Advanced Statistics: Nasdaq Stock Swing
Advanced Statistics module contributed by Jules Ellis, C2 Member. Jules has written a very helpful guide for these statistics. | |||||
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| ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.029 | ||||
| SD | 0.072 | ||||
| Sharpe ratio (Glass type estimate) | -0.406 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.401 | ||||
| df | 57.000 | ||||
| t | -0.894 | ||||
| p | 0.812 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.299 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.490 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.296 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.493 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.662 | ||||
| Upside Potential Ratio | 0.947 | ||||
| Upside part of mean | 0.042 | ||||
| Downside part of mean | -0.071 | ||||
| Upside SD | 0.057 | ||||
| Downside SD | 0.044 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 54.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 58.000 | ||||
| Mean of predictor | 0.357 | ||||
| Mean of criterion | -0.029 | ||||
| SD of predictor | 0.260 | ||||
| SD of criterion | 0.072 | ||||
| Covariance | 0.003 | ||||
| r | 0.144 | ||||
| b (slope, estimate of beta) | 0.040 | ||||
| a (intercept, estimate of alpha) | -0.044 | ||||
| Mean Square Error | 0.005 | ||||
| DF error | 56.000 | ||||
| t(b) | 1.091 | ||||
| p(b) | 0.140 | ||||
| t(a) | -1.236 | ||||
| p(a) | 0.889 | ||||
| Lowerbound of 95% confidence interval for beta | -0.034 | ||||
| Upperbound of 95% confidence interval for beta | 0.114 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.114 | ||||
| Upperbound of 95% confidence interval for alpha | 0.027 | ||||
| Treynor index (mean / b) | -0.731 | ||||
| Jensen alpha (a) | -0.044 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.032 | ||||
| SD | 0.071 | ||||
| Sharpe ratio (Glass type estimate) | -0.449 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.443 | ||||
| df | 57.000 | ||||
| t | -0.987 | ||||
| p | 0.836 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.342 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.448 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.338 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.452 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.698 | ||||
| Upside Potential Ratio | 0.886 | ||||
| Upside part of mean | 0.040 | ||||
| Downside part of mean | -0.072 | ||||
| Upside SD | 0.054 | ||||
| Downside SD | 0.045 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 54.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 58.000 | ||||
| Mean of predictor | 0.320 | ||||
| Mean of criterion | -0.032 | ||||
| SD of predictor | 0.248 | ||||
| SD of criterion | 0.071 | ||||
| Covariance | 0.003 | ||||
| r | 0.177 | ||||
| b (slope, estimate of beta) | 0.050 | ||||
| a (intercept, estimate of alpha) | -0.048 | ||||
| Mean Square Error | 0.005 | ||||
| DF error | 56.000 | ||||
| t(b) | 1.343 | ||||
| p(b) | 0.092 | ||||
| t(a) | -1.403 | ||||
| p(a) | 0.917 | ||||
| Lowerbound of 95% confidence interval for beta | -0.025 | ||||
| Upperbound of 95% confidence interval for beta | 0.125 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.116 | ||||
| Upperbound of 95% confidence interval for alpha | 0.020 | ||||
| Treynor index (mean / b) | -0.630 | ||||
| Jensen alpha (a) | -0.048 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.036 | ||||
| Expected Shortfall on VaR | 0.044 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.020 | ||||
| Expected Shortfall on VaR | 0.037 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 58.000 | ||||
| Minimum | 0.930 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.112 | ||||
| Mean of quarter 1 | 0.990 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.014 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 4.000 | ||||
| Percentage of outliers low | 0.069 | ||||
| Mean of outliers low | 0.964 | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.069 | ||||
| Mean of outliers high | 1.054 | ||||
| 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) | -0.007 | ||||
| VaR(95%) (regression method) | 0.017 | ||||
| Expected Shortfall (regression method) | 0.049 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.070 | ||||
| Quartile 1 | 0.070 | ||||
| Median | 0.070 | ||||
| Quartile 3 | 0.070 | ||||
| Maximum | 0.070 | ||||
| Mean of quarter 1 | NA | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | NA | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 0.000 | ||||
| Percentage of outliers high | 0.000 | ||||
| Mean of outliers high | NA | ||||
| 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) | 0.013 | ||||
| Compounded annual return (geometric extrapolation) | 0.012 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.176 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.284 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.016 | ||||
| SD | 0.179 | ||||
| Sharpe ratio (Glass type estimate) | -0.088 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.088 | ||||
| df | 1268.000 | ||||
| t | -0.194 | ||||
| p | 0.503 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.979 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.802 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.979 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.802 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.135 | ||||
| Upside Potential Ratio | 2.155 | ||||
| Upside part of mean | 0.253 | ||||
| Downside part of mean | -0.269 | ||||
| Upside SD | 0.135 | ||||
| Downside SD | 0.118 | ||||
| N nonnegative terms | 53.000 | ||||
| N negative terms | 1216.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1269.000 | ||||
| Mean of predictor | 0.376 | ||||
| Mean of criterion | -0.016 | ||||
| SD of predictor | 0.339 | ||||
| SD of criterion | 0.179 | ||||
| Covariance | -0.004 | ||||
| r | -0.073 | ||||
| b (slope, estimate of beta) | -0.039 | ||||
| a (intercept, estimate of alpha) | -0.001 | ||||
| Mean Square Error | 0.032 | ||||
| DF error | 1267.000 | ||||
| t(b) | -2.611 | ||||
| p(b) | 0.547 | ||||
| t(a) | -0.016 | ||||
| p(a) | 0.500 | ||||
| Lowerbound of 95% confidence interval for beta | -0.068 | ||||
| Upperbound of 95% confidence interval for beta | -0.010 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.161 | ||||
| Upperbound of 95% confidence interval for alpha | 0.158 | ||||
| Treynor index (mean / b) | 0.409 | ||||
| Jensen alpha (a) | -0.001 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.032 | ||||
| SD | 0.178 | ||||
| Sharpe ratio (Glass type estimate) | -0.178 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.178 | ||||
| df | 1268.000 | ||||
| t | -0.392 | ||||
| p | 0.506 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.069 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.713 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.068 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.713 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.257 | ||||
| Upside Potential Ratio | 1.986 | ||||
| Upside part of mean | 0.245 | ||||
| Downside part of mean | -0.277 | ||||
| Upside SD | 0.129 | ||||
| Downside SD | 0.123 | ||||
| N nonnegative terms | 53.000 | ||||
| N negative terms | 1216.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1269.000 | ||||
| Mean of predictor | 0.316 | ||||
| Mean of criterion | -0.032 | ||||
| SD of predictor | 0.350 | ||||
| SD of criterion | 0.178 | ||||
| Covariance | -0.004 | ||||
| r | -0.067 | ||||
| b (slope, estimate of beta) | -0.034 | ||||
| a (intercept, estimate of alpha) | -0.021 | ||||
| Mean Square Error | 0.032 | ||||
| DF error | 1267.000 | ||||
| t(b) | -2.380 | ||||
| p(b) | 0.542 | ||||
| t(a) | -0.259 | ||||
| p(a) | 0.505 | ||||
| Lowerbound of 95% confidence interval for beta | -0.062 | ||||
| Upperbound of 95% confidence interval for beta | -0.006 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.180 | ||||
| Upperbound of 95% confidence interval for alpha | 0.138 | ||||
| Treynor index (mean / b) | 0.934 | ||||
| Jensen alpha (a) | -0.021 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.018 | ||||
| Expected Shortfall on VaR | 0.023 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.003 | ||||
| Expected Shortfall on VaR | 0.008 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1269.000 | ||||
| Minimum | 0.877 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.138 | ||||
| Mean of quarter 1 | 0.997 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.004 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 60.000 | ||||
| Percentage of outliers low | 0.047 | ||||
| Mean of outliers low | 0.982 | ||||
| Number of outliers high | 56.000 | ||||
| Percentage of outliers high | 0.044 | ||||
| Mean of outliers high | 1.022 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.034 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| 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 observations | 6.000 | ||||
| Minimum | 0.037 | ||||
| Quartile 1 | 0.075 | ||||
| Median | 0.091 | ||||
| Quartile 3 | 0.104 | ||||
| Maximum | 0.128 | ||||
| Mean of quarter 1 | 0.055 | ||||
| Mean of quarter 2 | 0.082 | ||||
| Mean of quarter 3 | 0.101 | ||||
| Mean of quarter 4 | 0.117 | ||||
| Inter Quartile Range | 0.029 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 0.000 | ||||
| Percentage of outliers high | 0.000 | ||||
| Mean of outliers high | NA | ||||
| 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) | 0.013 | ||||
| Compounded annual return (geometric extrapolation) | 0.012 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.096 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.106 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.548 | ||||
| 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 | ||||
| SD | 0.000 | ||||
| Sharpe ratio (Glass type estimate) | NA | ||||
| Sharpe ratio (Hedges UMVUE) | NA | ||||
| df | NA | ||||
| t | NA | ||||
| p | NA | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| 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 | -16.186 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 131.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.365 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.371 | ||||
| SD of criterion | 0.000 | ||||
| Covariance | 0.000 | ||||
| r | NA | ||||
| b (slope, estimate of beta) | NA | ||||
| a (intercept, estimate of alpha) | NA | ||||
| Mean Square Error | NA | ||||
| DF error | NA | ||||
| t(b) | NA | ||||
| p(b) | NA | ||||
| t(a) | NA | ||||
| p(a) | NA | ||||
| Lowerbound of 95% confidence interval for beta | NA | ||||
| Upperbound of 95% confidence interval for beta | NA | ||||
| Lowerbound of 95% confidence interval for alpha | NA | ||||
| Upperbound of 95% confidence interval for alpha | NA | ||||
| Treynor index (mean / b) | NA | ||||
| Jensen alpha (a) | NA | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.000 | ||||
| Sharpe ratio (Glass type estimate) | -12492933348697024.000 | ||||
| Sharpe ratio (Hedges UMVUE) | -12420719861132300.000 | ||||
| df | 130.000 | ||||
| t | -8833837887775228.000 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -13930479873814932.000 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -10910959848449668.000 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -16.186 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 131.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.293 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.368 | ||||
| SD of criterion | 0.000 | ||||
| Covariance | 0.000 | ||||
| r | 0.000 | ||||
| b (slope, estimate of beta) | 0.000 | ||||
| a (intercept, estimate of alpha) | -0.044 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 129.000 | ||||
| t(b) | 0.000 | ||||
| p(b) | 0.500 | ||||
| t(a) | -8598445978430870.000 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.000 | ||||
| Upperbound of 95% confidence interval for beta | 0.000 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.044 | ||||
| Upperbound of 95% confidence interval for alpha | -0.044 | ||||
| Treynor index (mean / b) | -49276654101684183229602304360448.000 | ||||
| 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 VaR | 0.000 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.000 | ||||
| Expected Shortfall on VaR | 0.000 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 1.000 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 0.000 | ||||
| Percentage of outliers high | 0.000 | ||||
| Mean of outliers high | NA | ||||
| 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 observations | 0.000 | ||||
| Minimum | NA | ||||
| Quartile 1 | NA | ||||
| Median | NA | ||||
| Quartile 3 | NA | ||||
| Maximum | NA | ||||
| Mean of quarter 1 | NA | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | NA | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | NA | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 0.000 | ||||
| Percentage of outliers high | NA | ||||
| Mean of outliers high | NA | ||||
| 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 downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||