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Advanced Statistics: Smart Forex

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
 Mean-0.077
 SD0.047
 Sharpe ratio (Glass type estimate) -1.641
 Sharpe ratio (Hedges UMVUE)-1.606
 df36.000
 t-2.881
 p0.997
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.809
 Upperbound of 95% confidence interval for Sharpe Ratio-0.452
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.783
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.430
Statistics related to Sortino ratio
 Sortino ratio-1.507
 Upside Potential Ratio0.055
 Upside part of mean0.003
 Downside part of mean-0.080
 Upside SD0.005
 Downside SD0.051
 N nonnegative terms1.000
 N negative terms36.000
Statistics related to linear regression on benchmark
 N of observations37.000
 Mean of predictor0.011
 Mean of criterion-0.077
 SD of predictor0.203
 SD of criterion0.047
 Covariance0.003
 r0.342
 b (slope, estimate of beta)0.079
 a (intercept, estimate of alpha)-0.078
 Mean Square Error0.002
 DF error35.000
 t(b)2.153
 p(b)0.019
 t(a)-3.058
 p(a)0.998
 Lowerbound of 95% confidence interval for beta0.004
 Upperbound of 95% confidence interval for beta0.153
 Lowerbound of 95% confidence interval for alpha-0.129
 Upperbound of 95% confidence interval for alpha-0.026
 Treynor index (mean / b)-0.974
 Jensen alpha (a)-0.078
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.078
 SD0.048
 Sharpe ratio (Glass type estimate) -1.611
 Sharpe ratio (Hedges UMVUE)-1.577
 df36.000
 t-2.829
 p0.996
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.777
 Upperbound of 95% confidence interval for Sharpe Ratio-0.425
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.751
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.403
Statistics related to Sortino ratio
 Sortino ratio-1.484
 Upside Potential Ratio0.053
 Upside part of mean0.003
 Downside part of mean-0.081
 Upside SD0.005
 Downside SD0.053
 N nonnegative terms1.000
 N negative terms36.000
Statistics related to linear regression on benchmark
 N of observations37.000
 Mean of predictor-0.010
 Mean of criterion-0.078
 SD of predictor0.209
 SD of criterion0.048
 Covariance0.003
 r0.340
 b (slope, estimate of beta)0.079
 a (intercept, estimate of alpha)-0.077
 Mean Square Error0.002
 DF error35.000
 t(b)2.139
 p(b)0.020
 t(a)-2.937
 p(a)0.997
 Lowerbound of 95% confidence interval for beta0.004
 Upperbound of 95% confidence interval for beta0.153
 Lowerbound of 95% confidence interval for alpha-0.131
 Upperbound of 95% confidence interval for alpha-0.024
 Treynor index (mean / b)-0.990
 Jensen alpha (a)-0.077
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.029
 Expected Shortfall on VaR0.035
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.023
 Expected Shortfall on VaR0.043
ORDER STATISTICS
Quartiles of return rates
 Number of observations37.000
 Minimum0.928
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.012
 Mean of quarter 10.988
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.002
 Inter Quartile Range0.000
 Number outliers low7.000
 Percentage of outliers low0.189
 Mean of outliers low0.984
 Number of outliers high4.000
 Percentage of outliers high0.108
 Mean of outliers high1.004
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)-1.877
 VaR(95%) (moments method)0.002
 Expected Shortfall (moments method)0.002
 Extreme Value Index (regression method)0.672
 VaR(95%) (regression method)0.018
 Expected Shortfall (regression method)0.110
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations1.000
 Minimum0.110
 Quartile 10.110
 Median0.110
 Quartile 30.110
 Maximum0.110
 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 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)-0.032
 Compounded annual return (geometric extrapolation)-0.033
 Calmar ratio (compounded annual return / max draw down)-0.302
 Compounded annual return / average of 25% largest draw downsNA
 Compounded annual return / Expected Shortfall lognormal-0.962
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-0.076
 SD0.045
 Sharpe ratio (Glass type estimate) -1.692
 Sharpe ratio (Hedges UMVUE)-1.691
 df1077.000
 t-2.995
 p0.558
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.801
 Upperbound of 95% confidence interval for Sharpe Ratio-0.582
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.800
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.581
Statistics related to Sortino ratio
 Sortino ratio-1.733
 Upside Potential Ratio0.421
 Upside part of mean0.019
 Downside part of mean-0.095
 Upside SD0.010
 Downside SD0.044
 N nonnegative terms14.000
 N negative terms1064.000
Statistics related to linear regression on benchmark
 N of observations1078.000
 Mean of predictor0.084
 Mean of criterion-0.076
 SD of predictor0.317
 SD of criterion0.045
 Covariance-0.000
 r-0.018
 b (slope, estimate of beta)-0.003
 a (intercept, estimate of alpha)-0.076
 Mean Square Error0.002
 DF error1076.000
 t(b)-0.586
 p(b)0.509
 t(a)-2.986
 p(a)0.545
 Lowerbound of 95% confidence interval for beta-0.011
 Upperbound of 95% confidence interval for beta0.006
 Lowerbound of 95% confidence interval for alpha-0.126
 Upperbound of 95% confidence interval for alpha-0.026
 Treynor index (mean / b)29.980
 Jensen alpha (a)-0.076
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.077
 SD0.046
 Sharpe ratio (Glass type estimate) -1.668
 Sharpe ratio (Hedges UMVUE)-1.667
 df1077.000
 t-2.953
 p0.557
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.777
 Upperbound of 95% confidence interval for Sharpe Ratio-0.558
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.776
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.557
Statistics related to Sortino ratio
 Sortino ratio-1.705
 Upside Potential Ratio0.407
 Upside part of mean0.018
 Downside part of mean-0.096
 Upside SD0.010
 Downside SD0.045
 N nonnegative terms14.000
 N negative terms1064.000
Statistics related to linear regression on benchmark
 N of observations1078.000
 Mean of predictor0.034
 Mean of criterion-0.077
 SD of predictor0.317
 SD of criterion0.046
 Covariance-0.000
 r-0.018
 b (slope, estimate of beta)-0.003
 a (intercept, estimate of alpha)-0.077
 Mean Square Error0.002
 DF error1076.000
 t(b)-0.583
 p(b)0.509
 t(a)-2.948
 p(a)0.545
 Lowerbound of 95% confidence interval for beta-0.011
 Upperbound of 95% confidence interval for beta0.006
 Lowerbound of 95% confidence interval for alpha-0.129
 Upperbound of 95% confidence interval for alpha-0.026
 Treynor index (mean / b)29.755
 Jensen alpha (a)-0.077
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.004
 Expected Shortfall on VaR0.005
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.001
 Expected Shortfall on VaR0.002
ORDER STATISTICS
Quartiles of return rates
 Number of observations1078.000
 Minimum0.932
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.010
 Mean of quarter 10.999
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.000
 Inter Quartile Range0.000
 Number outliers low51.000
 Percentage of outliers low0.047
 Mean of outliers low0.997
 Number of outliers high45.000
 Percentage of outliers high0.042
 Mean of outliers high1.001
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)1.168
 VaR(95%) (moments method)-0.000
 Expected Shortfall (moments method)NA
 Extreme Value Index (regression method)1.538
 VaR(95%) (regression method)0.000
 Expected Shortfall (regression method)NA
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations1.000
 Minimum0.114
 Quartile 10.114
 Median0.114
 Quartile 30.114
 Maximum0.114
 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 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)-0.032
 Compounded annual return (geometric extrapolation)-0.033
 Calmar ratio (compounded annual return / max draw down)-0.287
 Compounded annual return / average of 25% largest draw downsNA
 Compounded annual return / Expected Shortfall lognormal-6.111
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 predictor0.280
 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 predictor0.609
 Mean of criterion-0.044
 SD of predictor0.280
 SD of criterion0.000
 Covariance0.000
 r0.000
 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)-5557154359609737.000
 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)-87389924737078860097109849276416.000
 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