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Advanced Statistics: FOREX Formula

Advanced Statistics module contributed by Jules Ellis, C2 Member.

Jules has written a very helpful guide for these statistics.

MonthlyDaily (all)Daily (last 6 mo.)
ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.001
 SD0.155
 Sharpe ratio (Glass type estimate) 0.005
 Sharpe ratio (Hedges UMVUE)0.005
 df71.000
 t0.012
 p0.495
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.795
 Upperbound of 95% confidence interval for Sharpe Ratio0.805
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.795
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.805
Statistics related to Sortino ratio
 Sortino ratio0.008
 Upside Potential Ratio1.139
 Upside part of mean0.103
 Downside part of mean-0.102
 Upside SD0.124
 Downside SD0.090
 N nonnegative terms9.000
 N negative terms63.000
Statistics related to linear regression on benchmark
 N of observations72.000
 Mean of predictor0.020
 Mean of criterion0.001
 SD of predictor0.216
 SD of criterion0.155
 Covariance-0.002
 r-0.069
 b (slope, estimate of beta)-0.049
 a (intercept, estimate of alpha)0.002
 Mean Square Error0.024
 DF error70.000
 t(b)-0.575
 p(b)0.716
 t(a)0.027
 p(a)0.489
 Lowerbound of 95% confidence interval for beta-0.219
 Upperbound of 95% confidence interval for beta0.121
 Lowerbound of 95% confidence interval for alpha-0.125
 Upperbound of 95% confidence interval for alpha0.128
 Treynor index (mean / b)-0.015
 Jensen alpha (a)0.002
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.011
 SD0.151
 Sharpe ratio (Glass type estimate) -0.070
 Sharpe ratio (Hedges UMVUE)-0.069
 df71.000
 t-0.172
 p0.568
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.870
 Upperbound of 95% confidence interval for Sharpe Ratio0.730
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.870
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.731
Statistics related to Sortino ratio
 Sortino ratio-0.108
 Upside Potential Ratio0.974
 Upside part of mean0.096
 Downside part of mean-0.106
 Upside SD0.113
 Downside SD0.098
 N nonnegative terms9.000
 N negative terms63.000
Statistics related to linear regression on benchmark
 N of observations72.000
 Mean of predictor-0.004
 Mean of criterion-0.011
 SD of predictor0.222
 SD of criterion0.151
 Covariance-0.002
 r-0.064
 b (slope, estimate of beta)-0.044
 a (intercept, estimate of alpha)-0.011
 Mean Square Error0.023
 DF error70.000
 t(b)-0.538
 p(b)0.704
 t(a)-0.174
 p(a)0.569
 Lowerbound of 95% confidence interval for beta-0.205
 Upperbound of 95% confidence interval for beta0.118
 Lowerbound of 95% confidence interval for alpha-0.134
 Upperbound of 95% confidence interval for alpha0.112
 Treynor index (mean / b)0.242
 Jensen alpha (a)-0.011
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.070
 Expected Shortfall on VaR0.086
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.027
 Expected Shortfall on VaR0.057
ORDER STATISTICS
Quartiles of return rates
 Number of observations72.000
 Minimum0.810
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.261
 Mean of quarter 10.979
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.036
 Inter Quartile Range0.000
 Number outliers low17.000
 Percentage of outliers low0.236
 Mean of outliers low0.977
 Number of outliers high16.000
 Percentage of outliers high0.222
 Mean of outliers high1.041
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)2.030
 VaR(95%) (moments method)0.007
 Expected Shortfall (moments method)NA
 Extreme Value Index (regression method)2.278
 VaR(95%) (regression method)0.006
 Expected Shortfall (regression method)NA
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations3.000
 Minimum0.047
 Quartile 10.072
 Median0.097
 Quartile 30.162
 Maximum0.227
 Mean of quarter 10.047
 Mean of quarter 20.097
 Mean of quarter 3NA
 Mean of quarter 40.227
 Inter Quartile Range0.090
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high0.000
 Percentage of outliers high0.000
 Mean of outliers highNA
Risk estimates based on draw downs (based on Extreme Value Theory)
 Extreme Value Index (moments method)NA
 VaR(95%) (moments method)NA
 Expected Shortfall (moments method)NA
 Extreme Value Index (regression method)NA
 VaR(95%) (regression method)NA
 Expected Shortfall (regression method)NA
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)0.037
 Compounded annual return (geometric extrapolation)0.034
 Calmar ratio (compounded annual return / max draw down)0.150
 Compounded annual return / average of 25% largest draw downs0.150
 Compounded annual return / Expected Shortfall lognormal0.394
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-0.000
 SD0.146
 Sharpe ratio (Glass type estimate) -0.001
 Sharpe ratio (Hedges UMVUE)-0.001
 df2071.000
 t-0.003
 p0.501
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.800
 Upperbound of 95% confidence interval for Sharpe Ratio0.797
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.800
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.797
Statistics related to Sortino ratio
 Sortino ratio-0.002
 Upside Potential Ratio3.400
 Upside part of mean0.305
 Downside part of mean-0.305
 Upside SD0.116
 Downside SD0.090
 N nonnegative terms240.000
 N negative terms1832.000
Statistics related to linear regression on benchmark
 N of observations2072.000
 Mean of predictor0.036
 Mean of criterion-0.000
 SD of predictor0.253
 SD of criterion0.146
 Covariance0.001
 r0.021
 b (slope, estimate of beta)0.012
 a (intercept, estimate of alpha)-0.001
 Mean Square Error0.021
 DF error2070.000
 t(b)0.941
 p(b)0.174
 t(a)-0.011
 p(a)0.504
 Lowerbound of 95% confidence interval for beta-0.013
 Upperbound of 95% confidence interval for beta0.037
 Lowerbound of 95% confidence interval for alpha-0.118
 Upperbound of 95% confidence interval for alpha0.116
 Treynor index (mean / b)-0.017
 Jensen alpha (a)-0.001
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.011
 SD0.144
 Sharpe ratio (Glass type estimate) -0.074
 Sharpe ratio (Hedges UMVUE)-0.074
 df2071.000
 t-0.182
 p0.572
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.873
 Upperbound of 95% confidence interval for Sharpe Ratio0.724
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.873
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.724
Statistics related to Sortino ratio
 Sortino ratio-0.116
 Upside Potential Ratio3.244
 Upside part of mean0.298
 Downside part of mean-0.309
 Upside SD0.111
 Downside SD0.092
 N nonnegative terms240.000
 N negative terms1832.000
Statistics related to linear regression on benchmark
 N of observations2072.000
 Mean of predictor0.004
 Mean of criterion-0.011
 SD of predictor0.253
 SD of criterion0.144
 Covariance0.001
 r0.021
 b (slope, estimate of beta)0.012
 a (intercept, estimate of alpha)-0.011
 Mean Square Error0.021
 DF error2070.000
 t(b)0.970
 p(b)0.166
 t(a)-0.183
 p(a)0.573
 Lowerbound of 95% confidence interval for beta-0.012
 Upperbound of 95% confidence interval for beta0.037
 Lowerbound of 95% confidence interval for alpha-0.126
 Upperbound of 95% confidence interval for alpha0.105
 Treynor index (mean / b)-0.881
 Jensen alpha (a)-0.011
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.013
 Expected Shortfall on VaR0.016
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.003
 Expected Shortfall on VaR0.006
ORDER STATISTICS
Quartiles of return rates
 Number of observations2072.000
 Minimum0.905
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.155
 Mean of quarter 10.997
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.004
 Inter Quartile Range0.000
 Number outliers low439.000
 Percentage of outliers low0.212
 Mean of outliers low0.996
 Number of outliers high447.000
 Percentage of outliers high0.216
 Mean of outliers high1.004
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.649
 VaR(95%) (moments method)0.001
 Expected Shortfall (moments method)0.008
 Extreme Value Index (regression method)0.255
 VaR(95%) (regression method)0.002
 Expected Shortfall (regression method)0.008
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations19.000
 Minimum0.000
 Quartile 10.003
 Median0.009
 Quartile 30.043
 Maximum0.273
 Mean of quarter 10.001
 Mean of quarter 20.006
 Mean of quarter 30.027
 Mean of quarter 40.155
 Inter Quartile Range0.040
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high3.000
 Percentage of outliers high0.158
 Mean of outliers high0.224
Risk estimates based on draw downs (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.176
 VaR(95%) (moments method)0.140
 Expected Shortfall (moments method)0.227
 Extreme Value Index (regression method)0.743
 VaR(95%) (regression method)0.140
 Expected Shortfall (regression method)0.515
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)0.037
 Compounded annual return (geometric extrapolation)0.034
 Calmar ratio (compounded annual return / max draw down)0.124
 Compounded annual return / average of 25% largest draw downs0.219
 Compounded annual return / Expected Shortfall lognormal2.126
ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-0.044
 SD0.000
 Sharpe ratio (Glass type estimate) NA
 Sharpe ratio (Hedges UMVUE)NA
 dfNA
 tNA
 pNA
 Lowerbound of 95% confidence interval for Sharpe RatioNA
 Upperbound of 95% confidence interval for Sharpe RatioNA
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)NA
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)NA
Statistics related to Sortino ratio
 Sortino ratio-18.547
 Upside Potential Ratio0.000
 Upside part of mean0.000
 Downside part of mean-0.044
 Upside SD0.000
 Downside SD0.002
 N nonnegative terms0.000
 N negative terms172.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.648
 Mean of criterion-0.044
 SD of predictor0.302
 SD of criterion0.000
 Covariance0.000
 rNA
 b (slope, estimate of beta)NA
 a (intercept, estimate of alpha)NA
 Mean Square ErrorNA
 DF errorNA
 t(b)NA
 p(b)NA
 t(a)NA
 p(a)NA
 Lowerbound of 95% confidence interval for betaNA
 Upperbound of 95% confidence interval for betaNA
 Lowerbound of 95% confidence interval for alphaNA
 Upperbound of 95% confidence interval for alphaNA
 Treynor index (mean / b)NA
 Jensen alpha (a)NA
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.044
 SD0.000
 Sharpe ratio (Glass type estimate) -7936535306446244.000
 Sharpe ratio (Hedges UMVUE)-7901674975671223.000
 df171.000
 t-5611977934314593.000
 p1.000
 Lowerbound of 95% confidence interval for Sharpe RatioNA
 Upperbound of 95% confidence interval for Sharpe RatioNA
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-8739115425704417.000
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)-7064234525638030.000
Statistics related to Sortino ratio
 Sortino ratio-18.547
 Upside Potential Ratio0.000
 Upside part of mean0.000
 Downside part of mean-0.044
 Upside SD0.000
 Downside SD0.002
 N nonnegative terms0.000
 N negative terms172.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.603
 Mean of criterion-0.044
 SD of predictor0.300
 SD of criterion0.000
 Covariance-0.000
 r-0.000
 b (slope, estimate of beta)-0.000
 a (intercept, estimate of alpha)-0.044
 Mean Square Error0.000
 DF error170.000
 t(b)-0.000
 p(b)0.500
 t(a)-5562757747689063.000
 p(a)1.000
 Lowerbound of 95% confidence interval for beta-0.000
 Upperbound of 95% confidence interval for beta0.000
 Lowerbound of 95% confidence interval for alpha-0.044
 Upperbound of 95% confidence interval for alpha-0.044
 Treynor index (mean / b)105669131314030172227945485041664.000
 Jensen alpha (a)-0.044
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.000
 Expected Shortfall on VaR0.000
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.000
 Expected Shortfall on VaR0.000
ORDER STATISTICS
Quartiles of return rates
 Number of observations172.000
 Minimum1.000
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.000
 Mean of quarter 11.000
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.000
 Inter Quartile Range0.000
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high0.000
 Percentage of outliers high0.000
 Mean of outliers highNA
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)NA
 VaR(95%) (moments method)NA
 Expected Shortfall (moments method)NA
 Extreme Value Index (regression method)NA
 VaR(95%) (regression method)NA
 Expected Shortfall (regression method)NA
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations0.000
 MinimumNA
 Quartile 1NA
 MedianNA
 Quartile 3NA
 MaximumNA
 Mean of quarter 1NA
 Mean of quarter 2NA
 Mean of quarter 3NA
 Mean of quarter 4NA
 Inter Quartile Range0.000
 Number outliers low0.000
 Percentage of outliers lowNA
 Mean of outliers lowNA
 Number of outliers high0.000
 Percentage of outliers highNA
 Mean of outliers highNA
Risk estimates based on draw downs (based on Extreme Value Theory)
 Extreme Value Index (moments method)NA
 VaR(95%) (moments method)NA
 Expected Shortfall (moments method)NA
 Extreme Value Index (regression method)NA
 VaR(95%) (regression method)NA
 Expected Shortfall (regression method)NA
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)0.000
 Compounded annual return (geometric extrapolation)0.000
 Calmar ratio (compounded annual return / max draw down)NA
 Compounded annual return / average of 25% largest draw downsNA
 Compounded annual return / Expected Shortfall lognormal0.000