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ExamSuccess.ca Brian Y. Gordon, CFA, CFP, CIM, MBA, FCSI Exam Preparation & Investment Sales Training 1 Email: [email protected]

Level 1

Study Session 2

Quantitative Methods (QM) READINGS: 1. The Time Value of Money 2. Discounted Cash Flow Applications 3. Statistical Concepts and Market Returns 4. Probability Concepts


• Expect to see 28 questions that relate to QM, SS 2 and SS3 • 14 questions from SS2 and 14 questions from SS3

If you can handle the follow items from SS2 you should be in good shape for the exam.

1. Calculate EAR given stated annual interest rate

2. Calculate PV and FV for Annuities and Lump Sums and Perpetuities

3. Calculate NPV and IRR

4. State Problem with IRR

5. Calculate HPR (Total Return)

6. Calculate TWRR and MWRR

7. State difference between TWRR and MWRR

8. Calculate BDY, HPR, EAY, BEY and MMKT YIELD for a T-Bill

9. Calculate relative and cumulative frequencies

10. Comment on dataset presented

11. Calculate mean, Geometric Mean, harmonic mean, median and mode

12. Calculate range, mean absolute

13. Calculate standard deviation for a sample

14. Use Chebyshev

15. Calculate CV and Sharpe

16. Comment on skewness

17. Calculate covariance and correlation using probabilities

18. Calculate standard deviation using probability

19. Calculate standard deviation and expected return for a portfolio

20. Use Bayes formula


Time Value of Money The purpose of this reading is to establish a basic foundation in the calculation of present value and future values. If you have a strong math background, I think you can just quickly skim the reading. This is the math which underlies the valuation of securities. The main idea to take away is the value of any security is equal to the present value of its future cash flows. Discount Rates, Interest Rates and Opportunity Cost Cash flows that occur at a future date can be discounted to provide a present value and present values can be grown out to future values by applying an interest rate. When we are forced to make a decision, the next best alternative that we forego is referred to as the opportunity cost of the decision. Interest Rate Components r = Real risk free rate + expected inflation + specific risk premium Stated annual rate (r) – the nominal rate usually given in the question Periodic rate (r/n) – the stated annual rate adjusted for the compounding frequency (also known as the Holding Period Return)

Effective annual rate = (1 + r/n)n – 1 Effective Annual Rate Example: Calculate the EAR given the following situations: a) 8% return compounded semiannually b) 8% return compounded monthly


TVM Examples: 1. As of January 1, 2013, an annuity offers $5,000 per year for seven years with the first

payment due January 1, 2018. If the annual interest rate is 11.5%, what is the present value of the annuity?

A. $13,453 B. $23,185

C. $15,000 2. What is the present value of a ten-payment annuity of $1,000 at 8% interest? A. $5,002

B. $6,710 C. $7,247

3. Three years ago an investor’s portfolio was worth $55,000. If it is worth $92,000 today,

then the compound annual growth rate is closest to:

A. 67.2% B. 55.7% C. 18.7%

Solutions: EAR Example: EAR = ( 1 + i/n)n – 1 EAR = ( 1 + 8%/2)2 – 1 = 8.16% EAR = ( 1 + 8%/12)12 – 1 = 8.29% TVM Examples: 1.C First find value of annuity as of January 1, 2018:

BGN, FV = 0, I = 11.5, N = 7, PMT = 5,000, CPT PV = 25,851.47

Now find value as of January 1, 2013: FV = 25,851.47, I = 11.5, N = 5, PMT = 0, CPT PV = 15,000.68

2.B END, FV = 0, I = 8, N= 10, PMT = 1,000, CPT PV = 6,710.08 3.C g = [92,000/55,000]1/3 – 1 = 0.187 or 18.7%


Discounted Cash flow Applications Net Present Value (NPV) is equal to the present value of the future cash flows associated with an investment opportunity less the cost of the investment

• If NPV is positive, make the investment as it will increase your wealth • If NPV is negative, decline the investment as it will reduce your wealth

Internal Rate of Return (IRR) is the discount rate which sets the NPV equal to zero

• If IRR is greater than the cost of capital, make the investment as it will have a positive NPV

• If IRR is less than the cost of capital, decline the investment as it will have a negative NPV

IRR problem is related to multiple IRRs produced by “non-normal” cash flow patterns Holding Period Return In the readings you will see that there are three ways to calculate the holding period return. Be aware that they all say the same thing!

HPR = End – Beginning HPR = (P1 – P0) + D1 HPR = (P1 + D1) – P0 Beginning P0 P0 Where: P1 = the security’s price at the end of the period P0 = the security’s price at the beginning of the period D1 = the cash flow (dividends or coupons) at the end of the period Bottom Line: The timing of the cash flows will affect the reported return performance, so we must use a return calculation method that “accounts for the cash flows” Make sure you know the difference between the time weighted rate of return(TWRR) and the money weighted rate of return(MWRR)


MWRR vs. TWRR Example: An investor purchases one share of stock for $85. Exactly one year later, the share is worth $88 and the company pays a dividend of $2.00 per share. This is followed by two more annual dividends of $2.25 and $2.75 in successive years. At the end of the second year the share price falls back to $85 and upon receiving the third dividend, the investor sells the share for $100. 1. Calculate the MWRR 2. Calculate the TWRR


Solution: The money-weighted rate of return is the internal rate of return (IRR) of the cash flows associated with the investment. Use the cash flow (CF) function of a financial calculator and enter: CF0 = –85 CF1 = 2 CF2 = 2.25 CF3 = 102.75 Calculate the IRR to find the MWRR as 8.15%. The time weighted rate of return measures the compound rate of growth of $1 initially invested over a stated measurement period. The TWRR is not affected by cash withdrawals or additions and is calculated as the geometric mean of the holding period returns for each sub-time period included in the measurement period. HPR1 = [(88 – 85) + 2] / 85 = 0.0588235 HPR2 = [(85 – 88) + 2.25] / 88 = -0.008522 HPR3 = [(100 – 85) + 2.75] / 85 = 0.208823 TWRR = [(1 + HPR1)(1 + HPR2)….(1 + HPRN)]1/N – 1 TWRR = [(1 + 0.0588235)(1 - 0.008522)(1 + 0.208823)]1/3 – 1 TWRR = 8.2654% TWRR => GIPS!!!!


U.S. Treasury Bills On the CFA exam, if you are given a T-Bill yield you should assume it is a Bank Discount Yield, unless you are told differently! I doubt you will see a stand-alone question on the exam about calculating a T-Bill yield, however you should like these concepts to the Fixed Income material. Bank Discount Yield = [ (Face Value – Purchase Price)/Face Value ] x (360/N) Money Market Yield = [ (Face Value – Purchase Price)/Purchase Price ] x (360/N) Look they are the same! Holding Period Return = (Face Value – Purchase Price)/Purchase Price Effective Yield = (1 + HPR)(365/N) – 1 T-Bill Example: A T-Bill matures in 75 days and has a yield of 3.75% Based on the information given above, calculate the following: a) Holding Period Return b) Money Markey Yield c) Bank Discount Yield d) Effective Annual Yield

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