What Is Autocorrelation?

Autocorrelation is a mathematical representation of the degree of similarity between a given time series and a lagged version of itself over successive time intervals. It’s conceptually similar to the correlation between two different time series, but autocorrelation uses the same time series twice: once in its original form and once lagged one or more time periods. 

For example, if it’s rainy today, the data suggests that it’s more likely to rain tomorrow than if it’s clear today. When it comes to investing, a stock might have a strong positive autocorrelation of returns, suggesting that if it’s “up” today, it’s more likely to be up tomorrow, too.

Naturally, autocorrelation can be a useful tool for traders to utilize; particularly for technical analysts.

Understanding Autocorrelation

Autocorrelation can also be referred to as lagged correlation or serial correlation, as it measures the relationship between a variable’s current value and its past values.

As a very simple example, take a look at the five percentage values in the chart below. We are comparing them to the column on the right, which contains the same set of values, just moved up one row.

What Is Aggregate Demand?

Aggregate demand is a measurement of the total amount of demand for all finished goods and services produced in an economy. Aggregate demand is commonly expressed as the total amount of money exchanged for those goods and services at a specific price level and point in time.

Understanding Aggregate Demand

Aggregate demand is a macroeconomic term and can be compared with the gross domestic product (GDP). GDP represents the total amount of goods and services produced in an economy while aggregate demand is the demand or desire for those goods. Aggregate demand and GDP commonly increase or decrease together.

Aggregate demand equals GDP only in the long run after adjusting for the price level. Short-run aggregate demand measures total output for a single nominal price level without adjusting for inflation. Other variations in calculations can occur depending on the methodologies used and the various components.

Aggregate demand consists of all consumer goods, capital goods, exports, imports, and government spending programs. All variables are considered equal if they trade at the same market value.

Aggregate Demand Components

Aggregate demand is determined by the overall collective spending on products and services by all economic sectors on the procurement of goods and services by four components:

Consumption Spending

Consumer spending represents the demand by individuals and households within the economy. While there are several factors in determining consumer demand, the most important is consumer incomes and the level of taxation.

Investment Spending

Investment spending represents businesses’ investment to support current output and increase production capability. It may include spending on new capital assets such as equipment, facilities, and raw materials.

Government Spending

Government spending represents the demand produced by government programs, such as infrastructure spending and public goods. This does not include services such as Medicare or social security, because these programs simply transfer demand from one group to another.

Net Exports

Net exports represent the demand for foreign goods, as well as the foreign demand for domestic goods. It is calculated by subtracting the total value of a country’s exports from the total value of all imports.

Aggregate Demand Formula

The equation for aggregate demand adds the amount of consumer spending, investment spending, government spending, and the net of exports and imports. The formula is shown as follows:

$\begin{aligned} &\text{Aggregate Demand} = \text{C} + \text{I} + \text{G} + \text{Nx} \\ &\textbf{where:}\\ &\text{C} = \text{Consumer spending on goods and services} \\ &\text{I} = \text{Private investment and corporate spending on} \\ &\text{non-final capital goods (factories, equipment, etc.)} \\ &\text{G} = \text{Government spending on public goods and social} \\ &\text{services (infrastructure, Medicare, etc.)} \\ &\text{Nx} = \text{Net exports (exports minus imports)} \\ \end{aligned}$​Aggregate Demand=C+I+G+Nxwhere:C=Consumer spending on goods and servicesI=Private investment and corporate spending onnon-final capital goods (factories, equipment, etc.)G=Government spending on public goods and socialservices (infrastructure, Medicare, etc.)Nx=Net exports (exports minus imports)​

The aggregate demand formula above is also used by the Bureau of Economic Analysis to measure GDP in the U.S.

What Affects Aggregate Demand?

Interest Rates

Interest rates affect decisions made by consumers and businesses. Lower interest rates will lower the borrowing costs for big-ticket items such as appliances, vehicles, and homes and companies will be able to borrow at lower rates, often leading to capital spending increases. Higher interest rates increase the cost of borrowing for consumers and companies and spending tends to decline or grow at a slower pace.

Income and Wealth

As household wealth increases, aggregate demand typically increases. Conversely, a decline in wealth usually leads to lower aggregate demand. When consumers are feeling good about the economy, they tend to spend more and save less.

Inflation Expectations

Consumers who anticipate that inflation will increase or prices will rise tend to make immediate purchases leading to rises in aggregate demand. But if consumers believe prices will fall in the future, aggregate demand typically falls.

Currency Exchange Rates

When the value of the U.S. dollar falls, foreign goods will become more expensive. Meanwhile, goods manufactured in the U.S. will become cheaper for foreign markets. Aggregate demand will, therefore, increase. When the value of the dollar increases, foreign goods are cheaper and U.S. goods become more expensive to foreign markets, and aggregate demand decreases.

Economic Conditions and Aggregate Demand

Economic conditions can impact aggregate demand whether those conditions originated domestically or internationally. The financial crisis of 2007-08, sparked by massive amounts of mortgage loan defaults, and the ensuing Great Recession, offer a good example of a decline in aggregate demand due to economic conditions.

With businesses suffering from less access to capital and fewer sales, they began to lay off workers and GDP growth contracted in 2008 and 2009, resulting in a total production contraction in the economy during that period. A poor-performing economy and rising unemployment led to a decline in personal consumption or consumer spending. Personal savings also surged as consumers held onto cash due to an uncertain future and instability in the banking system.

In 2020, the COVID-19 pandemic caused reductions in both aggregate supply or production, and aggregate demand or spending. Social distancing measures and concerns about the spread of the virus caused a significant decrease in consumer spending, particularly in services as many businesses closed. These dynamics lowered aggregate demand in the economy. As aggregate demand fell, businesses either laid off part of their workforces or otherwise slowed production as employees contracted COVID-19 at high rates.

Aggregate Demand vs. Aggregate Supply

In times of economic crises, economists often debate as to whether aggregate demand slowed, leading to lower growth, or GDP contracted, leading to less aggregate demand. Whether demand leads to growth or vice versa is economists’ version of the age-old question of what came first—the chicken or the egg.

Boosting aggregate demand also boosts the size of the economy regarding measured GDP. However, this does not prove that an increase in aggregate demand creates economic growth. Since GDP and aggregate demand share the same calculation, it only indicates that they increase concurrently. The equation does not show which is the cause and which is the effect.

Early economic theories hypothesized that production is the source of demand. The 18th-century French classical liberal economist Jean-Baptiste Say stated that consumption is limited to productive capacity and that social demands are essentially limitless, a theory referred to as Say’s Law of Markets.

Say’s law, the basis of supply-side economics, ruled until the 1930s and the advent of the theories of British economist John Maynard Keynes. By arguing that demand drives supply, Keynes placed total demand in the driver’s seat. Keynesian macroeconomists have since believed that stimulating aggregate demand will increase real future output and the total level of output in the economy is driven by the demand for goods and services and propelled by money spent on those goods and services.

Keynes considered unemployment to be a byproduct of insufficient aggregate demand because wage levels would not adjust downward fast enough to compensate for reduced spending. He believed the government could spend money and increase aggregate demand until idle economic resources, including laborers, were redeployed.

Other schools of thought, notably the Austrian School and real business cycle theorists stress consumption is only possible after production. This means an increase in output drives an increase in consumption, not the other way around. Any attempt to increase spending rather than sustainable production only causes maldistribution of wealth or higher prices, or both.

As a demand-side economist, Keynes further argued that individuals could end up damaging production by limiting current expenditures—by hoarding money, for example. Other economists argue that hoarding can impact prices but does not necessarily change capital accumulation, production, or future output. In other words, the effect of an individual’s saving money—more capital available for business—does not disappear on account of a lack of spending.

The Bottom Line

Aggregate demand is a concept of macroeconomics that represents the total demand within an economy for all kinds of goods and services at a certain price point. In the long term, aggregate demand is indistinguishable from GDP. However, aggregate demand is not a perfect metric and it is the subject of debate among economists.

What Is the Asset Turnover Ratio?

The asset turnover ratio measures the value of a company’s sales or revenues relative to the value of its assets. The asset turnover ratio can be used as an indicator of the efficiency with which a company is using its assets to generate revenue.

The higher the asset turnover ratio, the more efficient a company is at generating revenue from its assets. Conversely, if a company has a low asset turnover ratio, it indicates it is not efficiently using its assets to generate sales.

Formula and Calculation of the Asset Turnover Ratio

Below are the steps as well as the formula for calculating the asset turnover ratio.


$\begin{aligned} &\text{Asset Turnover} = \frac{ \text{Total Sales} }{ \frac { \text{Beginning Assets}\ +\ \text{Ending Assets} }{ 2 } } \\ &\textbf{where:}\\ &\text{Total Sales} = \text{Annual sales total} \\ &\text{Beginning Assets} = \text{Assets at start of year} \\ &\text{Ending Assets} = \text{Assets at end of year} \\ \end{aligned}$​Asset Turnover=2Beginning Assets + Ending Assets​Total Sales​where:Total Sales=Annual sales totalBeginning Assets=Assets at start of yearEnding Assets=Assets at end of year​

The asset turnover ratio uses the value of a company’s assets in the denominator of the formula. To determine the value of a company’s assets, the average value of the assets for the year needs to first be calculated.

1. Locate the value of the company’s assets on the balance sheet as of the start of the year.
2. Locate the ending balance or value of the company’s assets at the end of the year.
3. Add the beginning asset value to the ending value and divide the sum by two, which will provide an average value of the assets for the year.
4. Locate total sales—it could be listed as revenue—on the income statement.
5. Divide total sales or revenue by the average value of the assets for the year.

What the Asset Turnover Ratio Can Tell You

Typically, the asset turnover ratio is calculated on an annual basis. The higher the asset turnover ratio, the better the company is performing, since higher ratios imply that the company is generating more revenue per dollar of assets.

The asset turnover ratio tends to be higher for companies in certain sectors than in others. Retail and consumer staples, for example, have relatively small asset bases but have high sales volume—thus, they have the highest average asset turnover ratio. Conversely, firms in sectors such as utilities and real estate have large asset bases and low asset turnover.

Since this ratio can vary widely from one industry to the next, comparing the asset turnover ratios of a retail company and a telecommunications company would not be very productive. Comparisons are only meaningful when they are made for different companies within the same sector.

Example of How to Use the Asset Turnover Ratio

Let’s calculate the asset turnover ratio for four companies in the retail and telecommunication-utilities sectors for FY 2020—Walmart Inc. (WMT), Target Corporation (TGT), AT&T Inc. (T), and Verizon Communications Inc. (VZ).

What Is an Allowance for Doubtful Accounts?

An allowance for doubtful accounts is a contra account that nets against the total receivables presented on the balance sheet to reflect only the amounts expected to be paid. The allowance for doubtful accounts estimates the percentage of accounts receivable that are expected to be uncollectible. However, the actual payment behavior of customers may differ substantially from the estimate.

Understanding the Allowance for Doubtful Accounts

Regardless of company policies and procedures for credit collections, the risk of the failure to receive payment is always present in a transaction utilizing credit. Thus, a company is required to realize this risk through the establishment of the allowance for doubtful accounts and offsetting bad debt expense. In accordance with the matching principle of accounting, this ensures that expenses related to the sale are recorded in the same accounting period as the revenue is earned. The allowance for doubtful accounts also helps companies more accurately estimate the actual value of their account receivables.

Because the allowance for doubtful accounts is established in the same accounting period as the original sale, an entity does not know for certain which exact receivables will be paid and which will default. Therefore, generally accepted accounting principles (GAAP) dictate that the allowance must be established in the same accounting period as the sale, but can be based on an anticipated or estimated figure. The allowance can accumulate across accounting periods and may be adjusted based on the balance in the account.

How to Estimate the Allowance for Doubtful Accounts

Two primary methods exist for estimating the dollar amount of accounts receivables not expected to be collected.

Percentage of Sales Method

The sales method applies a flat percentage to the total dollar amount of sales for the period. For example, based on previous experience, a company may expect that 3% of net sales are not collectible. If the total net sales for the period is $100,000, the company establishes an allowance for doubtful accounts for $3,000 while simultaneously reporting $3,000 in bad debt expense.

If the following accounting period results in net sales of $80,000, an additional $2,400 is reported in the allowance for doubtful accounts, and $2,400 is recorded in the second period in bad debt expense. The aggregate balance in the allowance for doubtful accounts after these two periods is $5,400.

Accounts Receivable Aging Method

The second method of estimating the allowance for doubtful accounts is the aging method. All outstanding accounts receivable are grouped by age, and specific percentages are applied to each group. The aggregate of all group results is the estimated uncollectible amount.

For example, a company has $70,000 of accounts receivable less than 30 days outstanding and $30,000 of accounts receivable more than 30 days outstanding. Based on previous experience, 1% of accounts receivable less than 30 days old will be uncollectible, and 4% of those accounts receivable at least 30 days old will be uncollectible.

Therefore, the company will report an allowance of $1,900 (($70,000 * 1%) + ($30,000 * 4%)). If the next accounting period results in an estimated allowance of $2,500 based on outstanding accounts receivable, only $600 ($2,500 – $1,900) will be the adjusting entry amount.

Risk Classification Method

Some companies may classify different types of debt or different types of vendors using risk classifications. For example, a start-up customer may be considered a high risk, while an established, long-tenured customer may be a low risk. In this example, the company often assigns a percentage to each classification of debt. Then, it aggregates all receivables in each grouping, calculates each group by the percentage, and records an allowance equal to the aggregate of all products.

Historical Percentage Method

If a company has a history of recording or tracking bad debt, it can use the historical percentage of bad debt if it feels that historical measurement relates to its current debt. For example, a company may know that its 10-year average of bad debt is 2.4%. Therefore, it can assign this fixed percentage to its total accounts receivable balance since more often than not, it will approximately be close to this amount. The company must be aware of outliers or special circumstances that may have unfairly impacted that 2.4% calculation.

Pareto Analysis Method

A Pareto analysis is a risk measurement approach that states that a majority of activity is often concentrated among a small amount of accounts. In many different aspects of business, a rough estimation is that 80% of account receivable balances are made up of a small concentration (i.e. 20%) of vendors. This 80%/20% ratio is used throughout business.

Though the Pareto Analysis can not be used on its own, it can be used to weigh accounts receivable estimates differently. For example, a company may assign a heavier weight to the clients that make up a larger balance of accounts receivable due to conservatism.

Specific Identification Method

Assume a company has 100 clients and believes there are 11 accounts that may go uncollected. Instead of applying percentages or weights, it may simply aggregate the account balance for all 11 customers and use that figure as the allowance amount. Companies often have a specific method of identifying the companies that it wants to include and the companies it wants to exclude.

How to Account for the Allowance for Doubtful Accounts

Establishing the Allowance

The first step in accounting for the allowance for doubtful accounts is to establish the allowance. This is done by using one of the estimation methods above to predict what proportion of accounts receivable will go uncollected. For this example, let’s say a company predicts it will incur $500,000 of uncollected accounts receivable.

To create the allowance, the company must debit a loss. Most often, companies use an account called ‘Bad Debt Expense’. Then, the company establishes the allowance by crediting an allowance account often called ‘Allowance for Doubtful Accounts’. Though this allowance for doubtful accounts is presented on the balance sheet with other assets, it is a contra asset that reduces the balance of total assets.

• DR Bad Debt Expense $500,000
• CR Allowance for Doubtful Accounts $500,000

Adjusting the Allowance

Let’s say six months passes. The company now has a better idea of which account receivables will be collected and which will be lost. For example, say the company now thinks that a total of $600,000 of receivables will be lost. This means its allowance of $500,000 is $100,000 short. The company must record an additional expense for this amount to also increase the allowance’s credit balance.

• DR Bad Debt Expense $100,000
• CR Allowance for Doubtful Accounts $100,000

Writing Off Account

Now, let’s say a specific customer that owes a company $50,000 officially files for bankruptcy. This client’s account had previously been included in the estimate for the allowance. Because the company has a very low priority claim without collateral to the debt, the company decides it is unlikely it will every receive any of this $50,000. To properly reflect this change, the company must reduce its accounts receivable balance by this amount. On the other hand, once the receivable is removed from the books, there is no need to record an associated allowance for this account.

• DR Allowance for Doubtful Accounts $50,000
• CR Accounts Receivable $50,000

Note that the debit to the allowance for doubtful accounts reduces the balance in this account because contra assets have a natural credit balance. Also, note that when writing off the specific account, no income statement accounts are used. This is because the expense was already taken when creating or adjusting the allowance.

Recovering an Account

By miracle, it turns out the company ended up being rewarded a portion of their outstanding receivable balance they’d written off as part of the bankruptcy proceedings. Of the $50,000 balance that was written off, the company is notified that they will receive $35,000.

The company can recover the account by reversing the entry above to reinstate the accounts receivable balance and the corresponding allowance for doubtful account balance. Then, the company will record a debit to cash and credit to accounts receivable when the payment is collected. You’ll notice that because of this, the allowance for doubtful accounts increases. A company can further adjust the balance by following the entry under the “Adjusting the Allowance” section above.

• DR Accounts Receivable $35,000
• CR Allowance for Doubtful Accounts $35,000
• DR Cash $35,000
• CR Accounts Receivable $35,000

The Bottom Line

The allowance for doubtful accounts is a general ledger account that is used to estimate the amount of accounts receivable that will not be collected. A company uses this account to record how many accounts receivable it thinks will be lost. The balance may be estimated using several different methods, and management should periodically evaluate the balance of the allowance account to ensure the appropriate bad debt expense and net accounts receivables are being recorded.