CFA Quantitative Methods Syllabus

Quantitative Methods syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Quantitative Methods in CFA, not a summary of it.

1. 1

   The Time Value of Money

   2 topics

   • Discounted Cash Flow Applications
   • Annuities and Perpetuities
2. 2

   Statistical Concepts and Market Returns

   3 topics

   • Measures of Central Tendency
   • Measures of Dispersion
   • Probability Concepts
3. 3

   Hypothesis Testing

   3 topics

   • Types of Hypotheses
   • Type I and Type II Errors
   • Test Statistics and P-values

Quantitative Methods flashcards for CFA

19 of 51 cards from the Quantitative Methods deck — real questions with worked answers.

1. What is the Net Present Value (NPV) of an investment, and what is its formula?

   NPV is the present value of all expected cash flows discounted at the required rate of return, minus the initial outlay. $$NPV = \sum_{t=0}^{N} \frac{CF_t}{(1+r)^t}$$ where $CF_t$ is the cash flow at time $t$ and $r$ is the discount rate.

2. What is the NPV decision rule for a single independent project?

   Accept the project if $NPV > 0$ (it adds value); reject if $NPV < 0$. When $NPV = 0$ the project earns exactly the required return.

3. What is the Internal Rate of Return (IRR)?

   The IRR is the discount rate that makes the NPV of all cash flows equal to zero: $$\sum_{t=0}^{N} \frac{CF_t}{(1+IRR)^t} = 0$$

4. What is the IRR decision rule for an independent project?

   Accept if $IRR > r$ (the required rate of return / cost of capital); reject if $IRR < r$.

5. When NPV and IRR rankings conflict for mutually exclusive projects, which criterion should be used and why?

   Use NPV. It directly measures the dollar value added to the firm and assumes reinvestment at the more realistic required rate $r$, whereas IRR assumes reinvestment at the (often unrealistic) IRR.

6. What are the two main problems with the IRR method?

   (1) Multiple IRRs (or no real IRR) can occur when cash-flow signs change more than once; (2) IRR can give rankings that conflict with NPV for mutually exclusive projects due to differing scale and timing.

7. What is the Holding Period Return (HPR) formula for a single period?

   $$HPR = \frac{P_1 - P_0 + D_1}{P_0}$$ where $P_0$ is the beginning price, $P_1$ the ending price, and $D_1$ the cash flow/dividend received.

8. How is the money-weighted rate of return defined?

   It is the IRR of an investment's cash flows — the rate that sets the PV of all cash inflows equal to the PV of all cash outflows. It accounts for the timing and size of all deposits and withdrawals.

9. How is the time-weighted rate of return (TWRR) computed over multiple subperiods?

   Compute the HPR for each subperiod, then geometrically link them: $$TWRR = \left[\prod_{i=1}^{n}(1+HPR_i)\right]^{1/n} - 1$$ for an annualized rate. It is unaffected by the timing of cash flows.

10. How do you convert a Bank Discount Yield (BDY) into the formula form for a T-bill?

    $$r_{BD} = \frac{D}{F} \times \frac{360}{t}$$ where $D$ is the dollar discount, $F$ is face value, and $t$ is days to maturity. It uses face value (not price) and a 360-day year.

11. What is the formula for the Effective Annual Yield (EAY) from a holding period yield?

    $$EAY = (1 + HPY)^{365/t} - 1$$ where $t$ is the number of days in the holding period.

12. What is the bond-equivalent yield given a 6-month (semiannual) yield?

    The bond-equivalent yield doubles the effective semiannual yield: $$BEY = 2 \times \text{semiannual yield}$$

13. What is the present value of an ordinary annuity?

    $$PV = A \times \frac{1 - (1+r)^{-N}}{r}$$ where $A$ is the periodic payment, $r$ the per-period rate, and $N$ the number of payments (first payment one period from now).

14. What is the future value of an ordinary annuity?

    $$FV = A \times \frac{(1+r)^{N} - 1}{r}$$ where $A$ is the periodic payment occurring at the end of each period.

15. How does an annuity due differ from an ordinary annuity, and how do you adjust the PV/FV?

    In an annuity due payments occur at the beginning of each period (one period earlier). Multiply the ordinary annuity value by $(1+r)$: $$PV_{due} = PV_{ordinary} \times (1+r)$$

16. What is the present value of a perpetuity?

    $$PV = \frac{A}{r}$$ where $A$ is the constant periodic payment and $r$ is the per-period discount rate (payments continue forever).

17. What is the present value of a growing perpetuity?

    $$PV = \frac{A_1}{r - g}$$ where $A_1$ is next period's payment, $g$ is the constant growth rate, and $r > g$.

18. How do you find the present value of a deferred (delayed) annuity?

    Compute the ordinary-annuity PV as of one period before the first payment, then discount that lump sum back to today: $$PV_0 = \frac{PV_{annuity}}{(1+r)^{k}}$$ where $k$ is the number of periods of deferral.

19. How is the effective annual rate (EAR) computed from a stated annual rate with $m$ compounding periods?

    $$EAR = \left(1 + \frac{r_{stated}}{m}\right)^{m} - 1$$ With continuous compounding: $EAR = e^{r_{stated}} - 1$.

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