Quantitative Methods

Note: This page is useful for anyone wanting to learn these concepts. An excellent external resource is MrsHodgettsStatistics.com — even though it is written for A-Level Statistics, the explanations and worked examples overlap closely with the same core topics.

This guide provides concise explanations and formulas you’ll actually use in exams and modelling. Click any symbol to jump to its definition.

Key to Variables

PV — Present Value
FV — Future Value
C — Cash flow per period
r — Interest or discount rate per period
n — Number of periods
D — Dividends or distributions
P0 — Initial price
P1 — Ending price
σ — Standard deviation (volatility)
μ — Mean (expected value)
x̄ — Sample mean
s — Sample standard deviation
ρ — Correlation coefficient (−1 to +1)
Cov — Covariance
w1, w2 — Weights (portfolio/series)
α — Significance level (e.g., 0.05)
p-value — Probability of result as extreme as observed if H0 is true

Returns & Averages

Measures of investment performance. Used to summarise returns across time or assets.

Holding Period Return: (P1 − P0 + D) ÷ P0
Arithmetic mean: Simple average of returns
Geometric mean: Compounded average (more accurate over time)
Coefficient of Variation: Risk per unit of return = σ ÷ mean

Time Value of Money (TVM)

Money has a time value: cash today is worth more than cash in the future.

Future Value: FV = PV(1 + r)ⁿ
Present Value: PV = FV ÷ (1 + r)ⁿ
Annuity PV: PV = C × [1 − (1 + r)⁻ⁿ] ÷ r
Perpetuity PV: PV = C ÷ r

NPV & IRR

Discounted cash flow methods for investment appraisal.

NPV: Σ [CF_t ÷ (1 + r)^t] − initial outlay
IRR: Discount rate that sets NPV = 0

Descriptive Statistics

Summarise and describe data.

Central Tendency

Mean, Median, Mode

Dispersion

Variance, Standard Deviation (σ), Range

Shape

Skewness (asymmetry), Kurtosis (fat/thin tails)

Probability

Quantifies uncertainty of events.

Addition rule: P(A or B) = P(A) + P(B) − P(A and B)
Multiplication: P(A and B) = P(A) × P(B|A)
Conditional: P(A|B) = P(A and B) ÷ P(B)
Bayes’ theorem updates probabilities with new info

Distributions

Models of how outcomes are spread.

Normal: Bell curve, symmetric
Binomial: Fixed trials, two outcomes
Poisson: Counts of rare events
t-distribution: Small samples, fat tails

Covariance & Correlation

Measure how variables move together.

Covariance: Joint variability of two series
Correlation (ρ): Standardised, −1 to +1

Sampling & Estimation

How we estimate population parameters from samples.

Central Limit Theorem: large samples → mean ~ normal
Standard error: σ ÷ √n
Confidence intervals: mean ± margin of error

Hypothesis Testing

Framework for statistical inference.

Null (H0) vs Alternative (H1)
Type I error = false positive (α); Type II = false negative (β)
Use z-test, t-test, χ², or F depending on data
Decision: reject H0 if p-value < α

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