A simple risk model can estimate the probability that a daily loss exceeds a limit. The normal distribution provides one baseline for that calculation. This lesson uses mean and variance to specify the model, standardises a loss and reads its tail probability. It also explains why actual losses can exceed the model’s prediction.
Learning objectives. By the end of this note you should be able to:
- state the mean and variance parameters of a normal distribution;
- standardise a normal random variable;
- calculate interval and tail probabilities using the standard normal CDF;
- use the 68–95–99.7 rule as a rough check;
- explain why normality can understate financial tail risk.
In this lesson
- The bell-shaped model
- Standardisation
- Quick probability checks
- Where normality breaks in finance
- The loss threshold becomes a left tail
Before you start
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