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Advanced Statistics: SMA

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
 Mean0.154
 SD0.212
 Sharpe ratio (Glass type estimate) 0.725
 Sharpe ratio (Hedges UMVUE)0.713
 df45.000
 t1.420
 p0.081
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.291
 Upperbound of 95% confidence interval for Sharpe Ratio1.733
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.299
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.725
Statistics related to Sortino ratio
 Sortino ratio1.825
 Upside Potential Ratio2.949
 Upside part of mean0.249
 Downside part of mean-0.095
 Upside SD0.197
 Downside SD0.084
 N nonnegative terms13.000
 N negative terms33.000
Statistics related to linear regression on benchmark
 N of observations46.000
 Mean of predictor-0.033
 Mean of criterion0.154
 SD of predictor0.180
 SD of criterion0.212
 Covariance0.004
 r0.105
 b (slope, estimate of beta)0.123
 a (intercept, estimate of alpha)0.158
 Mean Square Error0.046
 DF error44.000
 t(b)0.699
 p(b)0.244
 t(a)1.447
 p(a)0.077
 Lowerbound of 95% confidence interval for beta-0.232
 Upperbound of 95% confidence interval for beta0.479
 Lowerbound of 95% confidence interval for alpha-0.062
 Upperbound of 95% confidence interval for alpha0.378
 Treynor index (mean / b)1.248
 Jensen alpha (a)0.158
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.132
 SD0.199
 Sharpe ratio (Glass type estimate) 0.663
 Sharpe ratio (Hedges UMVUE)0.652
 df45.000
 t1.299
 p0.100
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.351
 Upperbound of 95% confidence interval for Sharpe Ratio1.670
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.358
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.662
Statistics related to Sortino ratio
 Sortino ratio1.482
 Upside Potential Ratio2.584
 Upside part of mean0.231
 Downside part of mean-0.098
 Upside SD0.180
 Downside SD0.089
 N nonnegative terms13.000
 N negative terms33.000
Statistics related to linear regression on benchmark
 N of observations46.000
 Mean of predictor-0.049
 Mean of criterion0.132
 SD of predictor0.184
 SD of criterion0.199
 Covariance0.004
 r0.122
 b (slope, estimate of beta)0.133
 a (intercept, estimate of alpha)0.139
 Mean Square Error0.040
 DF error44.000
 t(b)0.818
 p(b)0.209
 t(a)1.354
 p(a)0.091
 Lowerbound of 95% confidence interval for beta-0.195
 Upperbound of 95% confidence interval for beta0.460
 Lowerbound of 95% confidence interval for alpha-0.068
 Upperbound of 95% confidence interval for alpha0.346
 Treynor index (mean / b)0.996
 Jensen alpha (a)0.139
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.080
 Expected Shortfall on VaR0.102
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.022
 Expected Shortfall on VaR0.048
ORDER STATISTICS
Quartiles of return rates
 Number of observations46.000
 Minimum0.873
 Quartile 11.000
 Median1.000
 Quartile 31.009
 Maximum1.239
 Mean of quarter 10.979
 Mean of quarter 21.000
 Mean of quarter 31.001
 Mean of quarter 41.083
 Inter Quartile Range0.009
 Number outliers low3.000
 Percentage of outliers low0.065
 Mean of outliers low0.921
 Number of outliers high8.000
 Percentage of outliers high0.174
 Mean of outliers high1.115
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.971
 VaR(95%) (moments method)0.001
 Expected Shortfall (moments method)0.069
 Extreme Value Index (regression method)0.985
 VaR(95%) (regression method)0.021
 Expected Shortfall (regression method)2.316
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations6.000
 Minimum0.000
 Quartile 10.001
 Median0.004
 Quartile 30.071
 Maximum0.143
 Mean of quarter 10.000
 Mean of quarter 20.002
 Mean of quarter 30.006
 Mean of quarter 40.118
 Inter Quartile Range0.070
 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)0.252
 Compounded annual return (geometric extrapolation)0.193
 Calmar ratio (compounded annual return / max draw down)1.348
 Compounded annual return / average of 25% largest draw downs1.636
 Compounded annual return / Expected Shortfall lognormal1.892
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.146
 SD0.184
 Sharpe ratio (Glass type estimate) 0.797
 Sharpe ratio (Hedges UMVUE)0.797
 df1338.000
 t1.573
 p0.479
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.197
 Upperbound of 95% confidence interval for Sharpe Ratio1.791
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.197
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.791
Statistics related to Sortino ratio
 Sortino ratio1.243
 Upside Potential Ratio6.288
 Upside part of mean0.741
 Downside part of mean-0.594
 Upside SD0.141
 Downside SD0.118
 N nonnegative terms227.000
 N negative terms1112.000
Statistics related to linear regression on benchmark
 N of observations1339.000
 Mean of predictor0.037
 Mean of criterion0.146
 SD of predictor0.298
 SD of criterion0.184
 Covariance0.002
 r0.044
 b (slope, estimate of beta)0.027
 a (intercept, estimate of alpha)0.145
 Mean Square Error0.034
 DF error1337.000
 t(b)1.616
 p(b)0.472
 t(a)1.563
 p(a)0.473
 Lowerbound of 95% confidence interval for beta-0.006
 Upperbound of 95% confidence interval for beta0.060
 Lowerbound of 95% confidence interval for alpha-0.037
 Upperbound of 95% confidence interval for alpha0.328
 Treynor index (mean / b)5.378
 Jensen alpha (a)0.145
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.130
 SD0.183
 Sharpe ratio (Glass type estimate) 0.709
 Sharpe ratio (Hedges UMVUE)0.708
 df1338.000
 t1.398
 p0.481
 Lowerbound of 95% confidence interval for Sharpe Ratio-0.285
 Upperbound of 95% confidence interval for Sharpe Ratio1.702
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-0.286
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.702
Statistics related to Sortino ratio
 Sortino ratio1.081
 Upside Potential Ratio6.098
 Upside part of mean0.731
 Downside part of mean-0.601
 Upside SD0.138
 Downside SD0.120
 N nonnegative terms227.000
 N negative terms1112.000
Statistics related to linear regression on benchmark
 N of observations1339.000
 Mean of predictor-0.008
 Mean of criterion0.130
 SD of predictor0.298
 SD of criterion0.183
 Covariance0.003
 r0.048
 b (slope, estimate of beta)0.029
 a (intercept, estimate of alpha)0.130
 Mean Square Error0.033
 DF error1337.000
 t(b)1.744
 p(b)0.470
 t(a)1.401
 p(a)0.476
 Lowerbound of 95% confidence interval for beta-0.004
 Upperbound of 95% confidence interval for beta0.062
 Lowerbound of 95% confidence interval for alpha-0.052
 Upperbound of 95% confidence interval for alpha0.312
 Treynor index (mean / b)4.433
 Jensen alpha (a)0.130
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.016
 Expected Shortfall on VaR0.020
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.005
 Expected Shortfall on VaR0.012
ORDER STATISTICS
Quartiles of return rates
 Number of observations1339.000
 Minimum0.942
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.081
 Mean of quarter 10.994
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.009
 Inter Quartile Range0.000
 Number outliers low224.000
 Percentage of outliers low0.167
 Mean of outliers low0.990
 Number of outliers high259.000
 Percentage of outliers high0.193
 Mean of outliers high1.011
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.262
 VaR(95%) (moments method)0.003
 Expected Shortfall (moments method)0.006
 Extreme Value Index (regression method)0.057
 VaR(95%) (regression method)0.007
 Expected Shortfall (regression method)0.014
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations27.000
 Minimum0.000
 Quartile 10.008
 Median0.018
 Quartile 30.060
 Maximum0.267
 Mean of quarter 10.002
 Mean of quarter 20.014
 Mean of quarter 30.042
 Mean of quarter 40.125
 Inter Quartile Range0.052
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high2.000
 Percentage of outliers high0.074
 Mean of outliers high0.220
Risk estimates based on draw downs (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.302
 VaR(95%) (moments method)0.138
 Expected Shortfall (moments method)0.230
 Extreme Value Index (regression method)1.104
 VaR(95%) (regression method)0.137
 Expected Shortfall (regression method)NA
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)0.248
 Compounded annual return (geometric extrapolation)0.190
 Calmar ratio (compounded annual return / max draw down)0.711
 Compounded annual return / average of 25% largest draw downs1.516
 Compounded annual return / Expected Shortfall lognormal9.593
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 predictor0.693
 Mean of criterion-0.044
 SD of predictor0.272
 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 predictor0.656
 Mean of criterion-0.044
 SD of predictor0.271
 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)-5548236841622975.000
 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)-64754550501638344001509763579904.000
 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