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Risk and Return Measures - Distribution of Returns


    1. Normal Distribution - A symmetrical return distribution, its mean and median are equal, approximately 68% of its observations lie between plus and minus one standard deviation from the mean; 95% lie between plus and minus two standard deviations; and 99% lie between plus and minus three standard deviations.

    2. Lognormal Distribution - Closely related to normal distribution. Its use is widespread in modeling probability distribution of asset prices.

    3. Skewness - The statistical measure of skew or asymmetry of distributions. An asymmetrical distribution is skewed. Positive skew is where the return distribution has frequent small losses and a few extreme gains; negative skew is the opposite.

    4. Kurtosis - The statistical measure indicating when a distribution is more or less peaked than a normal distribution.
      1. Mesokurtosis - a normal (symmetrical) distribution.
      2. Leptokurtosis - where the distribution of returns is more peaked than normal, i.e. returns cluster closely around the mean.
      3. Platykurtosis - a less than normal peaked distribution, e.g. returns are dispersed more widely around the mean.
Statistical Risk Measures

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