Lesson 14 of 22

Financial Data and Return Series

Document provenance, align calendars, define returns, and interpret quote direction before modelling.

Motivation

Why begin here

Return code can be mathematically correct and economically reversed when an adjustment field, currency quote, or calendar rule is misunderstood.

Why this matters

Document provenance, align calendars, define returns, and interpret quote direction before modelling.

Packages and data

Reproducible setup

Base R; xts, zoo, quantmod, tidyquant, and PerformanceAnalytics are optional.

Explanation 1

The live starter code is self-contained and uses only runner-compatible functions.

Explanation 2

Book-only outputs are labelled when the separate source dataset or advanced package was not supplied.

Explanation 3

R code, paths, function names, and formulas remain left-to-right in every locale.

Terminology

Core ideas and notation

Simple return

Price ratio minus one; compounds multiplicatively.

Pt/P(t-1)-1

Log return

Difference in log price; adds across time.

log(Pt)-log(P(t-1))

Quote direction

Units of one currency per another.

USD/CAD is CAD per USD

Notation and formulas

Key relationship

Rt = Pt/P(t-1)-1; rt = log(Pt)-log(P(t-1))

Simple and log returns are close for small movements but differ in tails and compounding.

Step 1Define every variable and unit.
Step 2Check assumptions and information timing.
Step 3Calculate, verify, and interpret in context.

Worked example

Worked analysis

Scenario

How close are simple and log returns for a short USD/CAD teaching path?

Variable: Six embedded CAD-per-USD monthly averages.
Model choice: Simple and log returns are close for small movements but differ in tails and compounding.
Calculation: The two return definitions are close for these small moves; cumulative log return equals the log price ratio up to numerical precision.
Interpretation: Because the quote is CAD per USD, a positive return means one U.S. dollar buys more Canadian dollars.
Reasonableness check: This tiny embedded path is not live market data and is not an investment recommendation.

R check

fx <- c(1.32,1.34,1.31,1.36,1.35,1.38)
simple <- 100*(fx[-1]/head(fx,-1)-1)
log_return <- 100*diff(log(fx))
print(data.frame(simple,log_return,difference=simple-log_return))
print(sum(log_return)/100)
print(log(tail(fx,1)/fx[1]))

Hints

Start by naming the question and unit.
Inspect intermediate values before the final result.
Explain what the calculation cannot establish.

Because the quote is CAD per USD, a positive return means one U.S. dollar buys more Canadian dollars. Limitation: This tiny embedded path is not live market data and is not an investment recommendation.

Visual

USD/CAD teaching path

The quote moves within a narrow range before return conversion.

R connection

Live, editable R practice

Run the self-contained starter code in the protected STATLAB R runner. The code prints an auditable result and avoids network or unrestricted file access.

Live R Lab

INTRO-R-CH14: Financial Data and Return Series

Run a self-contained example, verify its output, and explain one limitation for financial data and return series.

Editable R code

Results

Ready to run

Ready to run. Results, errors, tables, plots, and fallback messages will appear here.

State the question, data, and units.

Run and inspect the printed output.

Interpret the result and one limitation.

Common mistake

Do not log interest-rate levels as though they were positive asset prices, and do not reverse quote interpretation.

STATLAB Tip

Record source, code, field, currency, time zone, adjustment, coverage, and retrieval date.

Guided practice

Scenario

Invert the quote and verify that log returns change sign.

Hints

Reuse a small tested object.
Change one element at a time.
Finish with an interpretation and limitation.

Compare your result with the definition, units, and model assumptions—not only with a target number.

Exercises

Independent practice

Complete these without looking at the selected solutions. More than one defensible program may exist.

Explanation 1

Verify cumulative log return identity.

Explanation 2

Detect missing months in a date sequence.

Explanation 3

Explain why yields crossing zero need another transformation.

Selected solutions

Check one defensible route

These are compact solution routes. Confirm dimensions, units, and any changed modelling choices.

Explanation 1

sum(diff(log(fx))) equals log(tail(fx,1)/fx[1]).

Explanation 2

setdiff(seq(min(date),max(date),by='month'),date)

Explanation 3

A percentage change or log is undefined/problematic at zero or negative levels.

Chapter summary

What to carry forward

Document provenance, align calendars, define returns, and interpret quote direction before modelling.

Explanation 1

Provenance is part of the model.

Explanation 2

Simple returns compound; log returns add.

Explanation 3

Quote units determine meaning.

Explanation 4

Calendar alignment must be explicit.

Terminology

Chapter cheat sheet

diff(log(x))

log returns

Use in Financial Data and Return Series.

cumprod(1+r)

wealth index

Use in Financial Data and Return Series.

merge()

calendar alignment

Use in Financial Data and Return Series.

xts::xts()

dated series

Use in Financial Data and Return Series.

References and provenance

Safavi (2026), Chapter 14; Bank of Canada Valet documentation. Student notes: Mohammad Safavi, Ph.D., STATLAB Academy, Version 1.0.

Resource

Download the complete student notes

The authoritative 125-page English PDF accompanies this native lesson.

Download

Reflection

Pause and write

What assumption in financial data and return series most affects the conclusion?

Name the assumption, evidence you would seek, and how the recommendation might change.

Exit check

Chapter knowledge check

Reach 70% to complete the chapter. Explanations appear after submission.

Checkpoint