Should we be surprised?
In finance and many walks of life probability and statistics are used to calculate the likely outcome; from something as simple as the toss of a coin to complex calculations for trading options. When making investment decisions statistics can offer us guidance and comfort, but can we always rely on these models and the data that they provide?
Normal Distribution refers to how a variable is distributed around it’s mean and can tell us where we expect to find observations, for example: –
- A share has an average annual return of 5% over the last 20 years
- It has a Standard Deviation is 10%
- Assuming normal distribution 95.45% of all observations are within 2 Standard Deviations (20%)
- So ….expected returns are usually within a range of -25% to +20%
- It would be considered very rare for returns to fall outside of these
- Outside 3 Standard Deviations every year
- Outside 4 Standard Deviations every 43 years
- Outside 5 Standard Deviations every 4776 year
- Outside 6 Standard Deviations every 1.4 million years
So with these facts in mind we should be able to forget about crazy daily returns from the stock after all it would only loose 60% once every 1.4 million years! What are the chances of that??? Well turns out a bit more than probability suggests, take a look at the graph in image one for daily returns from the S&P 500 US Equity Index since 1961.
The red lines are 6 Standard Deviations away from the mean daily return! We have in fact seen the index move outside this range on 32 different occasions in the last 56 years – an event that should only happen every 1.4 million years!
Now this is nothing new, read a finance book by someone like Nassim Taleb and it will provide you with the facts and lead you to realise that things are a lot riskier than normal probability suggests!
