month return?

Suppose Texas employment grew 0.92 percent in the first five months of a particular year. Then in June and July, employment advanced 0.15 percent and 0.22 percent, respectively. Would employment growth in June and July be above or below the pace set in the first five months of the year?

While this simple problem could probably be tackled in a few different ways, the most common one is a process called data annualization. In this method, growth rates are adjusted to reflect the amount a variable would have changed over a year’s time, had it continued to grow at the given rate. The result is a percent change that is easily comparable to other annualized data.

In this case, the 0.92 percent translates into an annualized 2.22 percent. The 0.15 becomes 1.81 percent (annualized), and the 0.22 figure becomes 2.67 percent (annualized). Thus, employment growth in June was below the rate established in the first five months, while the July figure was above it, in annualized terms. This kind of data adjustment is very common in economic analysis. It allows for quick comparison of percent changes, no matter the time period.

The formula for annualizing monthly data is straightforward:

How do you annualize a 9 month return?
NOTE: For quarterly data, use 4 instead of 12.

where Xm and Xm – 1 are the values of the economic variable in months m and m –1, respectively (for example, m = February, then m – 1 = January), and gm is the annualized percent change.

For year-to-date calculations on monthly data, the formula is:

How do you annualize a 9 month return?
NOTE: For quarterly data, use the fourth quarter instead of December, and q = 1, 2, 3, 4 instead of m = 1, 2, 3…12.

where XDec is the value of the economic variable in the December of a given year, m is the number of the month in question, Xm is the value of the economic variable in the mth month of the given year, and hm is the annualized year-to-m percent change.

Table 1 uses these two formulas to calculate the values cited in the Economic Problem section above.Table 1MonthEmployment
(thousands)Monthly percent
change (not annualized)Monthly percent
change (annualized)December9,452.5n/an/aJanuary9,465.2.131.62February9,472.9.080.98March9,498.3.273.27April9,516.3.192.30May9,539.5.242.96June9,553.8.151.81July9,574.8.222.67May/Decn/a.922.22

On the July row, 0.22 is found by calculating the percent change between 9,553,800 (June) and 9,574,800 (July). The annualized figure of 2.67 is found by applying Equation 1: Divide 9,574,800 by 9,553,800, raise this quotient by 12, subtract 1, and multiply the whole thing by 100 (Calculation 1). This rate represents the amount employment would have increased for the year had it expanded at that monthly rate all 12 months. The calculation for the other months is the same.

How do you annualize a 9 month return?

In the last row, the 0.92 figure is found by calculating the simple percent change between 9,452,500 (December) and 9,539,500 (May). The annualized figure of 2.22 percent is found by applying Equation 2: Divide 9,539,500 by 9,452,500, raise this quotient by 2.4 (12/5), subtract 1, and multiply the whole thing by 100 (Calculation 2). This rate represents the amount employment would have increased for the year had it continued to expand at the pace set between January and May.

How do you annualize a 9 month return?

The annualizing methodology offers a simple way to compare the growth rates of economic variables presented across different periods. Analysts can regularly assess the monthly or quarterly performance of key economic indicators relative to their changes in recent years.

Note

Annualized rates of growth in monthly or quarterly data are generally only calculated for data that are not seasonal, or that have had the seasonality removed.

Often, you'll run into a situation in which it would be useful to know the cost per year, but you'll only have the cost over a shorter term. In some instances, you can figure the answer in your head – if you're paying 1 percent a month, you don't need a calculator to figure out that your annual rate is 12 percent. But in other instances, the answer isn't immediately evident, perhaps because the time period isn't a standard quantity – nine days, for instance – or, because you need to add or subtract from the initial number before coming up with the answer. What you need is a way of annualizing the return.

What Does it Mean to Annualize a Number?

You're a freelance photographer, and last week you had gross earnings of $875. If you earned the same amount every week for a year, how much will you have earned?

Arriving at the answer is pretty simple: you take that one week's earning, $875, and you multiply it by 52, which is the number of weeks in a year. You've earned $45,500. In the process of determining this, you've annualized the weekly income number.

You can generalize this process, and say that annualizing a number means converting a rate of return over any length of time, usually less than a year, into the annual return rate.

Why Annualize?

Individuals and institutions annualize rates for many reasons. Probably the most common is to enable you to make a meaningful comparison between two rates, each over a unique time span. If, for instance, as a photographer, you're offered an assignment from a regional design magazine that pays $2,500. Is this better or worse than your weekly $875 average income?

The first thing to figure out is this: how long will this assignment take? You might need to provide color photographs to accompany a feature article about a luxurious, new house designed by a well-known architect. You determine that this will be a six-day job, and that you'll incur various expenses, such as having an assistant and ordering supplies, which will total $1,100.

Figuring out the Rate of Return

With this information, you're ready to do the relatively simple math that enables you to compare the two rates of return, using a common annual return rate to make the comparison. Your net for the proposed assignment is $2,500, minus $1,100 in expenses, so you will net $1,400. As for the length of time it will take to earn this $1,400, you can convert this to an annual rate in a couple of ways.

For instance, you could first determine that in 2018, there are 216 working days in a year by Googling "the number of work days in [your current year]. Various sites have this information, including "The University of Iowa: 2018 Working Day Payroll Calendar," included in the References section.

You've concluded that the assignment will take six days. The number $1,400 divided by 6, equals the daily rate of $233.3333. This daily rate multiplied by the number of working days, 261, equals $60,900, which is the annualized earnings rate for this assignment; therefore, this number is higher your previously determined annual rate of $45,500. You should definitely take this job!

Alternative Ways of Annualizing

In the above example, you arrived at the annualized income rate, first by determining the daily rate, then by multiplying the daily rate by the number of working days in 2018.

In this instance, looking up the number of working days in the current year to make the calculation works well. In another instance, you may want to make some approximation of the answer – not down to the penny, but close enough for you to make a decision – without knowing the exact number of working days in a particular year, or, perhaps, without having a specific year in mind.

You know the assignment will take six days, which is a five-day work week plus a day. In terms of a week, this amounts to 6 divided by 5 work weeks, or 1.2 work weeks. The question then, becomes, if you can earn $1400 in 1.2 work weeks, how much can you earn in a year at that rate?

The Same Problem as Algebra

In algebra-speak, this problem becomes

1400/1.2 = X/52

You solve this by multiplying both sides by 52. In this computation, X equals 1400/1.2*52, which is $60,066, the annualized return of the proposed photography assignment.

This result isn't quite as accurate as the earlier computation, based on the number of actual working days in a specific year, because it doesn't account for U.S. holidays, among other factors. Still, $60,066 is reasonably close to the more accurate determination of $60,900, which is the computation based on the actual number of working days in 2018. Both methods answer the question: "Is this better or worse than my average income rate?" In many instances, an approximation of this kind will come close enough to provide a useful means of comparing two annualized rates of return.

How do you annualize a number for 9 months?

Divide the number of months in a year by the months of income. To annualize your income, use the ratio of the number of months in a year (12) over the number of months in the period you used to get your total. When you divide, your result will always be a number greater than 1.

How do you annualize a multi year return?

Calculate Annual Rate of Return Adding 1 to the multi-year decimal return and raising it to the power of this fraction gives you the annual multiplier. Subtracting 1 from the result and multiplying by 100 converts the multiplier into the percent annualized return.

How do you calculate the annualized return?

For example, if a person bought Stock A 2 years ago for $10 and it is currently selling at $15, it's period return is ($15-$10)/$10 = 50%. However, since one year is only 1/2 of the time of 2 years, it's annualized return is ($15/$10)^(1/2) - 1 = 22.47%.

How do you annualize a September number?

An Excel formula to annualize data.
=[Value for 1 month] * 12..
=[Value for 2 months] * 6..
=[Value for X months] * (12 / [Number of months]).