What Is Actuarial Science?

Actuarial science is a discipline that assesses financial risks in the insurance and finance fields, using mathematical and statistical methods. Actuarial science applies the mathematics of probability and statistics to define, analyze, and solve the financial implications of uncertain future events. Traditional actuarial science largely revolves around the analysis of mortality and the production of life tables, and the application of compound interest.

Understanding Actuarial Science

Actuarial science attempts to quantify the risk of an event occurring using probability analysis so that its financial impact can be determined. Actuarial science is typically used in the insurance industry by actuaries. Actuaries analyze mathematical models to predict or forecast the reasonableness of an event occurring so that an insurance company can allocate funds to pay out any claims that might result from the event. For example, studying mortality rates of individuals of a certain age would help insurance companies understand the likelihood or timeframe of paying out a life insurance policy.

Actuarial science became a formal mathematical discipline in the late 17th century with the increased demand for long-term insurance coverage. Actuarial science spans several interrelated subjects, including mathematics, probability theory, statistics, finance, economics, and computer science. Historically, actuarial science used deterministic models in the construction of tables and premiums. In the last 30 years, science has undergone revolutionary changes due to the proliferation of high-speed computers and the union of stochastic actuarial models with modern financial theory.

Applications of Actuarial Science

Life insurance and pension plans are the two main applications of actuarial science. However, actuarial science is also applied in the study of financial organizations to analyze their liabilities and improve financial decision-making. Actuaries employ this specialty science to evaluate the financial, economic, and other business applications of future events.

Insurance

In traditional life insurance, actuarial science focuses on the analysis of mortality, the production of life tables, and the application of compound interest, which is the accumulated interest from previous periods plus the interest on the principal investment. As a result, actuarial science can help develop policies for financial products such as annuities, which are investments that pay a fixed income stream. Actuarial science is also used to determine the various financial outcomes for investable assets held by non-profit corporations as a result of endowments. 

In health insurance, including employer-provided plans and social insurance, actuarial science includes analyzing rates of

• Disability in the population or the risk of a certain group of people becoming disabled
• Morbidity or the frequency and the extent to which a disease occurs in a population
• Mortality or mortality rate, which measures the number of deaths in a population that result from a specific disease or event
• Fertility or fertility rate, which measures the number of children born

For example, disability rates are determined for veterans that may have been wounded in the line of duty. Certain percentages are assigned to the extent of the disability to determine the payout from disability insurance.

Actuarial science is also applied to property, casualty, liability, and general insurance–instances in which coverage is generally provided on a renewable period, (such as yearly). Coverage can be canceled at the end of the period by either party.

Pensions

In the pension industry, actuarial science compares the costs of alternative strategies with regard to the design, funding, accounting, administration, and maintenance or redesign of pension plans. A pension plan is a defined-benefit plan, which is a type of retirement plan involving contributions from the employer to be set aside and paid out to the employees upon retirement.

Short-term and long-term bond rates greatly influence pension plans and their investment strategies. Bonds are debt instruments issued by governments and corporations that typically pay a periodic interest rate. For example, in a low-interest-rate environment, a pension plan might have difficulty earning income from the bonds that it has invested in, which increases the probability that the pension plan could run out of money.

Other factors impacting a pension plan’s viability include benefit arrangements, collective bargaining, the employer’s competitors, and changing demographics of the workforce. Tax laws and the policies of the Internal Revenue Service (IRS) regarding the calculation of pension surpluses also impact the finances of a pension plan. Additionally, economic conditions and trends in the financial markets can impact the probability of a pension plan remaining funded.

Universities and Professional Certifications

According to the Bureau of Labor Statistics, the number of actuaries employed is expected to grow 21% from 2021 to 2031. For this reason, many universities offer educational degrees and courses on actuarial science. In addition, there are professional designations for those interested in pursuing the field.

Universities

The Society of Actuaries identifies and reports colleges that meet one of three levels of recognition:

• UCAP-Introduction Curriculum: Universities that maintain course requirements for two professional actuarial exams in addition to having met other approved course requirements.
• UCAP-Advanced Curriculum: Universities that maintain course requirements for four professional exams in addition to having met other approved course requirements.
• Center of Actuarial Excellence: Universities that maintain eight specific requirements in connection with a variety of matters. This is the highest tier of competency identified by the SOA for a university.

As of December 2022, there are roughly 25 Center of Actuarial Excellence schools across the United States, Canda, Australia, Singapore, the United Kingdom, and China. Within the U.S., these schools include but are not limited to Brigham Young, Georgia State, Purdue, Connecticut, and Michigan.

Professional Designations and Credentials

There are a number of different professional designations an actuary can pursue to further gain credibility and proficiency in their field. The Casualty Actuarial Society offers the Associate (ACAS) and Fellow (FCAS) membership levels, each of the two with escalating requirements. For example, the ACAS credential can be achieved after passing six exams, while the FCAS is earned after nine exams. Areas of focus for the FCAS exam include:

• Probability
• Financial Mathematics
• Financial Economics
• Modern Actuarial Statistics
• Basic Techniques for Ratemaking and Estimating Claim Liabilities
• Regulation & Financial Reporting
• Policy Liabilities, Insurance Company Valuation, and Enterprise Risk Management
• Advanced Ratemaking

The Society of Actuaries promotes several different actuarial exams to demonstrate competency in the field.

• An Associate of the Society of Actuaries (ASA) demonstrates knowledge of fundamental concepts of modeling and managing risk. The examination requirements are changing as of Spring 2023, and the list of required examinations includes topics on predictive analysis, economics, probabilities, and financial markets.
• A Chartered Enterprise Risk Analyst (CERA) specializes in having knowledge in identifying, measuring, and managing risk in risk-bearing enterprises. Similar to the ASA requirements, the CERA requirements include a professional course covering code of conduct.
• A Fellow of the Society of Actuaries (FSA) demonstrates knowledge of financial decisions involving pensions, life insurance, health insurance, and investments. FSAs also must demonstrate in-depth knowledge and the application of appropriate techniques to these various areas.

The Bottom Line

Actuarial science is the study of mathematically predicting the probability of something happening in the future and assigning that outcome a financial value. Companies, pension funds, and insurance agencies rely on actuaries to develop models to assess areas of risk and devise policies to mitigate potential future challenges.

What Is an Auditor’s Opinion?

An auditor’s opinion is a certification that accompanies financial statements. It is based on an audit of the procedures and records used to produce the statements and delivers an opinion as to whether material misstatements exist in the financial statements. An auditor’s opinion may also be called an accountant’s opinion.

Understanding Auditor’s Opinions

An auditor’s opinion is presented in an auditor’s report. The audit report begins with an introductory section outlining the responsibility of management and the responsibility of the audit firm. The second section identifies the financial statements on which the auditor’s opinion is given. A third section outlines the auditor’s opinion on the financial statements. Although it is not found in all audit reports, a fourth section may be presented as a further explanation regarding a qualified opinion or an adverse opinion.

For audits of companies in the United States, the opinion may be an unqualified opinion in accordance with generally accepted accounting principles (GAAP), a qualified opinion, or an adverse opinion. The audit is performed by an accountant who is independent of the company being audited.

Unqualified Opinion Audit

An unqualified opinion is also known as a clean opinion. The auditor reports an unqualified opinion if the financial statements are presumed to be free from material misstatements. In addition, an unqualified opinion is given over the internal controls of an entity if management has claimed responsibility for its establishment and maintenance, and the auditor has performed fieldwork to test its effectiveness.

Qualified Audit

A qualified opinion is given when a company’s financial records have not followed GAAP in all financial transactions. Although the wording of a qualified opinion is very similar to an unqualified opinion, the auditor provides an additional paragraph including deviations from GAAP in the financial statements and points out why the auditor report is not unqualified.

A qualified opinion may be given due to either a limitation in the scope of the audit or an accounting method that did not follow GAAP. However, the deviation from GAAP is not pervasive and does not misstate the financial position of the company as a whole.

Adverse Opinion

The most unfavorable opinion a business may receive is an adverse opinion. An adverse opinion indicates financial records are not in accordance with GAAP and contain grossly material and pervasive misstatements. An adverse opinion may be an indicator of fraud. Investors, lenders, and other financial institutions do not typically accept financial statements with adverse opinions as part of their debt covenants.

Disclaimer of Opinion

In the event that the auditor is unable to complete the audit report due to the absence of financial records or insufficient cooperation from management, the auditor issues a disclaimer of opinion. This is referred to as a scope limitation and is an indication that no opinion over the financial statements was able to be determined. A disclaimer of opinion is not an opinion itself.

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.

What Is an Account Statement?

An account statement is a periodic summary of account activity with a beginning date and an ending date. The most commonly known are checking account statements, usually provided monthly, and brokerage account statements, which are provided monthly or quarterly. Monthly credit card bills are also considered account statements.

Understanding Account Statements

Account statements refer to almost any official summary of an account, wherever the account is held. Insurance companies may provide account statements summarizing paid-in cash values, for example. Statements can be generated for almost any type of accounts that represent ongoing transactions where funds are repeatedly exchanged. This can include online payment accounts such as PayPal, credit card accounts, brokerage accounts, and savings accounts.

Utility companies, as well as telephone and subscription television service providers, usually generate account statements for their customers detailing their usage and any overages during the payment cycle. Such statements typically list debits paid, incoming funds or credits received by the account holder, and fees associated with maintaining the account. For example, certain types of savings accounts might incur regular maintenance fees unless a certain minimum balance of funds is maintained in the account. Cable television subscriptions may include state taxes and other surcharges that are included in providing regular service.

How Account Statements Are Used

Account statements should be scrutinized for accuracy, and historical statements are critical for budgeting. A credit or loan account statement, for example, may show not only the outstanding balance due but the interest rate charged on that debt and any fees that have been added during the payment cycle. This can include late charges for payments not received by their due date as well as overdraft fees when bank account holders overspend. Your account statements are a window into your finances.

The statement may also list financial information that relates to the account holder such as their credit score, or the estimated time it will take to completely pay off a debt via installment payments. Alerts and notices to the account holder may also appear on these statements, calling attention to matters with the account that need to be addressed, such unusual charges that should be reviewed and verified.

Red Flags on Account Statements

Anomalous items on an account statement may be a sign the account has been compromised, perhaps through a stolen credit or debit card or through identity thieves who gained access to account information. For example, an account holder or the financial institution might spot a charge for concert tickets or a luxury item that seems out of the ordinary. Account-holders may be able to dispute such out-of-place charges and file a claim that they did not make the purchase themselves. Reviewing your account statements as they come in is a good financial habit that can catch these red flags before they become a financial disaster.