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Advanced Statistics: Momentum and Volatility Trading

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
 Mean0.158
 SD0.152
 Sharpe ratio (Glass type estimate) 1.043
 Sharpe ratio (Hedges UMVUE)0.832
 df4.000
 t0.673
 p0.269
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.131
 Upperbound of 95% confidence interval for Sharpe Ratio4.100
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.258
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)3.923
Statistics related to Sortino ratio
 Sortino ratio6.583
 Upside Potential Ratio9.095
 Upside part of mean0.219
 Downside part of mean-0.060
 Upside SD0.141
 Downside SD0.024
 N nonnegative terms1.000
 N negative terms4.000
Statistics related to linear regression on benchmark
 N of observations5.000
 Mean of predictor-0.008
 Mean of criterion0.158
 SD of predictor0.140
 SD of criterion0.152
 Covariance-0.004
 r-0.193
 b (slope, estimate of beta)-0.209
 a (intercept, estimate of alpha)0.157
 Mean Square Error0.030
 DF error3.000
 t(b)-0.341
 p(b)0.622
 t(a)0.588
 p(a)0.299
 Lowerbound of 95% confidence interval for beta-2.165
 Upperbound of 95% confidence interval for beta1.746
 Lowerbound of 95% confidence interval for alpha-0.692
 Upperbound of 95% confidence interval for alpha1.005
 Treynor index (mean / b)-0.757
 Jensen alpha (a)0.157
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.148
 SD0.145
 Sharpe ratio (Glass type estimate) 1.019
 Sharpe ratio (Hedges UMVUE)0.813
 df4.000
 t0.658
 p0.273
 Lowerbound of 95% confidence interval for Sharpe Ratio-2.150
 Upperbound of 95% confidence interval for Sharpe Ratio4.074
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-2.275
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)3.902
Statistics related to Sortino ratio
 Sortino ratio6.142
 Upside Potential Ratio8.651
 Upside part of mean0.209
 Downside part of mean-0.061
 Upside SD0.135
 Downside SD0.024
 N nonnegative terms1.000
 N negative terms4.000
Statistics related to linear regression on benchmark
 N of observations5.000
 Mean of predictor-0.016
 Mean of criterion0.148
 SD of predictor0.141
 SD of criterion0.145
 Covariance-0.004
 r-0.186
 b (slope, estimate of beta)-0.192
 a (intercept, estimate of alpha)0.145
 Mean Square Error0.027
 DF error3.000
 t(b)-0.328
 p(b)0.618
 t(a)0.568
 p(a)0.305
 Lowerbound of 95% confidence interval for beta-2.058
 Upperbound of 95% confidence interval for beta1.674
 Lowerbound of 95% confidence interval for alpha-0.669
 Upperbound of 95% confidence interval for alpha0.959
 Treynor index (mean / b)-0.771
 Jensen alpha (a)0.145
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.055
 Expected Shortfall on VaR0.071
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.014
 Expected Shortfall on VaR0.018
ORDER STATISTICS
Quartiles of return rates
 Number of observations5.000
 Minimum0.990
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.095
 Mean of quarter 10.995
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.095
 Inter Quartile Range0.000
 Number outliers low1.000
 Percentage of outliers low0.200
 Mean of outliers low0.990
 Number of outliers high1.000
 Percentage of outliers high0.200
 Mean of outliers high1.095
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
 Minimum0.011
 Quartile 10.011
 Median0.011
 Quartile 30.011
 Maximum0.011
 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)0.200
 Compounded annual return (geometric extrapolation)0.212
 Calmar ratio (compounded annual return / max draw down)20.188
 Compounded annual return / average of 25% largest draw downsNA
 Compounded annual return / Expected Shortfall lognormal2.968
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean0.122
 SD0.076
 Sharpe ratio (Glass type estimate) 1.599
 Sharpe ratio (Hedges UMVUE)1.592
 df168.000
 t1.121
 p0.457
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.205
 Upperbound of 95% confidence interval for Sharpe Ratio4.398
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.210
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)4.393
Statistics related to Sortino ratio
 Sortino ratio2.952
 Upside Potential Ratio8.824
 Upside part of mean0.365
 Downside part of mean-0.243
 Upside SD0.064
 Downside SD0.041
 N nonnegative terms34.000
 N negative terms135.000
Statistics related to linear regression on benchmark
 N of observations169.000
 Mean of predictor0.383
 Mean of criterion0.122
 SD of predictor0.199
 SD of criterion0.076
 Covariance-0.002
 r-0.160
 b (slope, estimate of beta)-0.061
 a (intercept, estimate of alpha)0.145
 Mean Square Error0.006
 DF error167.000
 t(b)-2.095
 p(b)0.601
 t(a)1.343
 p(a)0.434
 Lowerbound of 95% confidence interval for beta-0.119
 Upperbound of 95% confidence interval for beta-0.004
 Lowerbound of 95% confidence interval for alpha-0.068
 Upperbound of 95% confidence interval for alpha0.359
 Treynor index (mean / b)-1.989
 Jensen alpha (a)0.145
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean0.119
 SD0.076
 Sharpe ratio (Glass type estimate) 1.568
 Sharpe ratio (Hedges UMVUE)1.561
 df168.000
 t1.099
 p0.458
 Lowerbound of 95% confidence interval for Sharpe Ratio-1.236
 Upperbound of 95% confidence interval for Sharpe Ratio4.367
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-1.241
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)4.362
Statistics related to Sortino ratio
 Sortino ratio2.869
 Upside Potential Ratio8.736
 Upside part of mean0.362
 Downside part of mean-0.243
 Upside SD0.064
 Downside SD0.041
 N nonnegative terms34.000
 N negative terms135.000
Statistics related to linear regression on benchmark
 N of observations169.000
 Mean of predictor0.363
 Mean of criterion0.119
 SD of predictor0.198
 SD of criterion0.076
 Covariance-0.002
 r-0.160
 b (slope, estimate of beta)-0.061
 a (intercept, estimate of alpha)0.141
 Mean Square Error0.006
 DF error167.000
 t(b)-2.097
 p(b)0.602
 t(a)1.311
 p(a)0.436
 Lowerbound of 95% confidence interval for beta-0.119
 Upperbound of 95% confidence interval for beta-0.004
 Lowerbound of 95% confidence interval for alpha-0.071
 Upperbound of 95% confidence interval for alpha0.354
 Treynor index (mean / b)-1.941
 Jensen alpha (a)0.141
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.006
 Expected Shortfall on VaR0.008
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.002
 Expected Shortfall on VaR0.005
ORDER STATISTICS
Quartiles of return rates
 Number of observations169.000
 Minimum0.988
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.025
 Mean of quarter 10.998
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.004
 Inter Quartile Range0.000
 Number outliers low18.000
 Percentage of outliers low0.107
 Mean of outliers low0.994
 Number of outliers high34.000
 Percentage of outliers high0.201
 Mean of outliers high1.005
Risk estimates for a one-period unit investment (based on Extreme Value Theory)
 Extreme Value Index (moments method)-1.333
 VaR(95%) (moments method)0.002
 Expected Shortfall (moments method)0.003
 Extreme Value Index (regression method)-0.753
 VaR(95%) (regression method)0.004
 Expected Shortfall (regression method)0.007
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations5.000
 Minimum0.002
 Quartile 10.007
 Median0.008
 Quartile 30.017
 Maximum0.041
 Mean of quarter 10.004
 Mean of quarter 20.008
 Mean of quarter 30.017
 Mean of quarter 40.041
 Inter Quartile Range0.010
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high1.000
 Percentage of outliers high0.200
 Mean of outliers high0.041
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)0.170
 Compounded annual return (geometric extrapolation)0.177
 Calmar ratio (compounded annual return / max draw down)4.362
 Compounded annual return / average of 25% largest draw downs4.362
 Compounded annual return / Expected Shortfall lognormal21.961