Risk and Return Measures - Statistical Risk Measures

  1. Correlation Coefficient - A statistic gauging the relationship between two variables. The range is from -1 to +1. -1 indicates inverse correlation, 0 indicates no relationship between the variables and +1 indicates complete correlation between them.
  2. Coefficient of Determination (R2) - A statistical measure which one arrives at by squaring the correlation coefficient. This statistic describes the degree of variability of a dependent variable that is explained by changes in the independent variable. As an example, if the R2 is 63% between a large cap core stock and the S&P 500, that signifies that changes in the S&P 500 (systematic risk) explains 63% of the movement of the stock, whereas unsystematic risk accounts for the remaining 37%.

Look Out!

Expect a question or two on how to interpret R2 given a particular scenario.

  1. Coefficient of Variation - The measure of dispersion of a probability distribution. The standard deviation divided by the mean. In finance, the ratio measures the amount of risk per unit of mean return and is helpful in gauging relative risk in terms of degree of data dispersion. The formula is written as follows: Cv=σ/µ
  2. Standard Deviation (σ) - Standard deviation is a measure of total risk, defined as the sum of systematic and non systematic risk. One may define it as the dispersion of outcomes around the mean, which is the average return for a sample of data. Accordingly, it is a measure of central tendency. The greater an investment's standard deviation, the greater is its risk.
    • Approximately 68% of outcomes fall within one standard deviation of the mean, both above and below.
    • Approximately 95% of outcomes fall within two standard deviations of the mean, both above and below.
    • Approximately 99% of outcomes fall within three standard deviations of the mean, both above and below.
An example may illustrate these points. Six ? Corporation yields a mean return of 21% with a standard deviation of 9%.
    • 68% of outcomes fall between 30% and 12% (21% +/-9%, respectively)
    • 95% of outcomes fall between 39% and 3% (21% +/-2x9%, respectively)
    • 99% of outcomes fall between 48% and -6% (21% +/-3x9%, respectively)

      Look Out!
      Expect several questions on standard deviation, how it figures into risk-adjusted performance, how to interpret probabilities of outcomes under a bell-shaped curve, how to define it, etc.

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