ROR is the ratio of money gained on an investment relative to the amount of money invested. It is calculated using the compounding effect. With it the ROR for *n* months *R _{n}* is computed as:

where

Rate of return for the most current month as reported by the program manager.

Compounded rate of return for the last three months.

Current year's return, calculated by summing the returns of current year months using the compounding effect.

Compounded rate of return for the last twelve months.

Compounded rate of return for the last thirty-six months.

Compounded average annual rate of return, which is calculated using the final VAMI.

where *R* is the compounded return.

Compounded rate of return since inception.

This index reflects the growth of a hypothetical $1,000 in a given investment over time. The index is equal to $1,000 at inception. Subsequent month-end values are calculated by multiplying the previous month’s VAMI index by 1 plus the current month rate of return.

Standard deviation measures the degree of variation/uncertainty of returns around the mean/average return. The higher the volatility of the investment returns, the higher the standard deviation. That is why the standard deviation is often used as a measure of risk.

where *s ^{2}* also denoted as

The square root of the variance

Similar to Standard Deviation, but Downside Deviation only takes losing/negative periods into account. That´s why it does not penalize the program for higher then average return, but only for higher then average loss.

The Sharpe Ratio is a measure of the risk-adjusted return of an investment.

where *r* is the average monthly return, *r _{r f}* is the risk-free return (we use 0% per year as a risk-free return) and

This gives you

Return/risk ratio. The concept and formula as in Sharpe ratio. The only difference is that it is calculated using standard deviation of negative returns only as *?* (returns below a minimum acceptable threshold).

Return/risk ratio. Return is defined as the compound annualized rate of return over the last 3 years. Risk is defined as the average yearly maximum drawdown over the last 3 years less an arbitrary 10%.

Return/risk ratio. Return is defined as the compound annualized rate of return over the last 3 years, risk as the maximum drawdown over the last 3 years.

Skewness characterizes the degree of asymmetry of a distribution of returns 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.

where *r _{i}* is the return of the

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

where *r _{i}* is the return of the

A drawdown is any losing period during an investment. It is defined as the percent retrenchment from an equity peak to an equity valley. A drawdown starts with the beginning of an equity retrenchment and continuous until a new equity high is reached. (a drawdown encompasses both the period from the equity peak to the equity valley (length) and the time from the equity valley to the new equity high (recovery)). Maximum Drawdown is then the greatest cumulative percentage decline in equity.

Beta is the slope of the regression line. Beta measures the risk of a particular investment relative to the market as a whole (the “market” can be any index or investment you specify). It describes the sensitivity of the investment to broad market movements. For example, in equities, the stock market (the independent variable) is assigned a beta of 1.0. An investment which has a beta of 0.5 will tend to participate in broad market moves, but only half as much as the market as a whole.

Where:

R_{I} = The return of the independent variable for period I,

RD_{I} = The return of the dependent variable for period I,

M_{R} = The mean return of the independent variable,

M_{RD} = The mean return of the dependent variable and

N = Number of Periods

The correlation coefficient is a statistical measure of the degree of linear relationship between two variables. The correlation coefficient may take on any value between plus and minus one. The sign of the correlation coefficient (+ , -) defines the direction of the relationship, either positive or negative. A positive correlation coefficient means that as the value of one variable increases, the value of the other variable increases as well; as one decreases the other decreases too. Taking the absolute value of the correlation coefficient measures the strength of the relationship. Thus a correlation coefficient of zero indicates the absence of a linear relationship and correlation coefficients of one and minus one indicate a perfect linear relationship.

where *? _{X}* denotes standard deviation of the first variable,

where

Stress testing is a method of determining how the program will behave during a period of financial crisis. We use the worst monthly S&P500 returns as a stress time. You can also use hypothetical scenarios (for example Monte Carlo simulation) or known historical events (for example Russian debt default in 1998 or 9/11 terrorist attacks).

This is the maximum amount of capital that the position can expect to lose within a specified holding period (we use 1 month period) and with a specified confidence level (we use 95%). Example: if VaR is -10%, you can expect that 95% of the next month returns will be better than -10%.

Correlation vs. S&P 500.

Correlation vs. Dow Jones Credit Suisse Managed Futures Index.

Correlation vs. NewEdge CTA Index.

Percentage of positive months.

Average positive month in percentage.

Average losing/negative month in percentage.

The difference between a portfolio's returns and the benchmark.

Where:

R_{I} = The return of the independent variable for period I,

RD_{I} = The return of the dependent variable for period and

N = Number of Periods.

Measures how well the regression line fits the data. A high R^{2} value means that the regression line closely fits the data.

This measure uses beta as the volatility measure rather than standard deviation.

*Treynor Ratio = ( M _{R} - R_{RF} )*

Where:

M

R

Calculates the extent to which a fund has added value relative to a benchmark.

Where:

R_{I} = Benchmark Return for period I,

RD_{I} = Return for period I,

M_{R} = Mean of return set R (Benchmark),

M_{RD} = Mean of return set RD,

N = Number of Periods and

R_{RF} = Period Risk Free Return.

Gain Deviation

Calculates the fund’s average return only for the periods with a gain and measures the variation of only the winning periods around this gain mean.

Where:

N = Number of Periods,

R_{I }= Return for period I,

M_{G} = Gain Mean,

G_{I} = R_{I} ( IF R_{I} 3 0 ) or 0 ( IF R_{I} < 0 ),

GG_{I} = R_{I} - M G ( IF R_{I} 3 0 ) or 0 ( IF R_{I }< 0 ) and

N G = Number of periods that RI 3 0.

Calculates the fund’s average return only for the periods with a loss and measures the variation of only the losing periods around this loss mean.

Where:

N = Number of Periods,

R_{I} = Return for period I,

M*L* = Loss Mean,

L_{I} = R_{I} ( IF R_{I} < 0 ) or 0 ( IF R_{I} >= 0 ),

LL_{I} = R_{I} - M_{L} ( IF R_{I} < 0 ) or 0 ( IF R_{I} >= 0 ) and

N_{L }= Number of periods that R_{I} < 0.

Calculates the fund’s value added relative to a benchmark.

*Alpha = M _{RD} - Beta* x M_{R}*

Where:

M

M

A measurement of returns adjusted for risk that can be used to compare the performance of commodity trading advisors, hedge funds and trading strategies.

*The MAR Ratio is calculated by dividing the compound annual growth rate of a fund or strategy since inception by its biggest drawdown.
*The higher the ratio, the better the risk-adjusted returns.*

Measures how well a fund or portfolio outperformed a money market index over a 12 month period compared with its associated downside risk.

The simplest benchmark ratio. It takes the fund’s annualized return and subtracts the benchmark’s annualized return to yield the fund’s gain or loss that is over or under the benchmark.

*Active Premium = Investment’s annualized return - Benchmark’s annualized return*

Compares the fund’s active premium with the fund’s tracking error.

*Information Ratio = Active Premium / Tracking Error*

Timeframes in this table are calculated using rolling periods. Please see an example below.

Let's have the following monthly returns: 2.5 %, -2 %, 3 %, 1 % and 5 %.

**1. Winning Periods**

To get a value for the 3-Months Period, we first calculate the periods of 3 consecutive months:

I. 2 % -2 % +3 % = 3.5 %

II. -2 % +3 % +1 % = 2 %

III. 3 % +1 % +5 % = 8 %

As you can see, 100 % of 3-Months Periods is winning and 0 % lossing.

**2. Sharpe**

As we use 0% risk-free rate, Sharpe is calculated as the average monthly return divided by the standard deviation - both values are calculated using rolling periods (as shown in 1.).

3-Month (Compounded) Average is 4.88 and 3-Month Standard Deviation 3.84. This gives us monthly Sharpe 1.27 but the value in the TWA table is annualized, i.e. we have to multiply it by the square root of 12.