Invest with Confidence

How does it all work?

The underlying foundation of investing obviously lies in mathematics. Understanding a basic level of the mathematical mechanics involved in predictions goes a long way to making one a more confident, more risk savvy investor.

The following is not a comprehensive list of investment equations, but is instead meant to give you a general overview of definitions for the terms present in other parts of the web site and monthly fact sheets etc.

Value Added Monthly Index (VAMI)

The value-added monthly index charts the total return gained by an investor from reinvestment of any dividends and additional interest gained through compounding. The VAMI index is sometimes used to evaluate the performance of a fund manager.

Average Return (Mean)

This is a simple average return (arithmetic mean) which is calculated by summing the returns for each period and dividing the total by the number of periods. This does not take any compounding into account.

Average Gain (Gain Mean)

This is a simple average (arithmetic mean) of the periods with a gain. It is calculated by summing the returns for gain periods (return 0) and then dividing the total by the number of gain periods.

Average Loss (Loss Mean)

This is a simple average (arithmetic mean) of the periods with a loss. It is calculated by summing the returns for loss periods (return < 0) and then dividing the total by the number of loss periods.

Compound (Geometric) Average Return

The geometric mean is the monthly average return that assumes the same rate of return every period to arrive at the equivalent compound growth rate reflected in the actual return data. In other words, the geometric mean is the monthly average return that, if applied each period, would give you a final Vami (growth) index that is equivalent to the actual final Vami index for the return stream you are considering.

Standard Deviation

Standard Deviation measures the dispersal or uncertainty in a random variable (in this case, investment returns). It measures the degree of variation of returns around the mean (average) return. The higher the volatility of the investment returns, the higher the standard deviation will be. For this reason, standard deviation is often used as a measure of investment risk.

Gain Standard Deviation

Similar to standard deviation, except this statistic calculates an average (mean) return for only the periods with a gain and then measures the variation of only the gain periods around this gain mean. This statistic measures the volatility of upside performance.

Loss Standard Deviation

Similar to standard deviation, except this statistic calculates an average (mean) return for only the periods with a loss and then measures the variation of only the losing periods around this loss mean. This statistic measures the volatility of downside performance.

Downside Deviation

Similar to the loss standard deviation except the downside deviation considers only returns that fall below a defined Minimum Acceptable Return (MAR) rather then the arithmetic mean. For example, if the MAR is assumed to be 10%, the downside deviation would measure the variation of each period that falls below 10%. (The loss standard deviation, on the other hand, would take only losing periods, calculate an average return for the losing periods, and then measure the variation between each losing return and the losing return average).

Sharpe Ratio

A return/risk measure developed by William Sharpe. Return (numerator) is defined as the incremental average return of an investment over the risk free rate. Risk (denominator) is defined as the standard deviation of the investment returns.

Sortino Ratio

This is another return/risk ratio developed by Frank Sortino. Return (numerator) is defined as the incremental compound average period return over a Minimum Acceptable Return (MAR). Risk (denominator) is defined as the Downside Deviation below a Minimum Acceptable Return (MAR).

Skewness

Skewness characterizes the degree of asymmetry of a distribution around its mean. Positive skewness indicates a distribution with an asymmetric tail extending toward more positive values. Negative skewness indicates a distribution with an asymmetric tail extending toward more negative values.

Kurtosis

Kurtosis characterizes the relative peakedness or flatness of a distribution compared with the normal distribution. Positive kurtosis indicates a relatively peaked distribution. Negative kurtosis indicates a relatively flat distribution.

Calmar Ratio

This is a return/risk ratio. Return (numerator) is defined as the Compound Annualized Rate of Return over the last 3 years. Risk (denominator) is defined as the Maximum Drawdown over the last 3 years. If three years of data are not available, the available data is used. ABS is the Absolute Value.

Standard Error

This statistic is measuring the degree of variability of the actual Y-values (RDI) relative to the estimated Y-values (RDIest) from a regression equation. The statistic is often referred to as the standard error of the estimate (SEE), standard error of the residual or standard error of the regression. The (SEE) gauges the “fit” of the regression line. The smaller the standard error, the better the fit. This is not the standard error of the mean, beta or alpha coefficients.

Tracking Error (Annualized)

Tracking Error is a measure of the unexplained portion of an investments performance relative to a benchmark. Annualized Tracking Error is measured by taking the square root of the average of the squared deviations between the investment’s returns and the benchmark’s returns, then multiplying the result by the square root of 12.

Treynor Ratio

The Treynor Ratio, developed by Jack Treynor, is similar to the Sharpe Ratio, except that it uses Beta as the volatility measurement. Return (numerator) is defined as the incremental average return of an investment over the risk free rate. Risk (denominator) is defined as the Beta of the investment returns relative to a benchmark.

The Percent Gain Ratio

The Percent Gain Ratio is a measure of the number of periods that the Investment was up divided by the number of periods that the Benchmark was up. The larger the ratio, the better.

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