CFA Level I · CFA Level I Exam

Introduction to Financial Data Science: formula sheet

Full chapter guide

Key formulas

Big data characteristics (the Vs): Volume = how much; Velocity = how fast; Variety = what formats; Veracity = how reliable; Learn each V with a one-line test. Volume is size, velocity is speed of generation and processing, variety is mix of structured and unstructured forms, veracity is quality and trustworthiness.
Structured vs unstructured data: Structured = fixed fields (tables, prices); Unstructured = no fixed format (text, images, audio); Alternative data is mostly unstructured and needs processing before analysis.
Use case matching: Text/news/filings → NLP; pattern finding and prediction → machine learning; fast rule-based order execution → algorithmic trading; Most application questions reduce to picking the right tool for the described task.
Normalization (min-max scaling): X_norm = (X − X_min) ÷ (X_max − X_min); Result lies between 0 and 1. Sensitive to outliers because min and max are used.
Standardization (z-score scaling): X_std = (X − μ) ÷ σ; Result has mean 0 and standard deviation 1. It does not bound values to a fixed range.
IQR outlier rule: Outlier if X < Q1 − 1.5 × IQR or X > Q3 + 1.5 × IQR, where IQR = Q3 − Q1; Common rule of thumb; a larger multiplier such as 3 flags only extreme outliers.
Cleansing problems checklist: Missing, invalid, inaccurate, non-uniform, duplicate; Know the example for each type and its usual fix.
Bias-variance idea: Total error = bias error + variance error + base (irreducible) error; High bias error means underfitting. High variance error means overfitting. Complexity trades one against the other.
K-fold cross-validation: Each fold size ≈ N ÷ k; k training rounds; each fold used once for validation; Training uses k − 1 folds each round. Average the k validation results.
Fit pattern: overfit: Low training error, high out-of-sample error; The model memorized noise and does not generalize.
Fit pattern: underfit: High training error, high out-of-sample error; The model is too simple. Add features or complexity.
Fit pattern: good fit: Low training error, similar low out-of-sample error; The model generalizes well.
Classification metrics: Precision = TP ÷ (TP + FP); Recall = TP ÷ (TP + FN); Accuracy = (TP + TN) ÷ (TP + FP + TN + FN); F1 = 2 × P × R ÷ (P + R); Use precision when false positives are costly and recall when false negatives are costly. F1 balances both.
Text processing order: Raw text → cleansing → tokenization → normalization (lowercase, stop words, stem/lemma) → BOW / DTM → feature selection → model; Know the sequence and what each step does.
Stemming vs lemmatization: Stemming = rule-based suffix removal (may not be a real word); Lemmatization = dictionary-based base form (real word); Lemmatization is more accurate and more costly.
Document term matrix: Rows = documents; Columns = tokens; Cells = count or frequency; BOW ignores word order. N-grams retain some order.
Term frequency: TF = count of token in a document ÷ total tokens in that document; Shows how often a token appears relative to document length.
Chart choice: Distribution → histogram / box plot; Relationship → scatter plot; Trend → line chart; Categories → bar chart; Text frequency → word cloud; Match chart to the question being asked.

Quick revision

Structured data fits fixed fields and tables; unstructured data such as text, images and audio does not.
Supervised learning uses labelled data to predict a target; unsupervised learning finds patterns without labels.
Regression predicts a continuous target; classification predicts a category.
Clustering and dimension reduction are typical unsupervised tasks.
Overfitting means the model fits training data too closely and performs poorly on new data.
Underfitting means the model is too simple to capture the pattern, even in training data.
Split data into training, validation and test sets; the test set checks performance on unseen data.
Data cleaning deals with missing values, outliers, duplicates and inconsistent formats.
Tokenization splits text into units; stop-word removal and stemming or lemmatization reduce noise.
NLP turns text into structured form so it can be analysed, for example for sentiment.
Pick the chart for the message: trends over time, comparisons, distributions or relationships.
Always apply Ethics thinking: data privacy, bias and understanding a model before relying on it.

Common mistakes

Confusing velocity with volume Fix: Volume is how much data exists. Velocity is how quickly it is created and must be processed. Look for words like real-time or streaming.
Thinking big data means only structured data Fix: Variety includes unstructured sources such as text, images and audio. Alternative data is mostly unstructured.
Calling JSON or XML data unstructured. Fix: If it has tags or key-value pairs that give organization, it is semi-structured.
Mixing up normalization and standardization. Fix: Normalization uses min and max and gives 0 to 1. Standardization uses mean and standard deviation and gives mean 0 and standard deviation 1.
Calling clustering a supervised method because it produces groups. Fix: Check for labels in advance. Clustering discovers groups without labels; classification predicts known labels.
Saying a model with the lowest training error is the best model. Fix: Judge on out-of-sample error. A very low training error with high test error signals overfitting.
Saying stemming always returns a valid word. Fix: Remember that stemming just trims endings by rule, so outputs like 'analyz' can occur. Lemmatization returns real words.
Thinking bag-of-words keeps word order. Fix: A bag has no order. If order or phrases matter, use n-grams.

Exam tips

Expect short scenario questions: the stem gives a clue, and you name the V or the tool. Practise the clue-to-V conversion until it is automatic.
Watch for options that overstate technology, such as 'eliminates bias' or 'guarantees accuracy'. These are usually wrong.
Know the difference between structured and unstructured data and give a quick example of each.
With no penalty for wrong answers, never leave a question blank. Eliminate one option you can rule out and choose between the other two.
Read for limitations in the stem. A hint of poor data quality, overfitting or opaque models usually shapes the right answer.
Expect definition and classification questions. Memorize one example for each data type and each cleansing problem.
Know the contrast: normalization is bounded 0 to 1 and outlier-sensitive; standardization is not bounded and handles outliers better.
In a calculation, do the subtraction first and write it down. Mistakes usually come from wrong inputs, not from division.