Introduction to Actuarial Science PDF

INTRODUCTION TO ACTUARIAL SCIENCE WEEK 1 1 Introduction to Actuarial Science Objective Learning Outcome provides a foundational understanding of actuarial science, focusing on the mathematical and statistical principles...

INTRODUCTION TO ACTUARIAL SCIENCE WEEK 1 1 Introduction to Actuarial Science Objective Learning Outcome provides a foundational understanding of actuarial science, focusing on the mathematical and statistical principles that underpin the profession. 2  INTRODUCTION Name: Susana Yamoah Position: Lecturer Education TA: Solomon Baah Self-introduction - Your expectations 3  GRADING POLICY The course grade would be based on a final exam, quizzes and class participation as follows: Final exam (3- hour): 60% Quiz / Assignment 30% Class participation and conduct 10% ✓punctuality, attendance, good questions and class contributions 4 Pre-Requisites Introductory Basic calculus statistics 5  FOCUS Definition and scope Core areas of application Role of Actuaries Simple and Compound Interest 6 Definition and scope Actuarial science is a quantitative discipline that applies mathematical and statistical techniques to assess financial risk in the insurance, pensions, and other industries. Actuaries use their expertise to calculate premiums, reserves, and other financial metrics, ensuring the long-term solvency and stability of these organizations. 7  The goal of actuarial work is to manage financial risks through the evaluation and forecasting of uncertain future events. Definition and scope Actuarial science spans several interrelated subjects, including mathematics, probability theory, statistics, finance, economics, and computer science. 8  Definition and scope The scope of actuarial science is broad and encompasses a wide range of applications, including Insurance: Calculating premiums for life, health, property and other insurance products Pensions: Analyzing retirement risks and developing risk mitigation strategies Healthcare: Modeling healthcare costs and designing cost- effective insurance plans Investment: Assessing the risk and return of investments Risk Management: Identifying, quantifying, and managing various types of risk 9  Role of Actuaries Actuaries are professionals who use their expertise in mathematics, statistics, and finance to assess financial risk. They play a crucial role in various industries, including insurance, pensions, healthcare, and investment. Employment Sectors Insurance companies, pension funds, consultancy firms, government agencies, and financial institutions. Actuarial Jobs Pricing actuary, reserving actuary, pension actuary, enterprise risk manager, investment actuary, and consultant. 10  Skills and Competencies Mathematical and Statistical Skills Calculus: Understanding derivatives, integrals, and differential equations is essential for actuarial modeling. Probability theory: Understanding probability distributions, statistical inference, and hypothesis testing is crucial for analyzing risk and uncertainty. Statistics: Knowledge of statistical methods, such as regression analysis, time series analysis, and survival analysis, is necessary for modeling actuarial data. Numerical methods: Proficiency in numerical methods is required for solving complex actuarial problems. 11 Skills and Competencies Financial Modeling and Analysis Time value of money: Understanding the concept of present and future values of money is fundamental for actuarial calculations. Interest theory: Knowledge of interest rates, annuities, and perpetuities is essential for financial modeling. Cash flow analysis: Actuaries must be able to analyze cash inflows and outflows to assess an organization's financial health. Financial ratios: Understanding financial ratios, such as liquidity ratios, profitability ratios, and solvency ratios, is helpful for evaluating an organization's financial performance. 12  Skills and Competencies Risk Assessment and Management Risk identification: Identifying potential risks that could impact an organization's financial performance. Risk quantification: Using statistical and mathematical techniques to assess the probability and severity of different types of risk. Risk management: Developing strategies to manage risk, such as risk transfer (e.g., through reinsurance), risk avoidance, or risk mitigation. Catastrophe modeling: Developing models to assess the potential financial impact of catastrophic events. 13  Skills and Competencies Communication and Interpersonal Skills Written communication: Writing clear and concise reports, presentations, and memos. Oral communication: Delivering effective presentations and participating in discussions. Interpersonal skills: Building relationships with colleagues, clients, and stakeholders. Negotiation skills: Negotiating contracts and resolving disputes. 14  Financial Mathematics Time Value of Money This is a fundamental financial concept that states that money available today is worth more than the same amount of money in the future Interest: the compensation one gets for lending a certain asset (usually expressed in monetary terms) for a period of time. The asset being lent out is called the capital/ principal 15  Simple interest is a method of calculating interest where the interest earned on the principal remains constant over the entire loan or investment period. Components of simple interest: Principal (P): The initial amount of money borrowed or invested. Interest rate (r): The percentage charged or earned Simple on the principal per period. Time period (r): The length of time for which the Interest money is borrowed or invested Formula I=P×r×t The total investment/ Accumulated Value (A) at the end of the period will be A = P(1+rt) 16  Suppose you invest $5,000 in a savings account that earns 4% simple interest annually for 3 years. How much interest will you earn, and what is the total amount at the Simple end of the investment period? Interest- Examples Suppose you put GH1000 in a savings account paying simple interest at 9% per annum for one year. Then, you withdraw the money with interest and put it for one year in another account paying simple interest at 9%. How much do you have in the end? 17  Applications Short-Term Loans Savings Accounts Bonds and Treasury Bills Trade Credit 18  Limitations Simple interest does not consider the effects of inflation, which can erode the purchasing power of future earnings. Not Suitable for Long-Term Investments 19  Compound Interest This is a method of calculating interest where the interest earned on the principal is added to the principal, and then the interest is calculated on the new total. Components of compound interest Principal: The initial amount of money borrowed or invested. Interest rate: The percentage charged or earned on the principal. Time period: The length of time for which the money is borrowed or invested. Compounding frequency: The number of times per year that interest is calculated and added to the principal. 20  Compound Interest Formula is given by; 𝑟 𝑛𝑡 𝐴=𝑃 1 + 𝑛 Where; A = Future value of the investment/loan P = Principal amount r = Annual nominal interest rate (as a decimal) n = Number of compounding periods per year; annually, quarterly, monthly, etc t = Time the money is invested or borrowed, in years Accumulated Interest (I) = A - P 21 Compound Interest You invest $1,000 at an interest rate of 6% compounded annually for 5 years. What is the future value of the investment? Solution 𝑟 𝑛𝑡 𝐴=𝑃 1 + 𝑛 ◦ P= 1000, r= 0.06, t= 5, n= 1 0.06 5 𝐴 = 1000 1 + = $1,338.23 1 Interest earned (I) is $338.23 22 Compound Interest- Continuous Compounding When interest is compounded continuously, it is being earned and added to the principal at every infinitesimal moment. Formula is given by; 𝐴 = 𝑃 × 𝑒 𝑟𝑡 Where 𝑒 is Euler’s number (approximately 2.71828) Example: If you invest $5,000 at a 6% annual interest rate compounded continuously, how much will you have after 10 years? 23 Compound Interest- Continuous Compounding Solution 𝐴 = 𝑃 × 𝑒 𝑟𝑡 P = 5000, r = 0.06 , t = 10 A = $9,110.59 24 Try Work If you invest GH1,500 at a 5% annual interest rate compounded monthly, how much will you have after 3 years? You want to have $5,000 in 5 years for a down payment on a car. If you can invest at a 4% annual interest rate compounded quarterly, how much should you invest today? At what annual interest rate compounded monthly will $2,000 grow to $2,500 in 4 years? 25 Try Work If you invest GH 500 at a 7% annual interest rate compounded continuously, how much will you have after 10 years? At what annual interest rate compounded continuously will $1,000 grow to $2,000 in 8 years? 26  Discounting is the process of determining the present value of a future cash flow, given a specific interest or discount rate. Discounting In essence, it is the reverse of compounding. The time value of money principle underlies discounting, which states that a sum of money today is worth more than the same sum in the future because of its potential earning capacity. 27  Discounting Formula is given by; 𝐹𝑉 𝑃𝑉 = (1+𝑟)𝑡 Where; PV = Present Value (today's value of the future sum) FV = Future Value (the amount to be received in the future) r = Discount rate (interest rate as a decimal) t = Time period (in years) 28 Applications of Discounting in Finance Bond Pricing: A bond promises to pay $1,000 at maturity in 10 years. If the market interest rate is 8%, what is the bond's current price? 29 Applications of Discounting in Finance Investment Analysis An investor is analyzing an investment that is expected to generate the following cash flows over the next 4 years: Year 1: $8,000, Year 2: $10,000, Year 3: $12,000, Year 4: $15,000 The investor's required rate of return is 7%. Question: What is the total present value of these cash flows (i.e., the discounted cash flow value)? 30 Applications of Discounting in Finance You are evaluating an investment that requires an initial outlay of $25,000 today and will return $30,000 in 3 years. What is the discount rate that will make the present value of the future return equal to the initial investment? An investment offers a perpetual payment of $2,500 per year. If your required rate of return is 8%, what is the maximum amount you should pay for this investment? What is the present value of the perpetuity? 𝑃 ◦ Hint: perpetuity formula= 𝑃𝑉 = 𝑟 Where P=Perpetual payment, r= rate of return 31