Is the euro–dollar exchange rate a random walk?

AI SLAI HLAA HL Ambitious Also in: Statistics, Probability

Research question

Are daily percentage changes in the EUR/USD reference rate normally distributed and independent, as a simple random-walk model assumes, and how often do extreme days occur compared with the normal model's prediction?

Adapt it: change the place, the data or the comparison until the question is yours.

Why it makes a good exploration

Financial models often assume normally distributed changes, and the 2008 crisis showed why that can be dangerous. Testing the assumption on ECB data is serious statistics about something that affects prices everywhere.

The mathematics you'll need

Percentage change and log returns
Normal distribution and z-scores
Chi-squared goodness-of-fit to a normal
Correlation between consecutive days
Tail probabilities

Course labels show where a technique sits; using maths from outside your course is fine if you explain it clearly and say it is new to you.

Where the data comes from

Download the daily EUR/USD reference rate history from the ECB Data Portal.

ECB Data Portal — exchange rates — Daily euro reference rates for 29 currencies and ECB interest rates.

Cite every source in a footnote where you use it and in your bibliography. Check the licence of any dataset you download.

A possible outline

Explain the random-walk model.
Compute daily changes and describe them.
Test normality and independence.
Count extreme days vs normal predictions.
Reflect on fat tails and risk management.

Pitfalls that cost marks

Testing prices instead of changes.
Ignoring that ECB rates are daily fixes, not trading prices.
Over-claiming about predictability.

Showing personal engagement

Link to a trip abroad and what the rate cost you.
Compare a calm and a crisis period.
Try (and fail) to beat a random walk with a simple rule.

See Criterion C: personal engagement for what examiners look for.

Taking it further

Fit a distribution with fatter tails (explain it) and compare its fit with the normal.

Turn this idea into your IA

Plan this IAOpens the planner with this question, the maths and data sources filled in. Desmos workspacePlot your data, fit models and keep your graphs with your plan. AI feedback on a draftCriterion-by-criterion feedback with evidence from your own text. Coaching, not rewriting. Examiner reviewPete, a practising IA examiner, reads your draft and talks it through with you (€100).