The Annual Returns Graph shows the distribution of historical returns for a given asset allocation to various factors. Also plotted is the average of the returns along with the upper and lower bounds of the standard deviation of returns. Portfolio statistics are provided to help you understand the risk and returns trade-offs for a given portfolio.
Calculations:
Average Return:
The average of the actual annual historical returns for every starting month. For every starting month, returns are calculated based on actual monthly returns that follow; the results are then averaged.
Standard Deviation:
Standard Deviation is a measure of how far apart returns are from the average. Portfolio returns approximate a normal distribution, which means that 68% of the time returns should fall within 1 Standard Deviation of the Average Return. This range of outcomes is shown in the graph above. Skewness and Kurtosis show us ways in which the portfolio’s returns are different from a normal distribution.
Sharpe Ratio:
The Sharpe Ratio is a measure of the risk-adjusted performance of the portfolio. It is calculated as the average annual return in excess of the risk-free rate divided by the standard deviation of the return in excess of the risk-free rate. The risk-free rate is the return on treasury bills in whichever currency is selected. If the return on treasury bills is unavailable, the intermediate term treasury bond return is used.
Skewness:
Skewness measures how different the distribution of returns are from a normal distribution. A normal distribution (bell curve) exhibits zero skewness. If a distribution is negatively skewed the left tail of the distribution is longer. A simple way to think about this is to think about the difference between the average and the median. When the average is lower than the median, this is likely due to outliers in the left tail of the distribution (negative skewness).
Kurtosis:
Kurtosis here is technically excess Kurtosis, which measures how heavily the tails of a distribution differ from the tails of a normal distribution. A normal distribution exhibits no excess Kurtosis, meaning that the tails are accurately predicted by a normal distribution. Higher excess kurtosis is associated with more risk because it indicates higher probabilities of returns in the extreme left or right hand tails of the distribution.