Glossary of Statistical Terms

Annual Rate of Return

The rate of return (gain or loss) on an investment, relative to the amount invested, over a one-year period.

Calmar Ratio

A ratio used to determine returns relative to a drawdown’s (downside) risk in a futures portfolio or other similar investment vehicle. The Calmar ratio is determined by dividing the compounded annual return by the maximum drawdown, using the absolute value.

Generally speaking, the higher the Calmar ratio the better. Some programs have high annual returns, but they also have extremely high drawdown risk. This ratio helps determine return on a downside risk–adjusted basis. Most Calmar ratios utilize 3 years of data.

Correlation

Correlation is a measure of the interdependence, or strength of the relationship, between two investments. It tells something about the degree to which the variations of returns from their respective means move together. If two investments are positively correlated, when one performs above its mean return it is likely that the other will also perform above its mean return. If two investments are negatively correlated, when one performs above its mean return it is likely that the other will perform below its mean return. Note that correlation says nothing about the mean returns themselves – they could both be up, or both down, or one could be up and one down. The correlation coefficient is used to measure the strength of the relationship. Values range from –1 (perfect negative correlation), through 0 (no correlation or uncorrelated) to +1 (perfect positive correlation). From a risk management perspective, it is generally favorable if two investments are uncorrelated because it means that there is no identifiable directional pattern or proportional relationship between the deviations of their monthly returns from each of their respective trends – sometimes investment B is positively correlated to investment A when the returns of A are positive and negatively correlated when they are negative, meaning that over a period of time the strategy returns move closer to non–correlation. This should produce a smoother overall return profile.

Drawdown

An investment is said to be in a drawdown when its price falls below its last peak. The drawdown is the percentage drop in the price of an investment from its last peak price. The period between the peak level and the trough is called the length of the drawdown period between the trough and the recapturing of the peak is called the recovery. The worst or maximum drawdown represents the greatest peak to trough decline over the life of an investment to-date.

Kurtosis

Kurtosis characterizes the relative peakness or flatness of a distribution compared with the normal distribution (with normal distribution being a bell curve). Positive kurtosis indicates relatively peaked distribution. Negative kurtosis indicates relatively flat distribution. An overabundance of activity to the left or right of the normal distribution may indicate that the program is subjected to excessive risk.

Sharpe ratio

The Sharpe Ratio is a measure of risk–adjusted performance that indicates the level of excess return per unit of risk. In the calculation of Sharpe ratio, excess return is the return over and above the short–term risk free rate of return and this figure is divided by the risk, which is represented by the annualized volatility or standard deviation. In summary the Sharpe Ratio is equal to the compound annual rate of return minus rate of return on a risk–free investment divided by the annualized monthly standard deviation. The greater the Sharpe ratio, the greater the risk–adjusted return.

Skewness

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.

Sortino ratio

The Sortino ratio is a measure of risk–adjusted performance that indicates the level of excess return per unit of downside risk. It differs from the Sharpe ratio in that it recognizes investors' preference for upside ("good") over downside ("bad") volatility and uses a measure of 'bad' volatility as provided by semi–deviation – the annualized standard deviation of the returns that fall below a target return, say the risk free rate.

Sterling Ratio

This ratio is also a comparison of historical reward and risk and was developed by Deane Sterling Jones. The Sterling Ratio is equal to the average annual rate of return for the past three calendar years divided by the average of the maximum annual drawdown in each of those three years plus 10%.

Value–Added Monthly Index (VAMI)

VAMI is defined as the growth in value of an average $1000 investment. VAMI is calculated by multiplying (1 + current monthly ROR) times (previous monthly VAMI). VAMI assumes the reinvestment of all profits and interest income. Incentive and Management Fees have been deducted.

Value–At–Risk (VAR)

A widely used risk measurement technique that estimates (at a pre–specified level of probability) the loss that would be experienced in a day or some other pre–specified time horizon in the event of an increase in volatility or an adverse correlated move in market prices, assets or the investments making up a portfolio.