Below we list the formulas used to calculate and define our ratios and statistics found
throughout the Absolute Returns managed futures site.
Return
Ri = return of i-th period, %.
Rate of Return
RoRi = rate of return of i-th period. Calculated as (Ri / 100) + 1.
VAMI
VAMI = growth of a hypothetical $1,000 in a given investment. Calculated as
VAMIn = 1000 * RoR1 * RoR2
* … * RoRn . Where RoRi
= rate of return of i-th period, N is number of periods in calculations.
Risk Free Rate
RRF = risk free return, %. Updated daily.
S&P Value
VS&Pi = value of S&P program in i-th month. Updated
monthly.
S&P Rate of Return
RoRS&Pi = rate of return of S&P program in i-th
month. Calculated as VS&Pi /VS&Pi-1.
Where VS&Pi = value of S&P program in i-th month
S&P Monthly Return %
RS&Pi = return of S&P program in i-th month. Calculated as (RoRS&Pi
– 1) * 100. Where RoRS&Pi = rate of return for S&P program in
i-th month.
Mean Return
M = mean of return for the specified period. Calculated as (R1
+ R2 + R3 + … RN)
/ N for all specified periods. Ri – return of i-th period, N is a number
of periods.
Total Compound Rate of Return
Total compound return = total return for the specified period. Calculated as
(RoR1 * RoR2 * RoR3
* … * RoRN - 1) * 100% for all specified periods.
Where RoRi = rate of return of i-th period, N is a number of periods.
Year to Date Return
Year to date return = total compound return since first month of the current
year.
1 Year Return
1 Year return = total compound return for past 12 months (N = 12).
3 Year Return
3 Year return = total compound return for past 36 months (N = 36).
Compounded Monthly Return
Compound monthly return = average compound return per 1 month. Calculated as
((RoR1 * RoR2 * RoR3
* … * RoRN )1/N - 1) * 100%.
Where RoRi = rate of return of i-th period, N is a number of periods.
Compounded Annual Return
Compound annual return = average compound return per 1 year. Calculated as ((RoR1
* RoR2 * RoR3 * … * RoRN
)12/N - 1) * 100%. Where RoRi = rate of return of i-th
period, N is a number of periods.
# of Losing Months
# Losing months = number of months where Ri < 0.
# of Winning Months
# Winning months = number of months where Ri ≥
0.
Avg Monthly Loss
Avg monthly loss = average negative return. Calculated as (R1
+ R2 + R3 + … RM)
/ M where Ri < 0, M = # Losing months.
Avg Monthly Gain
Avg monthly gain = average positive return. Calculated as (R1
+ R2 + R3 + … RK)
/ K where Ri ≥ 0, K = # Winning months.
Standard Deviation
Standard Deviation = degree of variation of returns. Calculated as (((R1
– M)2 + (R2 – M)2 + … + (RN
– M)2) / (N-1))1/2 where Ri – return
of specific month, M – mean of return, N – number of months.
Annualized Standard Deviation
Annualized standard deviation = Standard Deviation * (12/N)1/2
where N = number of months in calculation.
Downside Deviation
Downside deviation = ((L12 + L22
+ … + LN2) / N)1/2
. Where Li = min(Ri – RRF, 0), N – number of months in calculation.
Sharp Ratio
Sharpe Ratio = (M - RRF) / Standard deviation. Where
M = mean of return, RRF = risk free return.
Sortino Ratio
Sortino Ratio = (Compound monthly return - RRF) / Downside
deviation. Where RRF = risk free return.
Maximum Drawdown
Maximum drawdown = percent retrenchment from an equity peak to an equity valley.
Calculated as max ((VAMIi – VAMIj ) / VAMIi) * 100% where j > i and
for any j VAMIi > VAMIj.
Clamar Ratio
Clamar Ratio = Compound annual return / Maximum drawdown.
Sterling Ratio
Sterling Ratio = Compound annual return / ABS (Average Drawdown - 10%). Where
Average Drawdown = (DD1 + DD2
+ DD3) / 3. Where DD1 = Maximum
drawdown for first 12 months, DD2= Maximum drawdown for
next 12 months, DD3 = Maximum drawdown for last 12 months.
Beta
Beta = ((R1 - M) * (RS&P1
– MS&P) + (R2 - M) * (RS&P2
– MS&P) + … + (RN - M) * (RS&PN
– MS&P)) / ((RS&P1 – MS&P)2
+ (RS&P2 – MS&P)2 + … + (RS&PN
– MS&P)2). Where Ri = program return for i-th month, M = mean
return of the program, RS&Pi = return of S&P program for i-th month,
MS&P = mean of return of S&P program.
Alpha
Alpha = M – Beta * MS&P. Where M is mean of return of user program,
MS&P – mean of return of S&P program.
© AbsoluteReturns.com 2006
