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Advanced Statistics: MagicBox7

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-0.053
 SD0.013
 Sharpe ratio (Glass type estimate) -4.189
 Sharpe ratio (Hedges UMVUE)-4.056
 df24.000
 t-6.046
 p1.000
 Lowerbound of 95% confidence interval for Sharpe Ratio-5.962
 Upperbound of 95% confidence interval for Sharpe Ratio-2.366
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-5.834
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.279
Statistics related to Sortino ratio
 Sortino ratio-2.691
 Upside Potential Ratio0.000
 Upside part of mean0.000
 Downside part of mean-0.053
 Upside SD0.000
 Downside SD0.020
 N nonnegative terms0.000
 N negative terms25.000
Statistics related to linear regression on benchmark
 N of observations25.000
 Mean of predictor0.202
 Mean of criterion-0.053
 SD of predictor0.239
 SD of criterion0.013
 Covariance-0.000
 r-0.050
 b (slope, estimate of beta)-0.003
 a (intercept, estimate of alpha)-0.052
 Mean Square Error0.000
 DF error23.000
 t(b)-0.239
 p(b)0.593
 t(a)-5.693
 p(a)1.000
 Lowerbound of 95% confidence interval for beta-0.025
 Upperbound of 95% confidence interval for beta0.020
 Lowerbound of 95% confidence interval for alpha-0.071
 Upperbound of 95% confidence interval for alpha-0.033
 Treynor index (mean / b)20.075
 Jensen alpha (a)-0.052
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.053
 SD0.013
 Sharpe ratio (Glass type estimate) -4.151
 Sharpe ratio (Hedges UMVUE)-4.019
 df24.000
 t-5.991
 p1.000
 Lowerbound of 95% confidence interval for Sharpe Ratio-5.916
 Upperbound of 95% confidence interval for Sharpe Ratio-2.335
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-5.791
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.248
Statistics related to Sortino ratio
 Sortino ratio-2.682
 Upside Potential Ratio0.000
 Upside part of mean0.000
 Downside part of mean-0.053
 Upside SD0.000
 Downside SD0.020
 N nonnegative terms0.000
 N negative terms25.000
Statistics related to linear regression on benchmark
 N of observations25.000
 Mean of predictor0.173
 Mean of criterion-0.053
 SD of predictor0.232
 SD of criterion0.013
 Covariance-0.000
 r-0.056
 b (slope, estimate of beta)-0.003
 a (intercept, estimate of alpha)-0.052
 Mean Square Error0.000
 DF error23.000
 t(b)-0.271
 p(b)0.606
 t(a)-5.678
 p(a)1.000
 Lowerbound of 95% confidence interval for beta-0.027
 Upperbound of 95% confidence interval for beta0.021
 Lowerbound of 95% confidence interval for alpha-0.071
 Upperbound of 95% confidence interval for alpha-0.033
 Treynor index (mean / b)17.048
 Jensen alpha (a)-0.052
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.010
 Expected Shortfall on VaR0.012
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.012
 Expected Shortfall on VaR0.014
ORDER STATISTICS
Quartiles of return rates
 Number of observations25.000
 Minimum0.982
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.000
 Mean of quarter 10.997
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.000
 Inter Quartile Range0.000
 Number outliers low3.000
 Percentage of outliers low0.120
 Mean of outliers low0.994
 Number of outliers high2.000
 Percentage of outliers high0.080
 Mean of outliers high1.000
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 observations1.000
 Minimum0.018
 Quartile 10.018
 Median0.018
 Quartile 30.018
 Maximum0.018
 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)-0.009
 Compounded annual return (geometric extrapolation)-0.009
 Calmar ratio (compounded annual return / max draw down)-0.482
 Compounded annual return / average of 25% largest draw downsNA
 Compounded annual return / Expected Shortfall lognormal-0.737
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-0.053
 SD0.013
 Sharpe ratio (Glass type estimate) -4.184
 Sharpe ratio (Hedges UMVUE)-4.180
 df718.000
 t-6.049
 p1.000
 Lowerbound of 95% confidence interval for Sharpe Ratio-5.556
 Upperbound of 95% confidence interval for Sharpe Ratio-2.810
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-5.553
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.807
Statistics related to Sortino ratio
 Sortino ratio-4.085
 Upside Potential Ratio0.022
 Upside part of mean0.000
 Downside part of mean-0.053
 Upside SD0.000
 Downside SD0.013
 N nonnegative terms8.000
 N negative terms711.000
Statistics related to linear regression on benchmark
 N of observations719.000
 Mean of predictor0.214
 Mean of criterion-0.053
 SD of predictor0.229
 SD of criterion0.013
 Covariance-0.000
 r-0.026
 b (slope, estimate of beta)-0.001
 a (intercept, estimate of alpha)-0.052
 Mean Square Error0.000
 DF error717.000
 t(b)-0.685
 p(b)0.753
 t(a)-6.005
 p(a)1.000
 Lowerbound of 95% confidence interval for beta-0.005
 Upperbound of 95% confidence interval for beta0.003
 Lowerbound of 95% confidence interval for alpha-0.070
 Upperbound of 95% confidence interval for alpha-0.035
 Treynor index (mean / b)37.467
 Jensen alpha (a)-0.052
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.053
 SD0.013
 Sharpe ratio (Glass type estimate) -4.152
 Sharpe ratio (Hedges UMVUE)-4.148
 df718.000
 t-6.003
 p1.000
 Lowerbound of 95% confidence interval for Sharpe Ratio-5.523
 Upperbound of 95% confidence interval for Sharpe Ratio-2.778
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-5.520
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.775
Statistics related to Sortino ratio
 Sortino ratio-4.055
 Upside Potential Ratio0.022
 Upside part of mean0.000
 Downside part of mean-0.053
 Upside SD0.000
 Downside SD0.013
 N nonnegative terms8.000
 N negative terms711.000
Statistics related to linear regression on benchmark
 N of observations719.000
 Mean of predictor0.188
 Mean of criterion-0.053
 SD of predictor0.229
 SD of criterion0.013
 Covariance-0.000
 r-0.026
 b (slope, estimate of beta)-0.001
 a (intercept, estimate of alpha)-0.053
 Mean Square Error0.000
 DF error717.000
 t(b)-0.689
 p(b)0.754
 t(a)-5.964
 p(a)1.000
 Lowerbound of 95% confidence interval for beta-0.006
 Upperbound of 95% confidence interval for beta0.003
 Lowerbound of 95% confidence interval for alpha-0.070
 Upperbound of 95% confidence interval for alpha-0.035
 Treynor index (mean / b)36.924
 Jensen alpha (a)-0.053
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.001
 Expected Shortfall on VaR0.002
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.001
 Expected Shortfall on VaR0.001
ORDER STATISTICS
Quartiles of return rates
 Number of observations719.000
 Minimum0.982
 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 low9.000
 Percentage of outliers low0.013
 Mean of outliers low0.998
 Number of outliers high8.000
 Percentage of outliers high0.011
 Mean of outliers high1.000
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 observations1.000
 Minimum0.018
 Quartile 10.018
 Median0.018
 Quartile 30.018
 Maximum0.018
 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)-0.009
 Compounded annual return (geometric extrapolation)-0.009
 Calmar ratio (compounded annual return / max draw down)-0.481
 Compounded annual return / average of 25% largest draw downsNA
 Compounded annual return / Expected Shortfall lognormal-5.585
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 predictor0.680
 Mean of criterion-0.044
 SD of predictor0.295
 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 predictor0.637
 Mean of criterion-0.044
 SD of predictor0.293
 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)-5557310464224278.000
 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)-76826176697078381939663187214336.000
 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