Modern Portfolio Theory

As with the Portfolio Level statistics, the Modern Portfolio Theory statistics are calculated from the month ending account values that you entered in the Equity Charts tab. These statistics are used to compare the performance of your portfolio to that of the selected benchmark index. They give you a better idea of expected return in relation to the risk and volatility present.

NOTE: A minimum of 4 months are needed to calculate these values.

R (Correlation): - This is the correlation between the portfolio and the benchmark index. It can be used to determine if a portfolio follows a market-neutral investment strategy. A value of 1.0 would be a perfect correlation to the benchmark index; when the benchmark index goes up, the portfolio goes up the same. A value of -1.0 would be a perfect inverse correlation; when the benchmark index goes up, the portfolio goes down the same amount the benchmark went up (and vice versa). A value of 0 would mean no correlation and movements are completely random. It is used in the calculation of R-Squared.

R-Squared: - R-Squared helps affirm the predictability of the Beta statistic. The higher the value (closer to 1.0), the greater the statistical chance of continuing to have a beta of said value. Although, many factors could lead a high past R-Squared to not be predictive. A low R-Squared typically means you should ignore the beta. Calculated by taking the square of the R (Correlation) value.

Beta: - Beta measures the risk, in terms of volatility, of the portfolios past returns in relation to the returns of the selected benchmark index. If beta is exactly 1.0, the portfolio and the benchmark index are expected to move in sync with each other. If beta is 1.1, the portfolio’s return is expected to move up and down 10% more than that of the benchmark index. If beta is 0.9, the portfolio’s return is expected to move up and down 10% less than that of the benchmark index.

Calculated by taking the monthly percentage returns of both the benchmark index and the portfolio. The benchmark index returns are plotted along the x-axis, and the portfolio returns along the y-axis. The slope of the best fit linear regression line through these data points is the Beta.

Beta-

Alpha: - Alpha is a measure of increased or decreased performance return in relation to that of the benchmark. Unlike Beta, Alpha considers the Risk Free Rate in its calculation. An alpha value of 5 means the portfolio will yield returns 5% greater than the average of the benchmark index. A value of 0 means the portfolio will yield the same returns as the benchmark index. A value of -5 means alpha will yield a return that is 5% lower than the benchmark index. Alpha is calculated using the results of Beta. Therefore, if Beta is deemed not predictable, then the Alpha value will also be not predictable.

Alpha=-Beta*

Calculated by taking the monthly percentage returns, minus the risk free returns, of both the benchmark index and the portfolio. The benchmark index returns are plotted along the x-axis, and the portfolio returns along the y-axis. The y-axis intercept of the best fit linear regression line through these points is the Alpha.