Return forecasts and risk estimates rely on assumptions about the observed data. This lesson checks those assumptions. It distinguishes simple and log returns, explains skewness and tail diagnostics, and shows how volatility clustering can coexist with uncorrelated returns. The aim is to choose a defensible sampling model, not to declare all returns Gaussian or all standard errors too small.
Learning objectives. By the end of this note you should be able to:
- define simple and log returns, convert between them, and explain serial additivity of logs vs cross-sectional additivity of simple returns;
- compute sample skewness and excess kurtosis and read them against the normal benchmarks and ;
- use moments and QQ-plots to assess tail behaviour, and check whether a Gaussian loss threshold has the intended exceedance rate;
- describe volatility clustering as positive dependence in or , and say what that does to ;
- state precisely what the CLT justifies for averages of returns and what it does not justify for a single day.
In this lesson
- Simple and log returns
- Skewness, kurtosis, and non-normality
- Heavy tails
- Volatility clustering
- What the CLT licenses for daily returns
- A minimal empirical checklist
- Bridging back to the programme
Before you start
- Random Variables and Distributions
- Laws of Large Numbers and the Central Limit Theorem
- Estimation and Maximum Likelihood
The full lesson, with worked examples and exercise solutions, is for members.
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