What Is Average Life?

The average life is the length of time the principal of a debt issue is expected to be outstanding. Average life does not take into account interest payments, but only principal payments made on the loan or security. In loans, mortgages, and bonds, the average life is the average period of time before the debt is repaid through amortization or sinking fund payments.

Investors and analysts use the average life calculation to measure the risk associated with amortizing bonds, loans, and mortgage-backed securities. The calculation gives investors an idea of how quickly they can expect returns and provides a useful metric for comparing investment options. In general, most investors will choose to receive their financial returns earlier and will, therefore, choose the investment with the shorter average life.

Understanding Average Life

Also called the weighted average maturity and weighted average life, the average life is calculated to determine how long it will take to pay the outstanding principal of a debt issue, such as a Treasury Bill (T-Bill) or bond. While some bonds repay the principal in a lump sum at maturity, others repay the principal in installments over the term of the bond. In cases where the bond’s principal is amortized, the average life allows investors to determine how quickly the principal will be repaid.

The payments received are based on the repayment schedule of the loans backing the particular security, such as with mortgage-backed securities (MBS) and asset-backed securities (ABS). As borrowers make payments on the associated debt obligations, investors are issued payments reflecting a portion of these cumulative interest and principal payments.

Calculating the Average Life on a Bond

To calculate the average life, multiply the date of each payment (expressed as a fraction of years or months) by the percentage of total principal that has been paid by that date, add the results, and divide by the total issue size.

For example, assume an annual-paying four-year bond has a face value of $200 and principal payments of $80 during the first year, $60 for the second year, $40 during the third year, and $20 for the fourth (and final) year. The average life for this bond would be calculated with the following formula:

($80 x 1) + ($60 x 2) + ($40 x 3) + ($20 x 4) = 400

Then divide the weighted total by the bond face value to get the average life. In this example, the average life equals 2 years (400 divided by 200 = 2).

This bond would have an average life of two years against its maturity of four years.

Mortgage-Backed and Asset-Backed Securities

In the case of an MBS or ABS, the average life represents the average length of time required for the associated borrowers to repay the loan debt. An investment in an MBS or ABS involves purchasing a small portion of the associated debt that is packaged within the security.

The risk associated with an MBS or ABS centers on whether the borrower associated with the loan will default. If the borrower fails to make a payment, the investors associated with the security will experience losses. In the financial crisis of 2008, a large number of defaults on home loans, particularly in the subprime market, led to significant losses in the MBS arena.

Special Considerations

While certainly not as dire as default risk, another risk bond investors face is prepayment risk. This occurs when the bond issuer (or the borrower in the case of mortgage-backed securities) pays back the principal earlier than scheduled. These prepayments will reduce the average life of the investment. Because the principal is paid back early, the investor will not receive future interest payments on that part of the principal.

This interest reduction can represent an unexpected challenge for investors of fixed-income securities dependent on a reliable stream of income. For this reason, some bonds with payment risk include prepayment penalties.

What is the Average Daily Balance Method?

The average daily balance is a common accounting method that calculates interest charges by considering the balance invested or owed at the end of each day of the billing period, rather than the balance invested or owed at the end of the week, month, or year.

Understanding the Average Daily Balance Method

The federal Truth-In-Lending-Act (TILA) requires lenders to disclose their method of calculating finance charges, as well as annual percentage rates (APR), fees, and other terms, in their terms and conditions statement. Providing these details makes it easier to compare different credit cards.

TILA permits the interest owed on credit card balances to be calculated in various different ways. The most common methods are:

• Average daily balance method: Uses the balance on each day of the billing cycle, rather than an average balance throughout the billing cycle, to calculate finance charges.
• Previous balance method: Interest charges are based on the amount owed at the beginning of the previous month’s billing cycle.
• Adjusted balance method: Bases finance charges on the amount(s) owed at the end of the current billing cycle after credits and payments have been posted.

How the Average Daily Balance Method Works

The average daily balance totals each day’s balance for the billing cycle and divides by the total number of days in the billing cycle. Then, the balance is multiplied by the monthly interest rate to assess the customer’s finance charge—dividing the cardholder’s APR by 12 calculates the monthly interest rate. However, if the lender or card issuer uses a method that compounds interest daily, the interest associated with the day’s ending balance gets added to the next day’s beginning balance. This will result in higher interest charges and the reader should confirm which method is being used.

The average daily balance credits a customer’s account from the day the credit card company receives a payment. To assess the balance due, the credit card issuer sums the beginning balance for each day in the billing period and subtracts any payments as they arrive and any credits made to the customer’s account that day.

Cash advances are usually included in the average daily balance. The total balance due may fluctuate daily because of payments and purchases.

Average Daily Balance Method Example

A credit card has a monthly interest rate of 1.5 percent, and the previous balance is $500. On the 15th day of a billing cycle, the credit card company receives and credits a customer’s payment of $300. On the 18th day, the customer makes a $100 purchase.

The average daily balance is ((14 x 500) + (3 x 200) + (13 x 300)) / 30 = (7,000 + 600 + 3,900) / 30 = 383.33. The bigger the payment a customer pays and the earlier in the billing cycle the customer makes a payment, the lower the finance charges assessed. The denominator, 30 in this example, will vary based on the number of days in the billing cycle for a given month.

Average Daily Balance Method Vs. Adjusted Balance Method Vs. Previous Balance Method

Interest charges using the average daily balance method should be lower than the previous balance method, which charges interest based on the amount of debt carried over from the previous billing cycle to the new billing cycle. On the other hand, the average daily balance method will likely incur higher interest charges than the adjusted balance method because the latter bases finance charges on the current billing period’s ending balance.

Card issuers use the adjusted balance method much less frequently than either the average daily balance method or the previous balance method.

Special Considerations

Some credit card companies previously used the double-cycle billing method, assessing a customer’s average daily balance over the last two billing cycles.

Double-cycle billing can add a significant amount of interest charges to customers whose average balance varies greatly from month to month. The Credit CARD Act of 2009 banned double-cycle billing on credit cards.

What Is an Autoregressive Model?

A statistical model is autoregressive if it predicts future values based on past values. For example, an autoregressive model might seek to predict a stock’s future prices based on its past performance.

Understanding Autoregressive Models

Autoregressive models operate under the premise that past values have an effect on current values, which makes the statistical technique popular for analyzing nature, economics, and other processes that vary over time. Multiple regression models forecast a variable using a linear combination of predictors, whereas autoregressive models use a combination of past values of the variable.

An AR(1) autoregressive process is one in which the current value is based on the immediately preceding value, while an AR(2) process is one in which the current value is based on the previous two values. An AR(0) process is used for white noise and has no dependence between the terms. In addition to these variations, there are also many different ways to calculate the coefficients used in these calculations, such as the least squares method.

These concepts and techniques are used by technical analysts to forecast security prices. However, since autoregressive models base their predictions only on past information, they implicitly assume that the fundamental forces that influenced the past prices will not change over time. This can lead to surprising and inaccurate predictions if the underlying forces in question are in fact changing, such as if an industry is undergoing rapid and unprecedented technological transformation.

Nevertheless, traders continue to refine the use of autoregressive models for forecasting purposes. A great example is the Autoregressive Integrated Moving Average (ARIMA), a sophisticated autoregressive model that can take into account trends, cycles, seasonality, errors, and other non-static types of data when making forecasts.

Example of an Autoregressive Model

Autoregressive models are based on the assumption that past values have an effect on current values. For example, an investor using an autoregressive model to forecast stock prices would need to assume that new buyers and sellers of that stock are influenced by recent market transactions when deciding how much to offer or accept for the security.

Although this assumption will hold under most circumstances, this is not always the case. For example, in the years prior to the 2008 Financial Crisis, most investors were not aware of the risks posed by the large portfolios of mortgage-backed securities held by many financial firms. During those times, an investor using an autoregressive model to predict the performance of U.S. financial stocks would have had good reason to predict an ongoing trend of stable or rising stock prices in that sector. 

However, once it became public knowledge that many financial institutions were at risk of imminent collapse, investors suddenly became less concerned with these stocks’ recent prices and far more concerned with their underlying risk exposure. Therefore, the market rapidly revalued financial stocks to a much lower level, a move which would have utterly confounded an autoregressive model.

It is important to note that, in an autoregressive model, a one-time shock will affect the values of the calculated variables infinitely into the future. Therefore, the legacy of the financial crisis lives on in today’s autoregressive models.

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What Is an Automatic Stabilizer?

Automatic stabilizers are a type of fiscal policy designed to offset fluctuations in a nation’s economic activity through their normal operation without additional, timely authorization by the government or policymakers.

The best-known automatic stabilizers are progressively graduated corporate and personal income taxes, and transfer systems such as unemployment insurance and welfare. Automatic stabilizers are called this because they act to stabilize economic cycles and are automatically triggered without additional government action.

Understanding Automatic Stabilizers

Automatic stabilizers are primarily designed to counter negative economic shocks or recessions, though they can also be intended to “cool off” an expanding economy or to combat inflation. By their normal operation, these policies take more money out of the economy as taxes during periods of rapid growth and higher incomes. They put more money back into the economy in the form of government spending or tax refunds when economic activity slows or incomes fall. This has the intended purpose of cushioning the economy from changes in the business cycle. 

Automatic stabilizers can include the use of a progressive taxation structure under which the share of income that is taken in taxes is higher when incomes are high. The amount then falls when incomes fall due to a recession, job losses, or failing investments. For example, as an individual taxpayer earns higher wages, their additional income may be subjected to higher tax rates based on the current tiered structure. If wages fall, the individual will remain in the lower tax tiers as dictated by their earned income.

Similarly, unemployment insurance transfer payments decline when the economy is in an expansionary phase since there are fewer unemployed people filing claims. Unemployment payments rise when the economy is mired in recession and unemployment is high. When a person becomes unemployed in a manner that makes them eligible for unemployment insurance, they need only file to claim the benefit. The amount of benefit offered is governed by various state and national regulations and standards, requiring no intervention by larger government entities beyond application processing.

Automatic Stabilizers and Fiscal Policy

When an economy is in a recession, automatic stabilizers may by design result in higher budget deficits. This aspect of fiscal policy is a tool of Keynesian economics that uses government spending and taxes to support aggregate demand in the economy during economic downturns.

By taking less money out of private businesses and households in taxes and giving them more in the form of payments and tax refunds, fiscal policy is supposed to encourage them to increase, or at least not decrease, their consumption and investment spending. In this case, the goal of fiscal policy is to help prevent an economic setback from deepening.

Real-World Examples of Automatic Stabilizers

Automatic stabilizers can also be used in conjunction with other forms of fiscal policy that may require specific legislative authorization. Examples of this include one-time tax cuts or refunds, government investment spending, or direct government subsidy payments to businesses or households.

Some examples of these in the United States were the 2008 one-time tax rebates under the Economic Stimulus Act and the $831 billion in federal direct subsidies, tax breaks, and infrastructure spending under the 2009 American Reinvestment and Recovery Act.

In 2020, the Coronavirus Aid, Relief, and Economic Security (CARES) Act became the largest stimulus package in U.S. history. It provided over $2 trillion in government relief in the form of expanded unemployment benefits, direct payments to families and adults, loans and grants to small businesses, loans to corporate America, and billions of dollars to state and local governments.

Special Considerations

Since they almost immediately respond to changes in income and unemployment, automatic stabilizers are intended to be the first line of defense to turn mild negative economic trends around. However, governments often turn to other types of larger fiscal policy programs to address more severe or lasting recessions or to target specific regions, industries, or politically favored groups in society for extra-economic relief.