Audit risk is the risk that financial statements are materially incorrect, even though the audit opinion states that the financial reports are free of any material misstatements.
Key Takeaways
Audit risk is the risk that financial statements are materially incorrect, even though the audit opinion states that the financial reports are free of any material misstatements.
Audit risk may carry legal liability for a certified public accountancy (CPA) firm performing audit work.
Auditing firms carry malpractice insurance to manage audit risk and the potential legal liability.
The two components of audit risk are risk of material misstatement and detection risk.
Understanding Audit Risk
The purpose of an audit is to reduce the audit risk to an appropriately low level through adequate testing and sufficient evidence. Because creditors, investors, and other stakeholders rely on the financial statements, audit risk may carry legal liability for a certified public accountancy (CPA) firm performing audit work.
Over the course of an audit, an auditor makes inquiries and performs tests on the general ledger and supporting documentation. If any errors are caught during the testing, the auditor requests that management propose correcting journal entries.
At the conclusion of an audit, after any corrections are posted, an auditor provides a written opinion as to whether the financial statements are free of material misstatement. Auditing firms carry malpractice insurance to manage audit risk and the potential legal liability.
Types of Audit Risk
The two components of audit risk are the risk of material misstatement and detection risk. Assume, for example, that a large sporting goods store needs an audit performed, and that a CPA firm is assessing the risk of auditing the store’s inventory.
Risk of Material Misstatement
Material misstatement risk is the risk that the financial reports are materially incorrect before the audit is performed. In this case, the word “material” refers to a dollar amount that is large enough to change the opinion of a financial statement reader, and the percentage or dollar amount is subjective. If the sporting goods store’s inventory balance of $1 million is incorrect by $100,000, a stakeholder reading the financial statements may consider that a material amount. The risk of material misstatement is even higher if there is believed to be insufficient internal controls, which is also a fraud risk.
Detection Risk
Detection risk is the risk that the auditor’s procedures do not detect a material misstatement. For example, an auditor needs to perform a physical count of inventory and compare the results to the accounting records. This work is performed to prove the existence of inventory. If the auditor’s test sample for the inventory count is insufficient to extrapolate out to the entire inventory, the detection risk is higher.
“All risks” refers to a type of insurance coverage that automatically covers any risk that the contract does not explicitly omit. For example, if an “all risk” homeowner’s policy does not expressly exclude flood coverage, then the house will be covered in the event of flood damage.
This type of policy is found only in the property-casualty market.
Key Takeaways
All risks is a comprehensive insurance policy offered in the property-casualty market.
All risks and named perils are two types of insurance commonly offered to homeowners and business owners.
Insurance that allows for all risks means the policyholder can seek compensation for any events that the contract hasn’t directly ruled out as being covered.
Policyholders can usually pay more to have a rider or floater added to the contract that would cover a specific event that was ruled out.
All risks insurance differs from named perils insurance, in which the policyholder can only seek compensation for events that are specified in the policy.
Understanding All Risks
Insurance providers generally offer two types of property coverage for homeowners and businesses—named perils and “all risks.” A named perils insurance contract only covers the perils stipulated explicitly in the policy.
For example, an insurance contract might specify that any home loss caused by fire or vandalism will be covered. Therefore, an insured who experiences a loss or damage caused by a flood cannot file a claim to his or her insurance provider, as a flood is not named as a peril under the insurance coverage. Under a named perils policy, the burden of proof is on the insured.
An all risks insurance contract covers the insured from all perils, except the ones specifically excluded from the list. Contrary to a named perils contract, an all risks policy does not name the risks covered, but instead, names the risks not covered. In so doing, any peril not named in the exclusions list is automatically covered.
The most common types of perils excluded from “all risks” include earthquake, war, government seizure or destruction, wear and tear, infestation, pollution, nuclear hazard, and market loss. An individual or business who requires coverage for any excluded event under “all risks” may have the option to pay an additional premium, known as a rider or floater, to have the peril included in the contract.
“All risks” are also called open perils, all perils, or comprehensive insurance.
Burden of Proof
The trigger for coverage under an “all risks” policy is physical loss or damage to property. An insured must prove physical damage or loss has occurred before the burden of proof shifts to the insurer, who then has to prove that an exclusion applies to the coverage.
For example, a small business that experienced a power outage may file a claim citing physical loss. The insurance company, on the other hand, might reject the claim stating that the company experienced a loss of income from a mere loss of property use, which is not the same thing as a physical loss of property.
Special Considerations
Because “all risks” is the most comprehensive type of coverage available and protects the insured from a greater number of possible loss events, it is priced proportionately higher than other types of policies. The cost of this type of insurance should, therefore, be measured against the probability of a claim.
It is possible to have named perils and “all risks” in the same policy. For example, an insured may have a property insurance policy that has all risks coverage on the building and named perils on his personal property. Everyone should read the fine print of any insurance agreement to ensure that they understand what is excluded in the policy.
Also, just because an insurance policy is termed “all risks” does not mean that it covers “all risks” since the exclusions reduce the level of coverage that is offered. Make sure you look for the exclusions in any prospective policy.
What Is the Meaning of All Risk?
All risk is a type of insurance product that requires a risk to be explicitly stated for it to not be covered. For example, if the contract does not state “tree damage” as an omitting risk, then if a tree were to fall on the insured property under an all risk policy, since the tree was not explicitly mentioned, the damage would be covered.
What Are the 4 Major Types of Insurance?
There are insurance products for almost everything, but for most people, there are four types of insurance products that are seen more than any other. Life insurance, auto insurance, health insurance, and long-term disability insurance are those that cover most of an individual’s risk factors. Once someone owns significant property like a house or something high-value like jewelry or other collector items, they will need additional policies tailored to these individual items. However, most people who rent will own the four major types listed above.
What Are All Risk Perils?
All risk perils is another name for all risk insurance as it relates to individual risks. Named perils is an insurance product that names what is insured in case of an accident. All risks, assuming there are no perils mentioned, could be considered all risk perils since all perils are assumed as risk (under the policy). However, these are rare as they put undue risk acceptance on the insurer, and it is much more common to see many perils listed, even on an all risks policy.
The Bottom Line
All risk insurance, also called all risk coverage, is an insurance product that covers any incident that isn’t explicitly mentioned. These policies assume a good deal of risk for the insurer and are less common than named risk coverage, which states exactly what is covered, versus stating only what is to be omitted (which is the case with all risk).
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.
Key Takeaways
Actuarial science assesses financial risks in the insurance and finance fields, using mathematical and statistical methods.
Actuarial science applies probability analysis and statistics to define, analyze, and solve the financial impact of uncertain future events.
Actuarial science helps insurance companies forecast the probability of an event occurring to determine the funds needed to pay claims.
The Casualty Actuarial Society (CAS) and Society of Actuaries (SOA) promote several professional certifications for actuaries to pursue beyond a bachelor’s degree in actuarial science.
The most recent salary information from the Bureau of Labor Statistics shows actuaries earned an average salary of nearly $106,000 as of May 2021.
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.
Actuaries may also work in the public sector to assist with proposed changes to Social Security, Medicare, or other programs.
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.
Compensation
According to the latest BLS wage data, the median annual wage for actuaries in 2021 was $105,900.
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.
Is Actuarial Science Difficult?
Actuarial science is a difficult profession. Actuarial exams usually last between 3 and 5 hours, and each requires rigorous preparation. Candidates must often have a bachelor’s degree, and it make take up to a decade for a candidate to complete all training and exams.
What Type of Math Do Actuaries Use?
Actuaries often have a background in probability, statistics, and financial mathematics. Most often, an actuary will assess the probability of an event happen, then apply statistical methods to determine what the financial impact of that outcome will be. Actuaries usually do not use calculus at work, though calculus may be a prerequisite to meeting other course requirements.
How Long Does It Take To Become an Actuary?
For most, it may take up to a decade or longer to become an actuary. A bachelor’s degree in actuarial science may take between 3 to 5 years, and it may take at least another several years to pass rigorous professional actuarial exams.
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.
The annual percentage yield (APY) is the real rate of return earned on an investment, taking into account the effect of compounding interest. Unlike simple interest, compounding interest is calculated periodically and the amount is immediately added to the balance. With each period going forward, the account balance gets a little bigger, so the interest paid on the balance gets bigger as well.
Key Takeaways
APY is the actual rate of return that will be earned in one year if the interest is compounded.
Compound interest is added periodically to the total invested, increasing the balance. That means each interest payment will be larger, based on the higher balance.
The more often interest is compounded, the higher the APY will be.
APY has a similar concept as annual percentage rate (APR), but APR is used for loans.
The APY on checking, savings, or certificate of deposit holdings will vary across product and may have a variable or fixed rate.
APR vs. APY: What’s the Difference?
Formula and Calculation of APY
APY standardizes the rate of return. It does this by stating the real percentage of growth that will be earned in compound interest assuming that the money is deposited for one year. The formula for calculating APY is:
Where:
r = period rate
n = number of compounding periods
What Annual APY Can Tell You
Any investment is ultimately judged by its rate of return, whether it’s a certificate of deposit (CD), a share of stock, or a government bond. The rate of return is simply the percentage of growth in an investment over a specific period of time, usually one year. But rates of return can be difficult to compare across different investments if they have different compounding periods. One may compound daily, while another compounds quarterly or biannually.
Comparing rates of return by simply stating the percentage value of each over one year gives an inaccurate result, as it ignores the effects of compounding interest. It is critical to know how often that compounding occurs, since the more often a deposit compounds, the faster the investment grows. This is due to the fact that every time it compounds the interest earned over that period is added to the principal balance and future interest payments are calculated on that larger principal amount.
Comparing the APY on 2 Investments
Suppose you are considering whether to invest in a one-year zero-coupon bond that pays 6% upon maturity or a high-yield money market account that pays 0.5% per month with monthly compounding.
At first glance, the yields appear equal because 12 months multiplied by 0.5% equals 6%. However, when the effects of compounding are included by calculating the APY, the money market investment actually yields (1 + .005)^12 – 1 = 0.06168 = 6.17%.
Comparing two investments by their simple interest rates doesn’t work as it ignores the effects of compounding interest and how often that compounding occurs.
APY vs. APR
APY is similar to the annual percentage rate (APR) used for loans. The APR reflects the effective percentage that the borrower will pay over a year in interest and fees for the loan. APY and APR are both standardized measures of interest rates expressed as an annualized percentage rate.
However, APY takes into account compound interest while APR does not. Furthermore, the equation for APY does not incorporate account fees, only compounding periods. That’s an important consideration for an investor, who must consider any fees that will be subtracted from an investment’s overall return.
Example of APY
If you deposited $100 for one year at 5% interest and your deposit was compounded quarterly, at the end of the year you would have $105.09. If you had been paid simple interest, you would have had $105.
The APY would be (1 + .05/4) * 4 – 1 = .05095 = 5.095%.
It pays 5% a year interest compounded quarterly, and that adds up to 5.095%. That’s not too dramatic. However, if you left that $100 for four years and it was being compounded quarterly then the amount your initial deposit would have grown to $121.99. Without compounding it would have been $120.
X = D(1 + r/n)n*y
= $100(1 + .05/4)4*4
= $100(1.21989)
= $121.99
where:
X = Final amount
D = Initial Deposit
r = period rate
n = number of compounding periods per year
y = number of years
Special Considerations
Compound Interest
The premise of APY is rooted in the concept of compounding or compound interest. Compound interest is the financial mechanism that allows investment returns to earn returns of their own.
Imagine investing $1,000 at 6% compounded monthly. At the start of your investment, you have $1,000.
After one month, your investment will have earned one month worth of interest at 6%. Your investment will now be worth $1,005 ($1,000 * (1 + .06/12)). At this point, we have not yet seen compounding interest.
After the second month, your investment will have earned a second month of interest at 6%. However, this interest is earned on both your initial investment as well as your $5 interest earned last month. Therefore, your return this month will be greater than last month because your investment basis will be higher. Your investment will now be worth $1,010.03 ($1,005 * (1 + .06/12)). Notice that the interest earned this second month is $5.03, different from the $5.00 from last month.
After the third month, your investment will earn interest on the $1,000, the $5.00 earned from the first month, and the $5.03 earned from the second month. This demonstrates the concept of compound interest: the monthly amount earned will continually increase as long as the APY doesn’t decrease and the investment principal is not reduced.
Banks in the U.S. are required to include the APY when they advertise their interest-bearing accounts. That tells potential customers exactly how much money a deposit will earn if it is deposited for 12 months.
Variable APY vs. Fixed APY
Savings or checking accounts may have either a variable APY or fixed APY. A variable APY is one that fluctuates and changes with macroeconomic conditions, while a fixed APY does not change (or changes much less frequently). One type of APY isn’t necessarily better than the other. While locking into a fixed APY sounds appealing, consider periods when the Federal Reserve is raising rates and APYs increase each month.
Most checking, savings, and money market accounts have variable APYs, though some promotional bank accounts or bank account bonuses may have a higher fixed APY up to a specific level of deposits. For example. a bank may reward 5% APY on the first $500 deposited, then pay 1% APY on all other deposits.
APY and Risk
In general, investors are usually awarded higher yields when they take on greater risk or agree to make sacrifices. The same can be said regarding the APY of checking, saving, and certificate of deposits.
When a consumer holds money in a checking account, the consumer is asking to have their money on demand to pay for expenses. At a given notice, the consumer may need to pull out their debit card, buy groceries, and draw down their checking account. For this reason, checking accounts often have the lowest APY because there is no risk or sacrifice for the consumer.
When a consumer holds money in a savings account, the consumer may not have immediate need. The consumer may need to transfer funds to their checking account before it can be used. Alternatively, you cannot write checks from normal savings accounts. For this reason, savings accounts usually have higher APYs than checking accounts because consumers face greater limits with savings accounts.
Last, when consumers hold a certificate of deposit, the consumer is agreeing to sacrifice liquidity and access to funds in return for a higher APY. The consumer can’t use or spend the money in a CD (or they can after paying a penalty to break the CD). For this reason, the APY on a CD is highest of three as the consumer is being rewarded for sacrificing immediate access to their funds.
What Is APY and How Does It Work?
APY is the annual percent yield that reflects compounding on interest. It reflects the actual interest rate you earn on an investment because it considers the interest you make on your interest.
Consider the example above where the $100 investment yields 5% compounded quarterly. During the first quarter, you earn interest on the $100. However, during the second quarter, you earn interest on the $100 as well as the interest earned in the first quarter.
What Is a Good APY Rate?
APY rates fluctuate often, and a good rate at one time may no longer be a good rate due to shifts in macroeconomic conditions. In general, when the Federal Reserve raises interest rates, the APY on savings accounts tends to increase. Therefore, APY rates on savings accounts are usually better when monetary policy is tight or tightening. In addition, there are often low-cost, high-yield savings accounts that consistently deliver competitive APYs.
How Is APY Calculated?
APY standardizes the rate of return. It does this by stating the real percentage of growth that will be earned in compound interest assuming that the money is deposited for one year. The formula for calculating APY is: (1+r/n)n – 1, where r = period rate and n = number of compounding periods.
How Can APY Assist an Investor?
Any investment is ultimately judged by its rate of return, whether it’s a certificate of deposit, a share of stock, or a government bond. APY allows an investor to compare different returns for different investments on an apples-to-apples basis, allowing them to make a more informed decision.
What Is the Difference Between APY and APR?
APY calculates that rate earned in one year if the interest is compounded and is a more accurate representation of the actual rate of return. APR includes any fees or additional costs associated with the transaction, but it does not take into account the compounding of interest within a specific year. Rather, it is a simple interest rate.
The Bottom Line
APY in banking is the actual rate of return you will earn on your checking or savings account. As opposed to simple interest calculations, APY considers the compounding effect of prior interest earned generating future returns. For this reason, APY will often be higher than simple interest, especially if the account compounds often.
