Financial Formulas Used In Our Calulations
Ri = return of i-th period, %. Example: 2.2%
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 - 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 * SQRT(N) where N = number of periods in 1 year.
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.
