Investment Management Certificate (IMC) Quantitative Methods and the Time Value of Money Syllabus

Quantitative Methods and the Time Value of Money 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 and the Time Value of Money in Investment Management Certificate (IMC), not a summary of it.

1. 1

   Time Value of Money

   4 topics

   • Simple and compound interest
     • Nominal versus effective rates
     • Frequency of compounding
   • Present and future value
     • Discounting single cash flows
     • Future value of lump sums
   • Annuities and perpetuities
     • Ordinary annuities and annuities due
     • Valuing perpetuities
   • Discounted cash flow applications
     • Net present value (NPV)
     • Internal rate of return (IRR)
2. 2

   Descriptive Statistics

   4 topics

   • Measures of central tendency
     • Arithmetic, geometric and harmonic mean
     • Median and mode
   • Measures of dispersion
     • Variance and standard deviation
     • Range, quartiles and coefficient of variation
   • Shape of distributions
     • Skewness
     • Kurtosis
   • Data presentation
     • Frequency distributions and histograms
     • Cumulative distributions
3. 3

   Probability and Distributions

   4 topics

   • Probability concepts
     • Independent and conditional probability
     • Expected value and variance of a random variable
   • The normal distribution
     • Properties and the empirical rule
     • Standardising and z-scores
   • Correlation and covariance
     • Interpreting the correlation coefficient
     • Application to portfolio risk
   • Regression analysis
     • Simple linear regression and beta estimation
     • R-squared and limitations
4. 4

   Investment Mathematics and Returns

   3 topics

   • Holding period and annualised returns
     • Money-weighted versus time-weighted returns
     • Arithmetic versus geometric averaging
   • Real versus nominal returns
     • Adjusting for inflation
     • The Fisher relationship
   • Index construction
     • Price-weighted, value-weighted and equal-weighted indices
     • Total return versus price indices

Quantitative Methods and the Time Value of Money flashcards for Investment Management Certificate (IMC)

24 of 50 cards from the Quantitative Methods and the Time Value of Money deck — real questions with worked answers.

1. What is the formula for the future value of a sum invested at simple interest?

   $FV = PV \times (1 + r \times n)$, where $r$ is the periodic interest rate and $n$ is the number of periods. Interest is earned only on the original principal.

2. What is the formula for the future value of a sum invested at compound interest?

   $FV = PV \times (1 + r)^{n}$, where interest is earned on both principal and previously accumulated interest.

3. How does compound interest differ from simple interest over time?

   Simple interest grows linearly (interest only on principal), while compound interest grows exponentially because interest is earned on accumulated interest. The gap widens as $n$ increases.

4. How do you adjust the compound interest formula for $m$ compounding periods per year?

   $FV = PV \times \left(1 + \frac{r}{m}\right)^{m \times t}$, where $r$ is the annual rate, $m$ is compounding frequency, and $t$ is years.

5. What is the formula for continuously compounded future value?

   $FV = PV \times e^{r t}$, where $e \approx 2.71828$, $r$ is the annual rate, and $t$ is time in years.

6. What is the relationship between present value and future value under compounding?

   $PV = \frac{FV}{(1 + r)^{n}}$. Present value is the future value discounted back at the required rate of return $r$.

7. What is the discount factor and how is it calculated?

   The discount factor is the present value of $1$ received in $n$ periods: $DF = \frac{1}{(1 + r)^{n}}$. Multiplying a future cash flow by it gives its present value.

8. Define an annuity.

   An annuity is a series of equal cash flows made at regular intervals for a fixed number of periods (e.g. a fixed mortgage payment or fixed coupon bond).

9. What is the present value formula for an ordinary annuity?

   $PV = C \times \frac{1 - (1 + r)^{-n}}{r}$, where $C$ is the periodic cash flow, $r$ the rate, and $n$ the number of payments occurring at period end.

10. What is the future value formula for an ordinary annuity?

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

11. How does an annuity due differ from an ordinary annuity, and how do you adjust its value?

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

12. Define a perpetuity and give its present value formula.

    A perpetuity is a constant cash flow continuing forever. Its present value is $PV = \frac{C}{r}$, where $C$ is the periodic cash flow and $r$ the discount rate.

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

    $PV = \frac{C_{1}}{r - g}$, where $C_{1}$ is next period's cash flow, $r$ the discount rate, and $g$ the constant growth rate (valid only when $r > g$).

14. What is Net Present Value (NPV) and what is its formula?

    NPV is the sum of all discounted cash flows minus initial outlay: $NPV = \sum_{t=0}^{n} \frac{CF_{t}}{(1 + r)^{t}}$. A positive NPV adds value and the project should be accepted.

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

    The IRR is the discount rate that makes the NPV equal to zero: $\sum_{t=0}^{n} \frac{CF_{t}}{(1 + IRR)^{t}} = 0$. A project is accepted if IRR exceeds the required rate of return.

16. What is the formula for the arithmetic mean?

    $\bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_{i}$ — the sum of all observations divided by the number of observations.

17. Define the median and explain when it is preferred over the mean.

    The median is the middle value when data are ranked in order. It is preferred over the mean when data are skewed or contain outliers, as it is not distorted by extreme values.

18. Define the mode.

    The mode is the most frequently occurring value in a data set. A distribution can have no mode, one mode (unimodal), or several modes (multimodal).

19. What is the geometric mean and when is it used in finance?

    $\bar{x}_{G} = \sqrt[n]{(1+R_{1})(1+R_{2})\cdots(1+R_{n})} - 1$. It is used to compute average compound returns over multiple periods, accounting for compounding.

20. How do the arithmetic and geometric means compare in size?

    The geometric mean is always less than or equal to the arithmetic mean for a given set of returns; they are equal only when all values are identical. The gap widens with greater volatility.

21. What is the range as a measure of dispersion?

    The range is the difference between the highest and lowest values: $\text{Range} = x_{max} - x_{min}$. It is simple but sensitive to outliers.

22. What is the formula for population variance?

    $\sigma^{2} = \frac{1}{N} \sum_{i=1}^{N} (x_{i} - \mu)^{2}$ — the average of squared deviations from the population mean $\mu$.

23. What is the formula for sample variance and why does it use $n-1$?

    $s^{2} = \frac{1}{n-1} \sum_{i=1}^{n} (x_{i} - \bar{x})^{2}$. The $n-1$ divisor (Bessel's correction) gives an unbiased estimate of the population variance.

24. How is standard deviation related to variance?

    Standard deviation is the square root of variance: $\sigma = \sqrt{\sigma^{2}}$. It expresses dispersion in the same units as the original data.

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