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

24 sample cards from the Quantitative Methods and the Time Value of Money deck

Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.

1. Define a negatively (left) skewed distribution.

   A negatively skewed distribution has a long left tail. Typically $\text{mean} < \text{median} < \text{mode}$, as large negative outliers pull the mean downward.

2. What does kurtosis measure?

   Kurtosis measures the 'peakedness' and tail thickness of a distribution. Leptokurtic ($>3$) distributions have fat tails; platykurtic ($<3$) have thin tails; the normal distribution has kurtosis of $3$ (excess kurtosis of $0$).

3. What is a histogram?

   A histogram is a bar chart displaying the frequency distribution of continuous data grouped into intervals (bins). The bar area/height represents the frequency of observations in each interval.

4. What is a frequency distribution?

   A frequency distribution tabulates data by grouping observations into classes/intervals and showing the number (frequency) of observations falling into each class.

5. What does a scatter plot display?

   A scatter plot shows the relationship between two variables by plotting paired observations as points on $x$ and $y$ axes, revealing the direction, strength, and form of any correlation.

6. What is the difference between a probability and an odds expression?

   Probability expresses likelihood as $P(E)$ between $0$ and $1$. Odds express the ratio of favourable to unfavourable outcomes; odds 'for' $= \frac{P(E)}{1 - P(E)}$.

7. State the addition rule of probability for two events.

   $P(A \cup B) = P(A) + P(B) - P(A \cap B)$. For mutually exclusive events, $P(A \cap B) = 0$, so $P(A \cup B) = P(A) + P(B)$.

8. State the multiplication rule of probability for independent events.

   For independent events, $P(A \cap B) = P(A) \times P(B)$. More generally $P(A \cap B) = P(A) \times P(B \mid A)$.

9. What is conditional probability?

   $P(A \mid B) = \frac{P(A \cap B)}{P(B)}$ — the probability that event $A$ occurs given that event $B$ has occurred.

10. What is expected value (mean) of a discrete random variable?

    $E(X) = \sum_{i} p_{i} x_{i}$ — the probability-weighted sum of all possible outcomes.

11. What are the key properties of the normal distribution?

    It is symmetric and bell-shaped, fully described by its mean $\mu$ and standard deviation $\sigma$, with mean = median = mode, and tails extending to infinity. It is the basis for much of modern finance theory.

12. State the empirical (68-95-99.7) rule for the normal distribution.

    About $68\%$ of observations lie within $\mu \pm 1\sigma$, about $95\%$ within $\mu \pm 2\sigma$ (more precisely $1.96\sigma$), and about $99.7\%$ within $\mu \pm 3\sigma$.

13. What is the standard normal distribution and the z-score formula?

    The standard normal distribution has $\mu = 0$ and $\sigma = 1$. Any value is standardised via $z = \frac{x - \mu}{\sigma}$, expressing how many standard deviations $x$ lies from the mean.

14. What is covariance and what does its sign indicate?

    Covariance measures how two variables move together: $\text{Cov}(X,Y) = \frac{1}{n}\sum (x_{i}-\bar{x})(y_{i}-\bar{y})$. A positive value means they move in the same direction; negative means opposite directions.

15. What is the correlation coefficient and its formula?

    $\rho_{X,Y} = \frac{\text{Cov}(X,Y)}{\sigma_{X}\,\sigma_{Y}}$ — a standardised measure of linear association ranging from $-1$ to $+1$.

16. What do correlation coefficients of $+1$, $0$, and $-1$ indicate?

    $+1$ = perfect positive linear relationship; $-1$ = perfect negative linear relationship; $0$ = no linear relationship. Values between indicate partial linear association.

17. Why does correlation not imply causation?

    A high correlation only shows that two variables move together; it does not prove one causes the other. The relationship may be coincidental (spurious) or driven by a third underlying variable.

18. What is the equation of a simple linear regression line?

    $y = a + bx + \epsilon$, where $a$ is the intercept, $b$ the slope (sensitivity of $y$ to $x$), $x$ the independent variable, and $\epsilon$ the error term.

19. What does the coefficient of determination $R^{2}$ measure?

    $R^{2}$ measures the proportion of the variation in the dependent variable explained by the independent variable(s). In simple regression it equals the square of the correlation coefficient and ranges from $0$ to $1$.

20. What is the holding period return (HPR) formula?

    $HPR = \frac{P_{1} - P_{0} + D}{P_{0}}$, where $P_{0}$ is the purchase price, $P_{1}$ the ending price, and $D$ the income/dividend received over the period.

21. How do you annualise a holding period return?

    $\text{Annualised return} = (1 + HPR)^{\frac{1}{t}} - 1$, where $t$ is the holding period in years. This converts a return into an equivalent compound annual rate.

22. What is the difference between real and nominal returns?

    The nominal return includes inflation; the real return strips inflation out, measuring purchasing-power gain. The real return reflects the actual increase in goods/services you can buy.

23. State the Fisher equation linking real and nominal returns.

    $1 + r_{nominal} = (1 + r_{real})(1 + i)$, where $i$ is inflation. The approximation $r_{real} \approx r_{nominal} - i$ holds for small rates.

24. What is the difference between a price-weighted and a market-capitalisation-weighted index?

    A price-weighted index (e.g. Dow Jones) weights constituents by share price, so high-priced shares dominate. A market-cap-weighted index (e.g. FTSE 100) weights by total market value, so large companies dominate, reflecting their economic size.

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Quantitative Methods and the Time Value of Money flashcards FAQ