Example:The mean monthly return on T-bills is 0.25%. The mean monthly return on the S&P 500 is 1.30% with a standard deviation of 7.30%. Calculate the Sharpe measure for the S&P 500 and interpret the results.
Sharpe measure = (1.30 - 0.25) / 7.30 = 0.144
The S&P 500 earned 0.144% of excess return per unit of risk, where risk is measured by standard deviation.
o: Describe the relative locations of the mean, median, and mode for a nonsymmetrical distribution.

  • For a symmetrical distribution, the mean, median, and mode are equal.

  • For a positively skewed distribution, the mode is less than the median, which is less than the mean. Recall that the mean is affected by outliers. In a positively skewed distribution, there are large, positive outliers which will tend to "pull" the mean upward.

  • For a negatively skewed distribution, the mean is less than the median, which is less than the mode. In this case, there are large, negative outliers which tend to "pull" the mean downward.

p: Define and interpret skewness and explain why a distribution might be positively or negatively skewed.
Skewnessrefers to a distribution that is not symmetrical.

  1. A positively skewed distribution is characterized by many outliers in its upper or right tail. Recall that an outlier is defined as an extraordinarily large outcome in absolute value. Positively skewed distributions have long righttails.