Advanced Statistics: Short-Term Stock Index Program (ER2)
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 | -0.008 | ||||
| SD | 0.153 | ||||
| Sharpe ratio (Glass type estimate) | -0.051 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.051 | ||||
| df | 82.000 | ||||
| t | -0.135 | ||||
| p | 0.553 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.796 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.694 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.796 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.695 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.079 | ||||
| Upside Potential Ratio | 0.749 | ||||
| Upside part of mean | 0.074 | ||||
| Downside part of mean | -0.082 | ||||
| Upside SD | 0.115 | ||||
| Downside SD | 0.099 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 78.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 83.000 | ||||
| Mean of predictor | 0.245 | ||||
| Mean of criterion | -0.008 | ||||
| SD of predictor | 0.325 | ||||
| SD of criterion | 0.153 | ||||
| Covariance | 0.002 | ||||
| r | 0.040 | ||||
| b (slope, estimate of beta) | 0.019 | ||||
| a (intercept, estimate of alpha) | -0.012 | ||||
| Mean Square Error | 0.024 | ||||
| DF error | 81.000 | ||||
| t(b) | 0.362 | ||||
| p(b) | 0.359 | ||||
| t(a) | -0.208 | ||||
| p(a) | 0.582 | ||||
| Lowerbound of 95% confidence interval for beta | -0.085 | ||||
| Upperbound of 95% confidence interval for beta | 0.123 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.132 | ||||
| Upperbound of 95% confidence interval for alpha | 0.107 | ||||
| Treynor index (mean / b) | -0.414 | ||||
| Jensen alpha (a) | -0.012 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.020 | ||||
| SD | 0.156 | ||||
| Sharpe ratio (Glass type estimate) | -0.126 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.124 | ||||
| df | 82.000 | ||||
| t | -0.330 | ||||
| p | 0.629 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.871 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.620 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.870 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.621 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.171 | ||||
| Upside Potential Ratio | 0.599 | ||||
| Upside part of mean | 0.068 | ||||
| Downside part of mean | -0.088 | ||||
| Upside SD | 0.105 | ||||
| Downside SD | 0.114 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 78.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 83.000 | ||||
| Mean of predictor | 0.193 | ||||
| Mean of criterion | -0.020 | ||||
| SD of predictor | 0.312 | ||||
| SD of criterion | 0.156 | ||||
| Covariance | 0.003 | ||||
| r | 0.054 | ||||
| b (slope, estimate of beta) | 0.027 | ||||
| a (intercept, estimate of alpha) | -0.025 | ||||
| Mean Square Error | 0.024 | ||||
| DF error | 81.000 | ||||
| t(b) | 0.484 | ||||
| p(b) | 0.315 | ||||
| t(a) | -0.409 | ||||
| p(a) | 0.658 | ||||
| Lowerbound of 95% confidence interval for beta | -0.083 | ||||
| Upperbound of 95% confidence interval for beta | 0.137 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.145 | ||||
| Upperbound of 95% confidence interval for alpha | 0.095 | ||||
| Treynor index (mean / b) | -0.729 | ||||
| Jensen alpha (a) | -0.025 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.073 | ||||
| Expected Shortfall on VaR | 0.090 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.023 | ||||
| Expected Shortfall on VaR | 0.050 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 83.000 | ||||
| Minimum | 0.746 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.221 | ||||
| Mean of quarter 1 | 0.987 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.025 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 6.000 | ||||
| Percentage of outliers low | 0.072 | ||||
| Mean of outliers low | 0.953 | ||||
| Number of outliers high | 8.000 | ||||
| Percentage of outliers high | 0.096 | ||||
| Mean of outliers high | 1.067 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -2.165 | ||||
| VaR(95%) (moments method) | -0.001 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 2.171 | ||||
| VaR(95%) (regression method) | -0.000 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.028 | ||||
| Quartile 1 | 0.085 | ||||
| Median | 0.141 | ||||
| Quartile 3 | 0.198 | ||||
| Maximum | 0.254 | ||||
| Mean of quarter 1 | 0.028 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.254 | ||||
| Inter Quartile Range | 0.113 | ||||
| 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) | 0.027 | ||||
| Compounded annual return (geometric extrapolation) | 0.025 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.097 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.097 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.276 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.008 | ||||
| SD | 0.233 | ||||
| Sharpe ratio (Glass type estimate) | 0.034 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.034 | ||||
| df | 1813.000 | ||||
| t | 0.089 | ||||
| p | 0.499 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.711 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.779 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.711 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.779 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.049 | ||||
| Upside Potential Ratio | 1.580 | ||||
| Upside part of mean | 0.254 | ||||
| Downside part of mean | -0.246 | ||||
| Upside SD | 0.168 | ||||
| Downside SD | 0.161 | ||||
| N nonnegative terms | 70.000 | ||||
| N negative terms | 1744.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1814.000 | ||||
| Mean of predictor | 0.314 | ||||
| Mean of criterion | 0.008 | ||||
| SD of predictor | 0.482 | ||||
| SD of criterion | 0.233 | ||||
| Covariance | 0.014 | ||||
| r | 0.124 | ||||
| b (slope, estimate of beta) | 0.060 | ||||
| a (intercept, estimate of alpha) | -0.011 | ||||
| Mean Square Error | 0.053 | ||||
| DF error | 1812.000 | ||||
| t(b) | 5.328 | ||||
| p(b) | 0.438 | ||||
| t(a) | -0.125 | ||||
| p(a) | 0.501 | ||||
| Lowerbound of 95% confidence interval for beta | 0.038 | ||||
| Upperbound of 95% confidence interval for beta | 0.082 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.183 | ||||
| Upperbound of 95% confidence interval for alpha | 0.162 | ||||
| Treynor index (mean / b) | 0.131 | ||||
| Jensen alpha (a) | -0.011 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.020 | ||||
| SD | 0.236 | ||||
| Sharpe ratio (Glass type estimate) | -0.083 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.083 | ||||
| df | 1813.000 | ||||
| t | -0.218 | ||||
| p | 0.503 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.828 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.662 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.828 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.662 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.110 | ||||
| Upside Potential Ratio | 1.360 | ||||
| Upside part of mean | 0.242 | ||||
| Downside part of mean | -0.261 | ||||
| Upside SD | 0.155 | ||||
| Downside SD | 0.178 | ||||
| N nonnegative terms | 70.000 | ||||
| N negative terms | 1744.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1814.000 | ||||
| Mean of predictor | 0.197 | ||||
| Mean of criterion | -0.020 | ||||
| SD of predictor | 0.484 | ||||
| SD of criterion | 0.236 | ||||
| Covariance | 0.014 | ||||
| r | 0.123 | ||||
| b (slope, estimate of beta) | 0.060 | ||||
| a (intercept, estimate of alpha) | -0.031 | ||||
| Mean Square Error | 0.055 | ||||
| DF error | 1812.000 | ||||
| t(b) | 5.286 | ||||
| p(b) | 0.438 | ||||
| t(a) | -0.353 | ||||
| p(a) | 0.504 | ||||
| Lowerbound of 95% confidence interval for beta | 0.038 | ||||
| Upperbound of 95% confidence interval for beta | 0.082 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.206 | ||||
| Upperbound of 95% confidence interval for alpha | 0.143 | ||||
| Treynor index (mean / b) | -0.326 | ||||
| Jensen alpha (a) | -0.031 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.024 | ||||
| Expected Shortfall on VaR | 0.030 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.003 | ||||
| Expected Shortfall on VaR | 0.007 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1814.000 | ||||
| Minimum | 0.766 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.230 | ||||
| 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 | 77.000 | ||||
| Percentage of outliers low | 0.042 | ||||
| Mean of outliers low | 0.982 | ||||
| Number of outliers high | 95.000 | ||||
| Percentage of outliers high | 0.052 | ||||
| Mean of outliers high | 1.019 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.262 | ||||
| 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 | 8.000 | ||||
| Minimum | 0.010 | ||||
| Quartile 1 | 0.035 | ||||
| Median | 0.098 | ||||
| Quartile 3 | 0.167 | ||||
| Maximum | 0.411 | ||||
| Mean of quarter 1 | 0.020 | ||||
| Mean of quarter 2 | 0.040 | ||||
| Mean of quarter 3 | 0.156 | ||||
| Mean of quarter 4 | 0.299 | ||||
| Inter Quartile Range | 0.131 | ||||
| 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 | 0.125 | ||||
| Mean of outliers high | 0.411 | ||||
| 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) | 0.027 | ||||
| Compounded annual return (geometric extrapolation) | 0.025 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.060 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.083 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.835 | ||||
| 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 | 1.013 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.449 | ||||
| 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 | 0.911 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.450 | ||||
| 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) | -8731177003729537.000 | ||||
| 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) | -99552839115989051501509745836032.000 | ||||
| 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 | ||||