New to stock investing hence reading up a few tutorial to better understand stocks/stock market. Came across a chapter that says, "Understanding risk with the stock market" and it says that traders and analysts use a number of metrics to assess the volatility and relative risk of potential investments (sharpe ratio, sortino ratio, beta, alpha, rsquared), but the most common metric is standard deviation.

I somewhat get what standard deviation is,

  • Standard deviation helps determine market volatility or the spread of asset prices from their average price.
  • When prices move wildly, standard deviation is high, meaning an investment will be risky.
  • Low standard deviation means prices are calm, so investments come with low risk.

There is an example too which says, in a stock with a mean price of $45 and a standard deviation of $5, it can be assumed with 95% certainty the next closing price remains between $35 and $55. However, price plummets or spikes outside of this range 5% of the time. A stock with high volatility generally has a high standard deviation, while the deviation of a stable blue-chip stock is usually fairly low.

What I did not understand is how did the above example calculate the range of the stock price to be in between $35 to $55?

How do you calculate the fluctuation price range if you know the stock price and the standard deviation value?


What a lot of financial analysis relies on is the idea that stock returns follow a Normal Distribution. This distribution relies on two parameters, the mean and standard deviation. Based on the properties of the normal distribution, it is said that any given value will fall between +-2 standard deviations from the mean 95% of the time. From your example, a stock with a mean price of $45 and a standard deviation of $5 will trade from $35 ($45 - 2($5)| -2 standard deviations) to $55 ($45+2($5) | +2 standard deviations) 95% of the time.

Example Normal Distribution

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