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Advanced Statistics: Ninja 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-0.118
 SD0.100
 Sharpe ratio (Glass type estimate) -1.183
 Sharpe ratio (Hedges UMVUE)-1.138
 df20.000
 t-1.565
 p0.665
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.695
 Upperbound of 95% confidence interval for Sharpe Ratio0.357
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.661
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.385
Statistics related to Sortino ratio
 Sortino ratio-1.350
 Upside Potential Ratio0.779
 Upside part of mean0.068
 Downside part of mean-0.186
 Upside SD0.055
 Downside SD0.088
 N nonnegative terms4.000
 N negative terms17.000
Statistics related to linear regression on benchmark
 N of observations21.000
 Mean of predictor0.118
 Mean of criterion-0.118
 SD of predictor0.198
 SD of criterion0.100
 Covariance0.001
 r0.046
 b (slope, estimate of beta)0.023
 a (intercept, estimate of alpha)-0.121
 Mean Square Error0.010
 DF error19.000
 t(b)0.199
 p(b)0.471
 t(a)-1.538
 p(a)0.708
 Lowerbound of 95% confidence interval for beta-0.219
 Upperbound of 95% confidence interval for beta0.266
 Lowerbound of 95% confidence interval for alpha-0.285
 Upperbound of 95% confidence interval for alpha0.044
 Treynor index (mean / b)-5.114
 Jensen alpha (a)-0.121
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.123
 SD0.100
 Sharpe ratio (Glass type estimate) -1.228
 Sharpe ratio (Hedges UMVUE)-1.181
 df20.000
 t-1.624
 p0.671
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.742
 Upperbound of 95% confidence interval for Sharpe Ratio0.316
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.707
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.345
Statistics related to Sortino ratio
 Sortino ratio-1.376
 Upside Potential Ratio0.743
 Upside part of mean0.066
 Downside part of mean-0.190
 Upside SD0.053
 Downside SD0.089
 N nonnegative terms4.000
 N negative terms17.000
Statistics related to linear regression on benchmark
 N of observations21.000
 Mean of predictor0.099
 Mean of criterion-0.123
 SD of predictor0.194
 SD of criterion0.100
 Covariance0.001
 r0.046
 b (slope, estimate of beta)0.024
 a (intercept, estimate of alpha)-0.125
 Mean Square Error0.011
 DF error19.000
 t(b)0.201
 p(b)0.471
 t(a)-1.597
 p(a)0.715
 Lowerbound of 95% confidence interval for beta-0.224
 Upperbound of 95% confidence interval for beta0.271
 Lowerbound of 95% confidence interval for alpha-0.290
 Upperbound of 95% confidence interval for alpha0.039
 Treynor index (mean / b)-5.191
 Jensen alpha (a)-0.125
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.056
 Expected Shortfall on VaR0.068
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.046
 Expected Shortfall on VaR0.073
ORDER STATISTICS
Quartiles of return rates
 Number of observations21.000
 Minimum0.942
 Quartile 10.979
 Median1.000
 Quartile 31.000
 Maximum1.065
 Mean of quarter 10.960
 Mean of quarter 20.995
 Mean of quarter 31.000
 Mean of quarter 41.027
 Inter Quartile Range0.021
 Number outliers low2.000
 Percentage of outliers low0.095
 Mean of outliers low0.942
 Number of outliers high2.000
 Percentage of outliers high0.095
 Mean of outliers high1.051
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)-1.488
 VaR(95%) (moments method)0.043
 Expected Shortfall (moments method)0.044
 Extreme Value Index (regression method)-1.735
 VaR(95%) (regression method)0.058
 Expected Shortfall (regression method)0.059
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations1.000
 Minimum0.139
 Quartile 10.139
 Median0.139
 Quartile 30.139
 Maximum0.139
 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)-0.074
 Compounded annual return (geometric extrapolation)-0.076
 Calmar ratio (compounded annual return / max draw down)-0.545
 Compounded annual return / average of 25% largest draw downsNA
 Compounded annual return / Expected Shortfall lognormal-1.126
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-0.114
 SD0.121
 Sharpe ratio (Glass type estimate) -0.938
 Sharpe ratio (Hedges UMVUE)-0.936
 df618.000
 t-1.258
 p0.896
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.399
 Upperbound of 95% confidence interval for Sharpe Ratio0.525
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.398
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.526
Statistics related to Sortino ratio
 Sortino ratio-1.373
 Upside Potential Ratio5.060
 Upside part of mean0.419
 Downside part of mean-0.532
 Upside SD0.089
 Downside SD0.083
 N nonnegative terms118.000
 N negative terms501.000
Statistics related to linear regression on benchmark
 N of observations619.000
 Mean of predictor0.208
 Mean of criterion-0.114
 SD of predictor0.236
 SD of criterion0.121
 Covariance-0.004
 r-0.140
 b (slope, estimate of beta)-0.072
 a (intercept, estimate of alpha)-0.099
 Mean Square Error0.014
 DF error617.000
 t(b)-3.509
 p(b)1.000
 t(a)-1.101
 p(a)0.864
 Lowerbound of 95% confidence interval for beta-0.112
 Upperbound of 95% confidence interval for beta-0.032
 Lowerbound of 95% confidence interval for alpha-0.275
 Upperbound of 95% confidence interval for alpha0.077
 Treynor index (mean / b)1.585
 Jensen alpha (a)-0.099
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.121
 SD0.121
 Sharpe ratio (Glass type estimate) -1.002
 Sharpe ratio (Hedges UMVUE)-1.000
 df618.000
 t-1.344
 p0.910
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.463
 Upperbound of 95% confidence interval for Sharpe Ratio0.461
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.463
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.462
Statistics related to Sortino ratio
 Sortino ratio-1.447
 Upside Potential Ratio4.963
 Upside part of mean0.415
 Downside part of mean-0.536
 Upside SD0.087
 Downside SD0.084
 N nonnegative terms118.000
 N negative terms501.000
Statistics related to linear regression on benchmark
 N of observations619.000
 Mean of predictor0.180
 Mean of criterion-0.121
 SD of predictor0.236
 SD of criterion0.121
 Covariance-0.004
 r-0.140
 b (slope, estimate of beta)-0.072
 a (intercept, estimate of alpha)-0.108
 Mean Square Error0.014
 DF error617.000
 t(b)-3.512
 p(b)1.000
 t(a)-1.210
 p(a)0.887
 Lowerbound of 95% confidence interval for beta-0.112
 Upperbound of 95% confidence interval for beta-0.032
 Lowerbound of 95% confidence interval for alpha-0.283
 Upperbound of 95% confidence interval for alpha0.067
 Treynor index (mean / b)1.689
 Jensen alpha (a)-0.108
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.011
 Expected Shortfall on VaR0.014
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.005
 Expected Shortfall on VaR0.010
ORDER STATISTICS
Quartiles of return rates
 Number of observations619.000
 Minimum0.960
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.053
 Mean of quarter 10.994
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.005
 Inter Quartile Range0.000
 Number outliers low144.000
 Percentage of outliers low0.233
 Mean of outliers low0.994
 Number of outliers high128.000
 Percentage of outliers high0.207
 Mean of outliers high1.006
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.299
 VaR(95%) (moments method)0.004
 Expected Shortfall (moments method)0.007
 Extreme Value Index (regression method)0.033
 VaR(95%) (regression method)0.005
 Expected Shortfall (regression method)0.009
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations3.000
 Minimum0.034
 Quartile 10.055
 Median0.077
 Quartile 30.130
 Maximum0.183
 Mean of quarter 10.034
 Mean of quarter 20.077
 Mean of quarter 3NA
 Mean of quarter 40.183
 Inter Quartile Range0.075
 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)-0.072
 Compounded annual return (geometric extrapolation)-0.074
 Calmar ratio (compounded annual return / max draw down)-0.405
 Compounded annual return / average of 25% largest draw downs-0.405
 Compounded annual return / Expected Shortfall lognormal-5.410
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 predictor0.716
 Mean of criterion-0.044
 SD of predictor0.293
 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 predictor0.673
 Mean of criterion-0.044
 SD of predictor0.291
 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)-5552233134898999.000
 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)163752174123358314840886578511872.000
 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