Rate of Return (ROR)
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
Rn is computed as:
where
Di are motnhly performance data (one value per month).
Last Month
Rate of return for the most current month as reported by the program manager.
3 Months ROR
Compounded rate of return for the last three months.
Year To Date
Current year's return, calculated by summing the returns of current year months
using the compounding effect.
12 Months ROR
Compounded rate of return for the last twelve months.
36 Months ROR
Compounded rate of return for the last thirty-six months.
Average ROR
Compounded average annual rate of return, which is calculated using the final VAMI.
where
R is the compounded return.
Total Return
Compounded rate of return since inception.
Value Added Monthly Index (VAMI)
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
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
s2 also denoted as
σ2 is variance,
xis
are values and
x is mean of
values.
The square root of the variance
σ is the standard deviation.
Down.Deviation
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.
Sharpe Ratio
The Sharpe Ratio is a measure of the risk-adjusted return of an investment.
where
r is the average monthly return,
rr f is the risk-free
return (we use 1% per year as a risk-free return) and
σ is the standard deviation
of the monthly returns over the same period.
This gives you
s, the monthly Sharpe you can annualize by multiplying it
by the square root of 12.
Sortino Ratio
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
σ
(returns below a minimum acceptable threshold).
Sterling Ratio
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%.
Calmar Ratio
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
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
ri is the return of the
i-th month,
r is the
average monthly return,
n denotes the number of months and
σ is the
standard deviation of the monthly returns.
Kurtosis
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
ri is the return of the
i-th month,
r is the
average monthly return,
n denotes the number of months and
σ is the
standard deviation of the monthly returns.
Drawdown
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
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.
Correlation and Correlation Coefficient
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
σX denotes standard deviation of the first variable,
σY
standard deviation of the second variable and
where
x and
y are means of first and second variable.
Stress testing
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).
Value at Risk
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%.
Correl.S&P 500
Correlation vs. S&P 500.
Correl.DJ/CS MF
Correlation vs. Dow Jones Credit Suisse Managed Futures Index.
Correl.NewEdge
Correlation vs. NewEdge CTA Index.
Positive months
Percentage of positive months.
Avg pos.month
Average positive month in percentage.
Avg losing month
Average losing/negative month in percentage.