Glossary

Annualised Standard Deviation

• A measure of the volatility of the returns of the fund around the mean return. The calculation is based on monthly returns and adjusted to reflect an annual number.
• The formula used for calculating annualised standard deviation is:

Where: ri  - The return in month i.
                            µ - Average monthly return over the period

• High standard deviation of returns, from a given asset, indicates a higher variability in the performance from that asset and is generally considered to imply higher levels of investment risk.

Downside Deviation (Downside Volatility)

• Measures the deviation of values below a specified minimal acceptable return (MAR). Only returns below MAR are considered in the calculation

Where: ri are the set of returns of the investment and n is the number of returns.

• In this report, Downside volatilities are calculated using MAR = rf, where rf is the risk-free rate at the time of ri (see Risk-free rate).

Drawdown

• Drawdown is the measure of the decline from a historical peak in some variable. In this report, it is used to represent the largest loss suffered by a fund from “peak-to-trough” (i.e. the largest percentage drop in the net asset value of the fund, during the period of observation).

Kurtosis

• In probability theory and statistics, kurtosis is a measure of the "peakedness" and “tailedness” of the probability distribution of (real-valued) random variables.
• Higher kurtosis means more of the variance is due to infrequent extreme deviations, as opposed to frequent modestly sized deviations.
• Or there is a greater probability of extreme values (returns) in the fund (both positive and negative).
• A high kurtosis distribution has a sharper "peak" and fatter "tails", while a low kurtosis distribution has a more rounded peak with wider "shoulders".
• Distributions with zero kurtosis are called Mesokurtic
• A distribution with positive kurtosis is called Leptokurtic
• A distribution with negative kurtosis is called Platykurtic

Omega

• Omega is a probability-weighted ratio of gains to losses based on the distribution of returns of an investment. This is in contrast to a simple ratio of the probabilities of gains to losses, which would not take into account the magnitude of each potential gain/loss.
• The ratio of gains to losses is not absolute (i.e. positive returns being gains and negative returns being losses). Instead, the ratio is dependent on a threshold level of minimum acceptable returns (MAR) defined by the investor. Any return above MAR is considered a gain; any return below MAR is considered a loss. Generally, MAR is set at the risk free rate but any level can be set depending on the investor’s risk-return appetite. Omega is given by:

• Where ‘F(x)’ is the distribution of ‘N’ returns and MAR is the variable minimum acceptable return.
• Financial returns rarely follow a normal distribution. Most metrics account for the mean and standard deviation but ignore skew, kurtosis and higher moments. Omega captures and incorporates all higher moment information from the distribution of returns into a single function. For return distributions for which the higher moments are insignificant, omega will rank historical performance of funds in a similar order to more traditional metrics but when the higher moments do contribute an effect (e.g. for a distribution with a high level of kurtosis), Omega will rank performance in a more accurate manner.
• In contrast, the commonly used, Sharpe ratio weights gains and losses equally; this is a result of using only the mean and variance of the distribution and disregarding the higher moments. Also, the Sharpe ratio does not take into account the different requirements of investors. Some investors will regard any return above zero as being positive; others require returns above the risk-free rate or higher minimum acceptable return levels.

Properties of Omega:

• Omega is always positive
• High Omega is always preferable
• A range of values of MAR will always produce a single value function of Omega
• With increasing MAR, Omega always decreases
• For MAR = mean return, Omega = 1
• As MAR ®  -¥, Omega ® ¥
• As MAR ® ¥, Omega ® 0

RAID Chart

• The RAID (Return from Alternative Investment Dates) chart displays the ultimate growth of many possible investments initiated at alternative start dates. Each bar (or marker) on the chart represents the cumulative return of the investment from that corresponding date to the most recent date shown (In this case, December 2005).
• A standard unit growth chart describes the growth in the value of an investment at different times in its history from a single starting date. In contrast to this, a RAID chart describes the growth of many possible investments each starting at different dates but all ending at the same date (usually the present). The RAID chart attempts to remove the inherent subjectivity associated with particular starting points when comparing the performance of different investments. This analysis provides a more robust form in which to represent a unit growth rates from investments.
• Returns are charted in reverse chronological order to represent the increasing term of investment.
• In the example shown in the figure below, the compound growth to January 2006, of the CSFB/ Tremont Hedge Fund Index, the MSCI World Equity Index and the Lehman Global Composite Index are compared. It can be observed that, from a starting date of January 1999, the CSFB Hedge Fund Index has produced a higher level of growth (88%) than the Lehman Composite Global Index (39%) or the MSCI World Equity Index (6%).

Risk-free rate (Rf)

• The risk free rate is calculated as the rate of interest on a 3 month US Treasury bill.

Sharpe Ratio

• A measure of risk-adjusted return. The Sharpe Ratio represents the returns achieved by the fund (in excess of a risk free return), per unit of risk taken. Where the risk is defined as standard deviation (or variability) of returns

 

• The higher Sharpe Ratio the better. A higher ratio indicates that the manager is more efficient at producing returns for each unit of risk taken.

• Dynamic Sharpe Ratio - In many cases the risk free return used in the Sharpe Ratio estimated for the period used in the calculation. In the case of the Dynamic Sharpe Ratio we use the actual risk free rates of return available in the market.
• Where: the risk free rate = the prevailing US 90-day T-Bill rates of return at that date.

Skewness

• In probability theory and statistics, skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable. Roughly speaking, a distribution has:
• Positive skew (right-skewed) if the higher tail is longer (there are more higher positive returns then there are low negative returns)
• Negative skew (left-skewed) if the lower tail is longer (there are more lower negative returns than there are higher positive returns)

Sortino Ratio

• Similar to the Sharpe Ratio, the Sortino Ratio is a measure of risk-adjusted return, but Risk is defined as downside deviation (and not standard deviation).

• The Sortino Ratio represents the returns achieved by the fund (in excess of a risk-free return), per unit of risk (downside deviation) taken.
• The higher Sortino Ratio the better. A higher ratio indicates that the manager is more efficient at producing returns for each unit of (downside) risk taken
• Dynamic Sortino Ratio - In many cases the risk free return used in the Sharpe Ratio estimated for the period used in the calculation. In the case of the Dynamic Sortino Ratio we use the actual risk free rates of return available in the market.
• Where: the risk free rate = the prevailing US 90-day T-Bill rates of return at that date.

 

Upside Deviation (Upside Volatility)

• Measures the deviation of values above a specified minimal acceptable return (MAR). Only returns above MAR are considered in the calculation

• Where ri are the set of returns of the investment and n is the number of returns.
• In this report, Upside volatilities are calculated using MAR = rf, where rf is the risk free rate at the time of ri (see Risk-free rate).