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Advanced Statistics: TimerSignals - SPY

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
 Mean0.025
 SD0.117
 Sharpe ratio (Glass type estimate) 0.212
 Sharpe ratio (Hedges UMVUE)0.202
 df16.000
 t0.252
 p0.469
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.440
 Upperbound of 95% confidence interval for Sharpe Ratio1.857
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.446
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.850
Statistics related to Sortino ratio
 Sortino ratio0.292
 Upside Potential Ratio1.904
 Upside part of mean0.162
 Downside part of mean-0.137
 Upside SD0.076
 Downside SD0.085
 N nonnegative terms10.000
 N negative terms7.000
Statistics related to linear regression on benchmark
 N of observations17.000
 Mean of predictor0.011
 Mean of criterion0.025
 SD of predictor0.154
 SD of criterion0.117
 Covariance0.009
 r0.518
 b (slope, estimate of beta)0.394
 a (intercept, estimate of alpha)0.020
 Mean Square Error0.011
 DF error15.000
 t(b)2.347
 p(b)0.185
 t(a)0.234
 p(a)0.462
 Lowerbound of 95% confidence interval for beta0.036
 Upperbound of 95% confidence interval for beta0.751
 Lowerbound of 95% confidence interval for alpha-0.165
 Upperbound of 95% confidence interval for alpha0.206
 Treynor index (mean / b)0.063
 Jensen alpha (a)0.020
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.018
 SD0.118
 Sharpe ratio (Glass type estimate) 0.154
 Sharpe ratio (Hedges UMVUE)0.147
 df16.000
 t0.184
 p0.477
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.496
 Upperbound of 95% confidence interval for Sharpe Ratio1.800
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.500
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.794
Statistics related to Sortino ratio
 Sortino ratio0.208
 Upside Potential Ratio1.810
 Upside part of mean0.159
 Downside part of mean-0.140
 Upside SD0.074
 Downside SD0.088
 N nonnegative terms10.000
 N negative terms7.000
Statistics related to linear regression on benchmark
 N of observations17.000
 Mean of predictor-0.000
 Mean of criterion0.018
 SD of predictor0.157
 SD of criterion0.118
 Covariance0.010
 r0.544
 b (slope, estimate of beta)0.408
 a (intercept, estimate of alpha)0.018
 Mean Square Error0.010
 DF error15.000
 t(b)2.508
 p(b)0.172
 t(a)0.213
 p(a)0.465
 Lowerbound of 95% confidence interval for beta0.061
 Upperbound of 95% confidence interval for beta0.755
 Lowerbound of 95% confidence interval for alpha-0.165
 Upperbound of 95% confidence interval for alpha0.202
 Treynor index (mean / b)0.045
 Jensen alpha (a)0.018
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.053
 Expected Shortfall on VaR0.066
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.023
 Expected Shortfall on VaR0.048
ORDER STATISTICS
Quartiles of return rates
 Number of observations17.000
 Minimum0.925
 Quartile 10.994
 Median1.012
 Quartile 31.026
 Maximum1.062
 Mean of quarter 10.966
 Mean of quarter 21.004
 Mean of quarter 31.018
 Mean of quarter 41.044
 Inter Quartile Range0.032
 Number outliers low1.000
 Percentage of outliers low0.059
 Mean of outliers low0.925
 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)-1.012
 VaR(95%) (moments method)0.022
 Expected Shortfall (moments method)0.025
 Extreme Value Index (regression method)-0.063
 VaR(95%) (regression method)0.064
 Expected Shortfall (regression method)0.094
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations3.000
 Minimum0.006
 Quartile 10.016
 Median0.026
 Quartile 30.072
 Maximum0.117
 Mean of quarter 10.006
 Mean of quarter 20.026
 Mean of quarter 3NA
 Mean of quarter 40.117
 Inter Quartile Range0.055
 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)0.065
 Compounded annual return (geometric extrapolation)0.064
 Calmar ratio (compounded annual return / max draw down)0.549
 Compounded annual return / average of 25% largest draw downs0.549
 Compounded annual return / Expected Shortfall lognormal0.967
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.020
 SD0.101
 Sharpe ratio (Glass type estimate) 0.197
 Sharpe ratio (Hedges UMVUE)0.196
 df515.000
 t0.241
 p0.405
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.404
 Upperbound of 95% confidence interval for Sharpe Ratio1.797
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.404
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.797
Statistics related to Sortino ratio
 Sortino ratio0.295
 Upside Potential Ratio6.659
 Upside part of mean0.449
 Downside part of mean-0.429
 Upside SD0.075
 Downside SD0.067
 N nonnegative terms130.000
 N negative terms386.000
Statistics related to linear regression on benchmark
 N of observations516.000
 Mean of predictor0.116
 Mean of criterion0.020
 SD of predictor0.219
 SD of criterion0.101
 Covariance0.003
 r0.144
 b (slope, estimate of beta)0.067
 a (intercept, estimate of alpha)0.012
 Mean Square Error0.010
 DF error514.000
 t(b)3.299
 p(b)0.001
 t(a)0.149
 p(a)0.441
 Lowerbound of 95% confidence interval for beta0.027
 Upperbound of 95% confidence interval for beta0.106
 Lowerbound of 95% confidence interval for alpha-0.149
 Upperbound of 95% confidence interval for alpha0.173
 Treynor index (mean / b)0.299
 Jensen alpha (a)0.012
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.015
 SD0.101
 Sharpe ratio (Glass type estimate) 0.146
 Sharpe ratio (Hedges UMVUE)0.146
 df515.000
 t0.179
 p0.429
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.454
 Upperbound of 95% confidence interval for Sharpe Ratio1.747
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.454
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)1.747
Statistics related to Sortino ratio
 Sortino ratio0.217
 Upside Potential Ratio6.553
 Upside part of mean0.446
 Downside part of mean-0.431
 Upside SD0.074
 Downside SD0.068
 N nonnegative terms130.000
 N negative terms386.000
Statistics related to linear regression on benchmark
 N of observations516.000
 Mean of predictor0.092
 Mean of criterion0.015
 SD of predictor0.219
 SD of criterion0.101
 Covariance0.003
 r0.145
 b (slope, estimate of beta)0.067
 a (intercept, estimate of alpha)0.009
 Mean Square Error0.010
 DF error514.000
 t(b)3.312
 p(b)0.000
 t(a)0.106
 p(a)0.458
 Lowerbound of 95% confidence interval for beta0.027
 Upperbound of 95% confidence interval for beta0.106
 Lowerbound of 95% confidence interval for alpha-0.152
 Upperbound of 95% confidence interval for alpha0.169
 Treynor index (mean / b)0.222
 Jensen alpha (a)0.009
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.009
 Expected Shortfall on VaR0.011
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.004
 Expected Shortfall on VaR0.008
ORDER STATISTICS
Quartiles of return rates
 Number of observations516.000
 Minimum0.959
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.046
 Mean of quarter 10.995
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.005
 Inter Quartile Range0.000
 Number outliers low111.000
 Percentage of outliers low0.215
 Mean of outliers low0.995
 Number of outliers high112.000
 Percentage of outliers high0.217
 Mean of outliers high1.006
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.462
 VaR(95%) (moments method)0.004
 Expected Shortfall (moments method)0.008
 Extreme Value Index (regression method)0.114
 VaR(95%) (regression method)0.004
 Expected Shortfall (regression method)0.007
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations12.000
 Minimum0.000
 Quartile 10.002
 Median0.008
 Quartile 30.021
 Maximum0.144
 Mean of quarter 10.001
 Mean of quarter 20.004
 Mean of quarter 30.014
 Mean of quarter 40.074
 Inter Quartile Range0.019
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high1.000
 Percentage of outliers high0.083
 Mean of outliers high0.144
Risk estimates based on draw downs (based on Extreme Value Theory)
 Extreme Value Index (moments method)0.196
 VaR(95%) (moments method)0.073
 Expected Shortfall (moments method)0.120
 Extreme Value Index (regression method)2.003
 VaR(95%) (regression method)0.145
 Expected Shortfall (regression method)NA
COMBINED STATISTICS
 Annualized return (arithmetic extrapolation)0.061
 Compounded annual return (geometric extrapolation)0.061
 Calmar ratio (compounded annual return / max draw down)0.419
 Compounded annual return / average of 25% largest draw downs0.814
 Compounded annual return / Expected Shortfall lognormal5.446
ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-0.005
 SD0.053
 Sharpe ratio (Glass type estimate) -0.099
 Sharpe ratio (Hedges UMVUE)-0.099
 df171.000
 t-0.070
 p0.503
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.871
 Upperbound of 95% confidence interval for Sharpe Ratio2.673
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.870
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.673
Statistics related to Sortino ratio
 Sortino ratio-0.151
 Upside Potential Ratio5.719
 Upside part of mean0.200
 Downside part of mean-0.205
 Upside SD0.040
 Downside SD0.035
 N nonnegative terms20.000
 N negative terms152.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.271
 Mean of criterion-0.005
 SD of predictor0.202
 SD of criterion0.053
 Covariance-0.000
 r-0.002
 b (slope, estimate of beta)-0.001
 a (intercept, estimate of alpha)-0.005
 Mean Square Error0.003
 DF error170.000
 t(b)-0.030
 p(b)0.501
 t(a)-0.068
 p(a)0.503
 Lowerbound of 95% confidence interval for beta-0.041
 Upperbound of 95% confidence interval for beta0.039
 Lowerbound of 95% confidence interval for alpha-0.155
 Upperbound of 95% confidence interval for alpha0.144
 Treynor index (mean / b)8.652
 Jensen alpha (a)-0.005
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.007
 SD0.053
 Sharpe ratio (Glass type estimate) -0.126
 Sharpe ratio (Hedges UMVUE)-0.125
 df171.000
 t-0.089
 p0.504
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.897
 Upperbound of 95% confidence interval for Sharpe Ratio2.646
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.897
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.647
Statistics related to Sortino ratio
 Sortino ratio-0.190
 Upside Potential Ratio5.666
 Upside part of mean0.199
 Downside part of mean-0.206
 Upside SD0.040
 Downside SD0.035
 N nonnegative terms20.000
 N negative terms152.000
Statistics related to linear regression on benchmark
 N of observations172.000
 Mean of predictor0.251
 Mean of criterion-0.007
 SD of predictor0.201
 SD of criterion0.053
 Covariance-0.000
 r-0.003
 b (slope, estimate of beta)-0.001
 a (intercept, estimate of alpha)-0.007
 Mean Square Error0.003
 DF error170.000
 t(b)-0.033
 p(b)0.501
 t(a)-0.086
 p(a)0.503
 Lowerbound of 95% confidence interval for beta-0.041
 Upperbound of 95% confidence interval for beta0.039
 Lowerbound of 95% confidence interval for alpha-0.156
 Upperbound of 95% confidence interval for alpha0.143
 Treynor index (mean / b)9.875
 Jensen alpha (a)-0.007
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.005
 Expected Shortfall on VaR0.006
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.002
 Expected Shortfall on VaR0.004
ORDER STATISTICS
Quartiles of return rates
 Number of observations172.000
 Minimum0.984
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.014
 Mean of quarter 10.998
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.002
 Inter Quartile Range0.000
 Number outliers low28.000
 Percentage of outliers low0.163
 Mean of outliers low0.997
 Number of outliers high21.000
 Percentage of outliers high0.122
 Mean of outliers high1.005
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)-0.379
 VaR(95%) (moments method)0.002
 Expected Shortfall (moments method)0.002
 Extreme Value Index (regression method)0.426
 VaR(95%) (regression method)0.002
 Expected Shortfall (regression method)0.004
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations6.000
 Minimum0.000
 Quartile 10.003
 Median0.012
 Quartile 30.017
 Maximum0.033
 Mean of quarter 10.001
 Mean of quarter 20.009
 Mean of quarter 30.016
 Mean of quarter 40.025
 Inter Quartile Range0.013
 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)0.038
 Compounded annual return (geometric extrapolation)0.038
 Calmar ratio (compounded annual return / max draw down)1.149
 Compounded annual return / average of 25% largest draw downs1.516
 Compounded annual return / Expected Shortfall lognormal6.429