Advanced Statistics: Short-Term Stock Index Program
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 | -0.016 | ||||
| SD | 0.105 | ||||
| Sharpe ratio (Glass type estimate) | -0.151 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.149 | ||||
| df | 87.000 | ||||
| t | -0.408 | ||||
| p | 0.658 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.874 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.574 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.874 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.575 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.234 | ||||
| Upside Potential Ratio | 0.770 | ||||
| Upside part of mean | 0.052 | ||||
| Downside part of mean | -0.068 | ||||
| Upside SD | 0.080 | ||||
| Downside SD | 0.068 | ||||
| N nonnegative terms | 7.000 | ||||
| N negative terms | 81.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 88.000 | ||||
| Mean of predictor | 0.227 | ||||
| Mean of criterion | -0.016 | ||||
| SD of predictor | 0.287 | ||||
| SD of criterion | 0.105 | ||||
| Covariance | 0.002 | ||||
| r | 0.081 | ||||
| b (slope, estimate of beta) | 0.030 | ||||
| a (intercept, estimate of alpha) | -0.023 | ||||
| Mean Square Error | 0.011 | ||||
| DF error | 86.000 | ||||
| t(b) | 0.749 | ||||
| p(b) | 0.228 | ||||
| t(a) | -0.564 | ||||
| p(a) | 0.713 | ||||
| Lowerbound of 95% confidence interval for beta | -0.049 | ||||
| Upperbound of 95% confidence interval for beta | 0.108 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.102 | ||||
| Upperbound of 95% confidence interval for alpha | 0.057 | ||||
| Treynor index (mean / b) | -0.538 | ||||
| Jensen alpha (a) | -0.023 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.021 | ||||
| SD | 0.105 | ||||
| Sharpe ratio (Glass type estimate) | -0.203 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.201 | ||||
| df | 87.000 | ||||
| t | -0.549 | ||||
| p | 0.708 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.926 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.522 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.925 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.524 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.287 | ||||
| Upside Potential Ratio | 0.664 | ||||
| Upside part of mean | 0.049 | ||||
| Downside part of mean | -0.071 | ||||
| Upside SD | 0.074 | ||||
| Downside SD | 0.074 | ||||
| N nonnegative terms | 7.000 | ||||
| N negative terms | 81.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 88.000 | ||||
| Mean of predictor | 0.184 | ||||
| Mean of criterion | -0.021 | ||||
| SD of predictor | 0.288 | ||||
| SD of criterion | 0.105 | ||||
| Covariance | 0.003 | ||||
| r | 0.094 | ||||
| b (slope, estimate of beta) | 0.034 | ||||
| a (intercept, estimate of alpha) | -0.028 | ||||
| Mean Square Error | 0.011 | ||||
| DF error | 86.000 | ||||
| t(b) | 0.876 | ||||
| p(b) | 0.192 | ||||
| t(a) | -0.698 | ||||
| p(a) | 0.757 | ||||
| Lowerbound of 95% confidence interval for beta | -0.043 | ||||
| Upperbound of 95% confidence interval for beta | 0.112 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.106 | ||||
| Upperbound of 95% confidence interval for alpha | 0.051 | ||||
| Treynor index (mean / b) | -0.621 | ||||
| Jensen alpha (a) | -0.028 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.050 | ||||
| Expected Shortfall on VaR | 0.062 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.019 | ||||
| Expected Shortfall on VaR | 0.040 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 88.000 | ||||
| Minimum | 0.824 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.200 | ||||
| Mean of quarter 1 | 0.991 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.019 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 7.000 | ||||
| Percentage of outliers low | 0.080 | ||||
| Mean of outliers low | 0.971 | ||||
| Number of outliers high | 10.000 | ||||
| Percentage of outliers high | 0.114 | ||||
| Mean of outliers high | 1.041 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.374 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | 0.000 | ||||
| Extreme Value Index (regression method) | 1.907 | ||||
| VaR(95%) (regression method) | 0.001 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.017 | ||||
| Quartile 1 | 0.057 | ||||
| Median | 0.096 | ||||
| Quartile 3 | 0.136 | ||||
| Maximum | 0.176 | ||||
| Mean of quarter 1 | 0.017 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.176 | ||||
| Inter Quartile Range | 0.079 | ||||
| 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) | 0.025 | ||||
| Compounded annual return (geometric extrapolation) | 0.023 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.131 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.131 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.370 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.021 | ||||
| SD | 0.290 | ||||
| Sharpe ratio (Glass type estimate) | 0.073 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.073 | ||||
| df | 1922.000 | ||||
| t | 0.198 | ||||
| p | 0.498 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.650 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.796 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.650 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.796 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.107 | ||||
| Upside Potential Ratio | 1.625 | ||||
| Upside part of mean | 0.321 | ||||
| Downside part of mean | -0.300 | ||||
| Upside SD | 0.213 | ||||
| Downside SD | 0.197 | ||||
| N nonnegative terms | 109.000 | ||||
| N negative terms | 1814.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1923.000 | ||||
| Mean of predictor | 0.310 | ||||
| Mean of criterion | 0.021 | ||||
| SD of predictor | 0.513 | ||||
| SD of criterion | 0.290 | ||||
| Covariance | 0.035 | ||||
| r | 0.238 | ||||
| b (slope, estimate of beta) | 0.135 | ||||
| a (intercept, estimate of alpha) | -0.021 | ||||
| Mean Square Error | 0.080 | ||||
| DF error | 1921.000 | ||||
| t(b) | 10.741 | ||||
| p(b) | 0.350 | ||||
| t(a) | -0.198 | ||||
| p(a) | 0.503 | ||||
| Lowerbound of 95% confidence interval for beta | 0.110 | ||||
| Upperbound of 95% confidence interval for beta | 0.159 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.225 | ||||
| Upperbound of 95% confidence interval for alpha | 0.184 | ||||
| Treynor index (mean / b) | 0.157 | ||||
| Jensen alpha (a) | -0.021 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.021 | ||||
| SD | 0.294 | ||||
| Sharpe ratio (Glass type estimate) | -0.073 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.073 | ||||
| df | 1922.000 | ||||
| t | -0.197 | ||||
| p | 0.502 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.796 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.651 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.796 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.651 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.096 | ||||
| Upside Potential Ratio | 1.354 | ||||
| Upside part of mean | 0.301 | ||||
| Downside part of mean | -0.323 | ||||
| Upside SD | 0.191 | ||||
| Downside SD | 0.222 | ||||
| N nonnegative terms | 109.000 | ||||
| N negative terms | 1814.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1923.000 | ||||
| Mean of predictor | 0.180 | ||||
| Mean of criterion | -0.021 | ||||
| SD of predictor | 0.509 | ||||
| SD of criterion | 0.294 | ||||
| Covariance | 0.036 | ||||
| r | 0.243 | ||||
| b (slope, estimate of beta) | 0.140 | ||||
| a (intercept, estimate of alpha) | -0.047 | ||||
| Mean Square Error | 0.081 | ||||
| DF error | 1921.000 | ||||
| t(b) | 10.989 | ||||
| p(b) | 0.347 | ||||
| t(a) | -0.443 | ||||
| p(a) | 0.506 | ||||
| Lowerbound of 95% confidence interval for beta | 0.115 | ||||
| Upperbound of 95% confidence interval for beta | 0.165 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.253 | ||||
| Upperbound of 95% confidence interval for alpha | 0.160 | ||||
| Treynor index (mean / b) | -0.152 | ||||
| Jensen alpha (a) | -0.047 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.029 | ||||
| Expected Shortfall on VaR | 0.037 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.009 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1923.000 | ||||
| Minimum | 0.723 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.317 | ||||
| Mean of quarter 1 | 0.996 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.005 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 106.000 | ||||
| Percentage of outliers low | 0.055 | ||||
| Mean of outliers low | 0.982 | ||||
| Number of outliers high | 136.000 | ||||
| Percentage of outliers high | 0.071 | ||||
| Mean of outliers high | 1.017 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.176 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| 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 | 0.006 | ||||
| Quartile 1 | 0.028 | ||||
| Median | 0.035 | ||||
| Quartile 3 | 0.202 | ||||
| Maximum | 0.384 | ||||
| Mean of quarter 1 | 0.016 | ||||
| Mean of quarter 2 | 0.035 | ||||
| Mean of quarter 3 | 0.036 | ||||
| Mean of quarter 4 | 0.321 | ||||
| Inter Quartile Range | 0.174 | ||||
| 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) | 0.025 | ||||
| Compounded annual return (geometric extrapolation) | 0.023 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.060 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.072 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.625 | ||||
| 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 | 1.008 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.491 | ||||
| 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 | 0.885 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.494 | ||||
| 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) | -8746048228050394.000 | ||||
| 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) | -110882199450951782636314586775552.000 | ||||
| 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 | ||||