Second Actuarial Exam:
Financial Mathematics

Learning Objectives

• Candidates will know definitions of key terms of financial mathematics: inflation; rates of interest [simple, compound (interest and discount), real, nominal, effective, dollar-weighted, time-weighted, spot, forward], term structure of interest rates; force of interest (constant and varying); equivalent measures of interest; yield rate; principal; equation of value; present value; future value; current value; net present value; accumulation function; discount function; annuity certain (immediate and due); perpetuity (immediate and due); stocks (common and preferred); bonds (including zero-coupon bonds); other financial instruments such as mutual funds, and guaranteed investment contracts.

  Specifically, candidates are expected to demonstrate the ability to:

  • Choose the term, given a definition.
  • Define a given term.
  • Determine an equation of value, given a valuation problem involving one or more sets of cash flows at specified times.
• Candidates will understand key procedures of financial mathematics: determining equivalent measures of interest; discounting; accumulating; determining yield rates; estimating the rate of return on a fund; and amortization.

  Specifically, candidates are expected to demonstrate the ability to:

• Calculate the equivalent annual effective rate of interest or discount, given a nominal annual rate and a frequency of interest conversion, discrete or continuous, other than annual.
• Calculate the equivalent effective rate of interest or discount per payment period given a payment period different from the interest conversion period.
• Estimate the interest return on a fund.
• Calculate the appropriate equivalent single value [present value, net present value, future (accumulated) value or combination], given a set of cash flows (level or varying), where the cash flows may occur as frequently or more frequently than interest or discount is accrued, an appropriate term structure of interest rates, the method of crediting interest (e.g., portfolio or investment year) as necessary, an appropriate set of inflation rates as necessary, and accounting for reinvestment interest rates as necessary.
For example:
• Calculate the loan amount or outstanding loan balance, given a set of loan payments (level or varying) and the desired yield rate (level or varying).
• Calculate the price of a bond (callable or non-callable), given the bond coupons, the redemption value, the term of the bond (constant or varying), the coupon interest rate, and the desired yield rate (level or varying).
• Calculate the value of a stock, given the pattern of dividends and the desired yield rate (level or varying).
• Calculate the net present value, given a set of investment contributions and investment returns.
• Calculate a unique yield rate, when it exists, given a set of investment cash flows.
• Calculate the amount(s) of investment contributions, given there is more than one contribution, and given a set of yield rates, the amount(s) and timing of investment return(s), and the desired timing of the investment contributions.
• Calculate the amount(s) of investment returns, given there is more than one return, and given a set of yield rates, the amount(s) and timing of investment contribution(s) and the desired timing of the investment returns; for example:
  • Calculate loan payments, given the loan amount(s), the term of the loan, and the desired yield rate (level or varying).
  • Calculate the principal and interest portions of a loan payment, given the loan amount, the set of loan payments (level or varying), and a set of interest rates (level or varying).
  • Calculate bond coupons or redemption values, given the bond price, the term of the bond, and the desired yield rate (level or varying).
• Calculate the term of an investment, given a set of cash flows (level or varying), and a set of interest rates (level or varying); for example:
  • Calculate the length of time required to accumulate a given amount, given the yield rate and an initial amount.
  • Calculate the length of time to repay a given loan amount, given the loan payments and the loan interest rate(s).
  • Calculate the time to maturity of a bond, given the price of the bond, the coupon payments, redemption value, and yield rate.
• Candidates will know definitions of key terms of modern financial analysis at an introductory and intuitive level, and be able to complete basic calculations involving such terms: yield curves, spot rates, forward rates, duration, convexity, and immunization.

  Specifically, candidates are expected to demonstrate the ability to:

• Choose the term, given a definition.
• Write the definition, given a term.
• Perform calculations such as:
• measuring interest rate risk using duration and convexity.
• basic immunization calculations.
• cash flow matching calculations (the terms dedication and asset-liability matching are used in the readings as equivalent to cash flow matching).
• Candidates will know definitions of key terms of financial economics at an introductory level: derivatives, forwards, futures, short and long positions, call and put options, spreads, collars, hedging, arbitrage, and swaps.

  Specifically, candidates are expected to demonstrate the ability to:

• Explain why firms might care about risk management.
• Evaluate the risk/return characteristics of the basic building blocks of financial derivatives: forward contracts, call and put options.
• Identify associated hedging and investment strategies.
• Explain the use of derivatives as risk management tools.
• Explain the cash-flow characteristics of forwards, futures and swaps.
• Use the concept of no-arbitrage to determine the theoretical value of forwards, futures and swaps.
• Manage financial risk through use of forwards, futures and swaps.

Note that probability-based calculations for applications of financial mathematics are in Exam 3.

Text References for Exam 2

Knowledge and understanding of the financial mathematics concepts are significantly enhanced through working out problems based on those concepts. Thus, in preparing for the Financial Mathematics exam, whichever source textbooks candidates choose to use, candidates are encouraged to work out the textbook exercises related to the listed readings.

Candidates may use either course of reading shown below:

Option A

Broverman, S.A.; Mathematics of Investment and Credit (Third Edition), 2004, ACTEX Publications, Chapters 1 (1.1-1.6); 2 (2.1-2.4 excluding 2.4.2, and 2.4.3); 3 (3.1-3.3 excluding pages 188-189); 4 (4.1-4.3.1); 5 (5.1-5.3 excluding 5.1.4, and 5.3.2); 6 (6.1-6.3 excluding 6.2); 7 (7.1-7.2); and 8 (8.2.1, 8.2.4, and 8.3.1-8.3.3).

McDonald, R.L., Derivatives Markets (Second Edition), 2006, Addison Wesley, Chapters 1 (1.1-1.4); 2 (2.1-2.6 and Appendix 2.A); 3 (3.1-3.5), 4 (4.1-4.4), 5 (5.1-5.4 and Appendix 5.B), 8 (8.1-8.2).

Option B

Ruckman, C.; and Francis, J., Financial Mathematics: A Practical Guide for Actuaries and other Business Professionals (Second Edition), 2005, BPP Professional Education, Chapters 1; 2; 3 (3.1-3.9); 4 (4.1-4.5); 5; 6 (6.1-6.3); 7 (7.1-7.9); and 8 (8.1-8.3).

McDonald, R.L., Derivatives Markets (Second Edition), 2006, Addison Wesley, Chapters 1 (1.1-1.4); 2 (2.1-2.6 and Appendix 2.A); 3 (3.1-3.5), 4 (4.1-4.4), 5 (5.1-5.4 and Appendix 5.B), 8 (8.1-8.2).

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Suggested Study Materials

• Arcones Study Manual for SOA Exam FM/CAS Exam 2 , by Miguel A. Arcones. Available at Actex Publications and The Actuarial Bookstore.

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Sample Questions

Here there are sample questions for the second actuarial exam: 2001-2003 questions; Sample Questions, solutions; May 2005, solutions; November 2005; solutions. Sample questions and solutions for Derivatives Markets.

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Party the Actuarial Association

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