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Discuss the standard deviation of a risky asset's return. What does it measure? Also discuss the...

Discuss the standard deviation of a risky asset's return. What does it measure? Also discuss the 95% confidence interval of a risky asset's return and how it's related to the asset's standard deviation

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Expert Solution

The standard deviation is often used by investors to measure the risk of a stock or a stock portfolio.

The basic concept is that the standard deviation is a measure of spread: the more a stock's returns vary from the stock's average return, the more volatile the stock.

standard deviation is used as an indicator of market volatility and therefore of risk. The more unpredictable the price action and the wider the range, the greater the risk. A security that has a very large trading range and tends to spike, reverse suddenly or gap, is much riskier.

While a normally-distributed random variable can have many potential outcomes, the shape of its distribution gives us confidence that the vast majority of these outcomes will fall relatively close to its mean. In fact, we can quantify just how confident we are.

By assuming normal distribution, we are 68% confident that a variable will fall within one standard deviation. Within two standard deviation intervals, our confidence grows to 95%. Within three standard deviations, 99%. Take an example of a distribution of returns of a security with a mean of 10% and a standard deviation of 5%:

  • 68% of the returns will be between 5% and 15% (within 1 standard deviation, 10 + 5).
  • 95% of the returns will be between 0% and 20% (within 2 std. devs., 10 + 2*5).
  • 99% of the returns will be between -5% and 25% (within 3 std. devs., 10 + 3*5)




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