# Formulas

## As a dedicated partner to our clients RCG Managed Futures strives to provide education and research that will help investors optimize their profitability. Below we provide some managed futures and alternative investment formulas that may be used on the RCG Managed Futures Database.

* Denotes investment formulas used by Barclay Hedge regarding the statistics and reports on the CTA profiles available on the RCG Managed Futures website.

*Total Return

(Final VAMI / Initial VAMI – 1)     (X 100 for %)

Example: Initial VAMI = 1000, Final VAMI = 2000
Total return = ((2000/1000) -1) = 2 – 1 = 1  or 100%

*Compound Annual Return

((Final VAMI / Initial VAMI) ^ (1 / number of years)) – 1   (X 100 for %)
If you don’t have an even number of years, use (12 / number of months) or (4 / number of quarters)

Example: Initial VAMI = 1000, Final VAMI = 4000, No. of years = 2
Cpd. Ann. ROR = ((4000 / 1000) ^ (1/2)) –1
Cpd. Ann. ROR = 4^1/2 -1 = 2 – 1  = 1   or 100%
Note: ^ = raised to the power of Raising a number to the 1/2 power is the same as taking the square root.

*Standard Deviation of Monthly Returns

Each monthly rate of return = ((VAMI at end of month / VAMI at beginning of month) – 1)
Standard deviation = SQRT ((Sum(monthly ROR – average monthly ROR) ^ 2)) / # of months)
Note: You are finding the square root of the sum of the squares of the differences.

*Annualized Standard Deviation of Monthly / Quarterly Return

(Std. Dev. of Monthly ROR)  X SQRT (12)  or  (Std. Dev. of Quarterly ROR) X  SQRT (4)
Note: Multiplying monthly Standard Deviation by the SQRT (12) is an industry standard method of approximating annualized Standard Deviations of Monthly Returns.

*Sharpe Ratio

(Compound Annual ROR – risk free ROR (calculated from T-bills)) / Annualized Std. Dev. of Mo. ROR or Annualized Std. Dev. of Quarterly ROR

*Sterling Ratio

Compound Annual ROR for the past three years / (Average Annual Maximum Drawdown + 10%)

*Barclay Ratio

Trend / Standard deviation of detrended VAMI’s
Example: First calculate the linear regression trend of the VAMI’s including the initial point. This is the numerator.  Next remove the trend from the VAMI’s (detrended VAMI = original VAMI – (slope X month number + intercept)).  Take the Standard Deviation of these detrended VAMI’s.

*Efficiency Ratio

(Compound Annual Return / Annualized Std. Dev. Mo. ROR.)

*Worst Drawdown

Drawdown = (1 – Valley VAMI / Peak VAMI)   (X 100 for %)

Example: Peak VAMI = 2000, Valley VAMI = 1500
Drawdown = 1 – 1500/2000 = .25  or 25%
Note: A drawdown is the Peak-to-Valley rate of return and is actually the negative, since in a drawdown the ROR is by definition negative.

*Average Recovery

The average time in a drawdown as measured from the previous peak to a new peak (New high ground).  If the program is still in a drawdown, the calculation assumes that the drawdown is over.

*Average Annual Return

(Sum ROR for each calendar year in program history)/(number of calendar years in program history)
Example: ABC program Start Date: Oct. 1995 End Date Aug. 1998 (Sum ROR 1996, ROR 1997)/2