Advanced Statistics: Weekend Stock Trader
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 | -0.065 | ||||
| SD | 0.064 | ||||
| Sharpe ratio (Glass type estimate) | -1.016 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.000 | ||||
| df | 49.000 | ||||
| t | -2.074 | ||||
| p | 0.978 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.992 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.030 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.981 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.020 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.103 | ||||
| Upside Potential Ratio | 0.534 | ||||
| Upside part of mean | 0.031 | ||||
| Downside part of mean | -0.096 | ||||
| Upside SD | 0.030 | ||||
| Downside SD | 0.059 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 45.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 50.000 | ||||
| Mean of predictor | 0.389 | ||||
| Mean of criterion | -0.065 | ||||
| SD of predictor | 0.347 | ||||
| SD of criterion | 0.064 | ||||
| Covariance | 0.005 | ||||
| r | 0.207 | ||||
| b (slope, estimate of beta) | 0.038 | ||||
| a (intercept, estimate of alpha) | -0.080 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 48.000 | ||||
| t(b) | 1.465 | ||||
| p(b) | 0.075 | ||||
| t(a) | -2.449 | ||||
| p(a) | 0.991 | ||||
| Lowerbound of 95% confidence interval for beta | -0.014 | ||||
| Upperbound of 95% confidence interval for beta | 0.090 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.145 | ||||
| Upperbound of 95% confidence interval for alpha | -0.014 | ||||
| Treynor index (mean / b) | -1.704 | ||||
| Jensen alpha (a) | -0.080 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.067 | ||||
| SD | 0.065 | ||||
| Sharpe ratio (Glass type estimate) | -1.028 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.012 | ||||
| df | 49.000 | ||||
| t | -2.098 | ||||
| p | 0.979 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.004 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.041 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.993 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.031 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.105 | ||||
| Upside Potential Ratio | 0.510 | ||||
| Upside part of mean | 0.031 | ||||
| Downside part of mean | -0.098 | ||||
| Upside SD | 0.029 | ||||
| Downside SD | 0.060 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 45.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 50.000 | ||||
| Mean of predictor | 0.334 | ||||
| Mean of criterion | -0.067 | ||||
| SD of predictor | 0.302 | ||||
| SD of criterion | 0.065 | ||||
| Covariance | 0.005 | ||||
| r | 0.246 | ||||
| b (slope, estimate of beta) | 0.053 | ||||
| a (intercept, estimate of alpha) | -0.084 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 48.000 | ||||
| t(b) | 1.756 | ||||
| p(b) | 0.043 | ||||
| t(a) | -2.578 | ||||
| p(a) | 0.993 | ||||
| Lowerbound of 95% confidence interval for beta | -0.008 | ||||
| Upperbound of 95% confidence interval for beta | 0.113 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.150 | ||||
| Upperbound of 95% confidence interval for alpha | -0.019 | ||||
| Treynor index (mean / b) | -1.261 | ||||
| Jensen alpha (a) | -0.084 | ||||
| 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 | 0.043 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.026 | ||||
| Expected Shortfall on VaR | 0.048 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 50.000 | ||||
| Minimum | 0.920 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.044 | ||||
| Mean of quarter 1 | 0.982 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.011 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 9.000 | ||||
| Percentage of outliers low | 0.180 | ||||
| Mean of outliers low | 0.974 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.120 | ||||
| Mean of outliers high | 1.025 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -2.890 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.001 | ||||
| Extreme Value Index (regression method) | 0.342 | ||||
| VaR(95%) (regression method) | 0.021 | ||||
| Expected Shortfall (regression method) | 0.054 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.044 | ||||
| Median | 0.087 | ||||
| Quartile 3 | 0.130 | ||||
| Maximum | 0.173 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.173 | ||||
| Inter Quartile Range | 0.086 | ||||
| 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) | -0.022 | ||||
| Compounded annual return (geometric extrapolation) | -0.022 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.129 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.129 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.519 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.064 | ||||
| SD | 0.068 | ||||
| Sharpe ratio (Glass type estimate) | -0.936 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.936 | ||||
| df | 1111.000 | ||||
| t | -1.929 | ||||
| p | 0.537 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.888 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.016 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.888 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.017 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.263 | ||||
| Upside Potential Ratio | 3.432 | ||||
| Upside part of mean | 0.174 | ||||
| Downside part of mean | -0.238 | ||||
| Upside SD | 0.046 | ||||
| Downside SD | 0.051 | ||||
| N nonnegative terms | 114.000 | ||||
| N negative terms | 998.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1112.000 | ||||
| Mean of predictor | 0.387 | ||||
| Mean of criterion | -0.064 | ||||
| SD of predictor | 0.298 | ||||
| SD of criterion | 0.068 | ||||
| Covariance | 0.004 | ||||
| r | 0.182 | ||||
| b (slope, estimate of beta) | 0.042 | ||||
| a (intercept, estimate of alpha) | -0.080 | ||||
| Mean Square Error | 0.005 | ||||
| DF error | 1110.000 | ||||
| t(b) | 6.183 | ||||
| p(b) | 0.409 | ||||
| t(a) | -2.449 | ||||
| p(a) | 0.537 | ||||
| Lowerbound of 95% confidence interval for beta | 0.029 | ||||
| Upperbound of 95% confidence interval for beta | 0.055 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.144 | ||||
| Upperbound of 95% confidence interval for alpha | -0.016 | ||||
| Treynor index (mean / b) | -1.531 | ||||
| Jensen alpha (a) | -0.080 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.066 | ||||
| SD | 0.068 | ||||
| Sharpe ratio (Glass type estimate) | -0.969 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.969 | ||||
| df | 1111.000 | ||||
| t | -1.997 | ||||
| p | 0.538 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.921 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.017 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.921 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.017 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.296 | ||||
| Upside Potential Ratio | 3.378 | ||||
| Upside part of mean | 0.173 | ||||
| Downside part of mean | -0.239 | ||||
| Upside SD | 0.046 | ||||
| Downside SD | 0.051 | ||||
| N nonnegative terms | 114.000 | ||||
| N negative terms | 998.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1112.000 | ||||
| Mean of predictor | 0.342 | ||||
| Mean of criterion | -0.066 | ||||
| SD of predictor | 0.301 | ||||
| SD of criterion | 0.068 | ||||
| Covariance | 0.004 | ||||
| r | 0.181 | ||||
| b (slope, estimate of beta) | 0.041 | ||||
| a (intercept, estimate of alpha) | -0.080 | ||||
| Mean Square Error | 0.005 | ||||
| DF error | 1110.000 | ||||
| t(b) | 6.141 | ||||
| p(b) | 0.409 | ||||
| t(a) | -2.454 | ||||
| p(a) | 0.537 | ||||
| Lowerbound of 95% confidence interval for beta | 0.028 | ||||
| Upperbound of 95% confidence interval for beta | 0.054 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.145 | ||||
| Upperbound of 95% confidence interval for alpha | -0.016 | ||||
| Treynor index (mean / b) | -1.612 | ||||
| Jensen alpha (a) | -0.080 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.007 | ||||
| Expected Shortfall on VaR | 0.009 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.003 | ||||
| Expected Shortfall on VaR | 0.006 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1112.000 | ||||
| Minimum | 0.960 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.045 | ||||
| Mean of quarter 1 | 0.997 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.003 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 142.000 | ||||
| Percentage of outliers low | 0.128 | ||||
| Mean of outliers low | 0.994 | ||||
| Number of outliers high | 116.000 | ||||
| Percentage of outliers high | 0.104 | ||||
| Mean of outliers high | 1.007 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.100 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.004 | ||||
| Extreme Value Index (regression method) | 0.145 | ||||
| VaR(95%) (regression method) | 0.004 | ||||
| Expected Shortfall (regression method) | 0.008 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 7.000 | ||||
| Minimum | 0.015 | ||||
| Quartile 1 | 0.023 | ||||
| Median | 0.031 | ||||
| Quartile 3 | 0.044 | ||||
| Maximum | 0.182 | ||||
| Mean of quarter 1 | 0.017 | ||||
| Mean of quarter 2 | 0.028 | ||||
| Mean of quarter 3 | 0.044 | ||||
| Mean of quarter 4 | 0.113 | ||||
| Inter Quartile Range | 0.022 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.143 | ||||
| Mean of outliers high | 0.182 | ||||
| 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) | -0.021 | ||||
| Compounded annual return (geometric extrapolation) | -0.022 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.121 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.194 | ||||
| Compounded annual return / Expected Shortfall lognormal | -2.469 | ||||
| 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 | 0.951 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.379 | ||||
| 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 | 0.877 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.382 | ||||
| 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) | -8711799167972760.000 | ||||
| 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) | -87270500708388169489183603163136.000 | ||||
| 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 | ||||