Statistical Definitions

A Quick Guide to Autumn Gold's Statistical Terms

2nd Edition
Coming Soon

Annualized Compound Rate of Return is a method that compounds return and is used by Autumn Gold in all of its calculations. There are a few traders that calculate their return based on a "straight addition" methodology with the result that the annual performance shown in their disclosure document differs from the annual return shown on the Autumn Gold website. These circumstances are denoted as such in the accounting notes on the individual CTA Profile page.

Monthly Annualized Compound ROR = ((Ending VAMI / Beginning VAMI) ^ (1/N)) - 1

Annualized Compound ROR = ((1 + Monthly Compound ROR) ^ 12) - 1

Maximum Drawdown (Peak to Valley Drawdown) reflects the greatest to date loss of a Commodity Trading Advisor. Maximum Drawdown can be defined as the potential cost of higher return.

Calmar Ratio represents the historical amount gained for each dollar risked. A higher number is better. Unless otherwise denoted Autumn Gold calculates the Calmar Ratio over a 36 month period.

Calmar Ratio = Annualized Compound ROR / Maximum Drawdown Calmar Ratio

Standard Deviation is one way to look at consistency of returns. It measures the degree by which the monthly returns vary from the average (mean) return.

Downside Deviation is a measure of downside volatility. It only considers those monthly performance results that are less than the monthly Minimum Acceptable Rate of Return.

Downside Deviation = Square Root of the (Sum of the (Monthly Underperformance squared) / the number of Periods)

Annualized Downside Deviation = Monthly Downside Deviation * Square Root of 12

Monthly Underperformance = Monthly ROR - Monthly Minimal Acceptable Rate of Return
for those months where the Monthly Underperformance < 0

Sharpe Ratio is a risk adjusted ratio that rewards consistancy of returns. Traders are penalized for volatility regardless of whether it is onthe up or downside. When comparing Sharpe Ratios it is important to use the same risk free rate of return. Currently Autumn Gold uses a 1% risk-free rate of return in its calculations.

Monthly Sharpe Ratio = (Monthly Rate of Return - Monthly Risk Free Rate of Return) / Monthly Standard Deviation

The Monthly Sharpe Ratio is then annualized

Sortino Ratio - is a risk adjusted ratio. The higher the number the better. Results are dependent upon the Minimum Acceptable Rate of Return. Autumn Gold uses a 5% Minimum Acceptable Rate of Return in its statistical calculations.

Sortino Ratio = (Average Monthly Compound ROR - Minimum Monthly Acceptable ROR*) / Downside Deviation

The Sterling Ratio is a risk-adjusted return measurement calculated by dividing the Annualized Compound ROR by the Average Yearly Maximum Drawdown less an arbitrary 10%. The Sterling Ratio is normally calculated using the last 36 months of data.

Sterling Ratio = Annualized Compound ROR / (the Average Yearly Maximum Drawdown - 10%)*

* We use the absolute value, so this becomes a positive number

The Average Yearly Maximum Drawdown =

((max drawdown for 1st 12 months) + (max drawdown for the 2nd 12 months) + (max drawdown for the 3rd 12 months))
3

Omega Function takes all of the performance data into consideration. The flatter the distribution the more risky the investment. "The distribution mean is where the omega function equals 1. "Omega provides practitioners with an extremely useful tool since it accounts for the non-normal distributions of returns which are commonplace in finance, particularly for alternative investments. ...omega incorporates all the moments of the distribution and is therefore appropriate for investment analysis when returns are not normally distributed. Second, even for normally distributed returns, omega provides additional information since it takes into account the investor's preferences for loss and gain. Finally, omega is computed directly from the returns distribution and measures the total impact of the moments instead of each one of them individually. It can therefore reduce the estimation error risk." [Abrams, Ray, Ranjan Bhaduri, PHD, CFA, CAIA, and Elizabeth Flores, CAIA. "Litner Revisted: A Quantitative Analysis of Managed Futures for Plan Sponsors, Endowments and Foundations. CME Group (May 2012): 12-14. Print]

Notes:

N = number of months

Autumn Gold currently uses a Minimum Acceptable Rate of Return of 5%

Autumn Gold currently uses 1% Risk Free Rate of Return