## Financial Formulas Used In Our Calulations

Click here to see our formulas in use

Click here to see our formulas in use

R_{i} = return of i-th period, %. Example: 2.2%

**Rate of Return**

RoR_{i} = rate of return of i-th period. Calculated as (R_{i} / 100) + 1.

**VAMI**

VAMI = growth of a hypothetical $1,000 in a given investment. Calculated as VAMI_{n} = 1000 * RoR_{1} * RoR_{2} * … * RoR_{n} . Where RoR_{i} = rate of return of i-th period, N is number of periods in calculations.

**Risk Free Rate**

R_{RF} = risk free return, %. Updated daily.

**S&P Value**

VS&P_{i} = value of S&P program in i-th month. Updated monthly.

**S&P Rate of Return**

RoRS&P_{i} = rate of return of S&P program in i-th month. Calculated as VS&P_{i} /VS&P_{i-1}. Where VS&P_{i} = value of S&P program in i-th month

**S&P Monthly Return %**

RS&P_{i} = return of S&P program in i-th month. Calculated as (RoRS&P_{i} – 1) * 100. Where RoRS&P_{i} = rate of return for S&P program in i-th month.

**Mean Return**

M = mean of return for the specified period. Calculated as (R_{1} + R_{2} + R_{3} + … R_{N}) / N for all specified periods. R_{i} – 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 (RoR_{1} * RoR_{2} * RoR_{3} * … * RoR_{N} - 1) * 100% for all specified periods. Where RoR_{i} = 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 ((RoR_{1} * RoR_{2} * RoR_{3} * … * RoR_{N} )^{1/N} - 1) * 100%. Where RoR_{i} = 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 ((RoR_{1} * RoR_{2} * RoR_{3} * … * RoR_{N} )^{12} - 1) * 100%. Where RoR_{i} = rate of return of i-th period, N is a number of periods.

**# of Losing Months**

# Losing months = number of months where R_{i} < 0.

**# of Winning Months**

# Winning months = number of months where R_{i} ≥ 0.

**Avg Monthly Loss**

Avg monthly loss = average negative return. Calculated as (R_{1} + R_{2} + R_{3} + … R_{M}) / M where R_{i} < 0, M = # Losing months.

**Avg Monthly Gain**

Avg monthly gain = average positive return. Calculated as (R_{1} + R_{2} + R_{3} + … R_{K}) / K where R_{i} ≥ 0, K = # Winning months.

**Standard Deviation**

Standard Deviation = degree of variation of returns. Calculated as (((R_{1} – M)^{2} + (R_{2} – M)^{2} + … + (R_{N} – M)^{2}) / (N-1))^{1/2} where R_{i} – 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 = ((L_{1}^{2} + L_{2}^{2} + … + L_{N}^{2}) / N)^{1/2} . Where L_{i} = min(R_{i} – R_{RF}, 0), N – number of months in calculation.

**Sharp Ratio**

Sharpe Ratio = (M - R_{RF}) / Standard deviation. Where M = mean of return, R_{RF} = risk free return.

**Sortino Ratio**

Sortino Ratio = (Compound monthly return - R_{RF}) / Downside deviation. Where R_{RF} = risk free return.

**Maximum Drawdown**

Maximum drawdown = percent retrenchment from an equity peak to an equity valley. Calculated as max ((VAMI_{i} – VAMI_{j} ) / VAMI_{i}) * 100% where j > i and for any j VAMI_{i} > VAMI_{j}.

**Clamar Ratio**

Clamar Ratio = Compound annual return / Maximum drawdown.

**Sterling Ratio**

Sterling Ratio = Compound annual return / ABS (Average Drawdown - 10%). Where Average Drawdown = (DD_{1} + DD_{2} + DD_{3}) / 3. Where DD_{1} = Maximum drawdown for first 12 months, DD_{2}= Maximum drawdown for next 12 months, DD_{3} = Maximum drawdown for last 12 months.

**Beta**

Beta = ((R_{1} - M) * (RS&P_{1} – MS&P) + (R_{2} - M) * (RS&P_{2} – MS&P) + … + (R_{N} - M) * (RS&P_{N} – MS&P)) / ((RS&P_{1} – MS&P)^{2} + (RS&P_{2} – MS&P)^{2} + … + (RS&P_{N} – MS&P)^{2}). Where R_{i} = program return for i-th month, M = mean return of the program, RS&P_{i} = 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.