Advanced Statistics: THE ROLLING STONES SP500
Advanced Statistics module contributed by Jules Ellis, C2 Member. Jules has written a very helpful guide for these statistics. | |||||
| |||||
| ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.111 | ||||
| SD | 0.155 | ||||
| Sharpe ratio (Glass type estimate) | 0.712 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.706 | ||||
| df | 81.000 | ||||
| t | 1.862 | ||||
| p | 0.033 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.048 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.468 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.052 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.463 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.155 | ||||
| Upside Potential Ratio | 2.443 | ||||
| Upside part of mean | 0.234 | ||||
| Downside part of mean | -0.124 | ||||
| Upside SD | 0.125 | ||||
| Downside SD | 0.096 | ||||
| N nonnegative terms | 45.000 | ||||
| N negative terms | 37.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 82.000 | ||||
| Mean of predictor | 0.203 | ||||
| Mean of criterion | 0.111 | ||||
| SD of predictor | 0.223 | ||||
| SD of criterion | 0.155 | ||||
| Covariance | -0.000 | ||||
| r | -0.001 | ||||
| b (slope, estimate of beta) | -0.001 | ||||
| a (intercept, estimate of alpha) | 0.111 | ||||
| Mean Square Error | 0.024 | ||||
| DF error | 80.000 | ||||
| t(b) | -0.007 | ||||
| p(b) | 0.503 | ||||
| t(a) | 1.791 | ||||
| p(a) | 0.039 | ||||
| Lowerbound of 95% confidence interval for beta | -0.156 | ||||
| Upperbound of 95% confidence interval for beta | 0.154 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.012 | ||||
| Upperbound of 95% confidence interval for alpha | 0.234 | ||||
| Treynor index (mean / b) | -200.208 | ||||
| Jensen alpha (a) | 0.111 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.098 | ||||
| SD | 0.155 | ||||
| Sharpe ratio (Glass type estimate) | 0.634 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.628 | ||||
| df | 81.000 | ||||
| t | 1.658 | ||||
| p | 0.051 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.124 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.389 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.128 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.384 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.965 | ||||
| Upside Potential Ratio | 2.224 | ||||
| Upside part of mean | 0.226 | ||||
| Downside part of mean | -0.128 | ||||
| Upside SD | 0.119 | ||||
| Downside SD | 0.102 | ||||
| N nonnegative terms | 45.000 | ||||
| N negative terms | 37.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 82.000 | ||||
| Mean of predictor | 0.178 | ||||
| Mean of criterion | 0.098 | ||||
| SD of predictor | 0.211 | ||||
| SD of criterion | 0.155 | ||||
| Covariance | 0.000 | ||||
| r | 0.014 | ||||
| b (slope, estimate of beta) | 0.010 | ||||
| a (intercept, estimate of alpha) | 0.096 | ||||
| Mean Square Error | 0.024 | ||||
| DF error | 80.000 | ||||
| t(b) | 0.126 | ||||
| p(b) | 0.450 | ||||
| t(a) | 1.571 | ||||
| p(a) | 0.060 | ||||
| Lowerbound of 95% confidence interval for beta | -0.153 | ||||
| Upperbound of 95% confidence interval for beta | 0.174 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.026 | ||||
| Upperbound of 95% confidence interval for alpha | 0.218 | ||||
| Treynor index (mean / b) | 9.523 | ||||
| Jensen alpha (a) | 0.096 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.063 | ||||
| Expected Shortfall on VaR | 0.080 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.022 | ||||
| Expected Shortfall on VaR | 0.048 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 82.000 | ||||
| Minimum | 0.846 | ||||
| Quartile 1 | 0.997 | ||||
| Median | 1.013 | ||||
| Quartile 3 | 1.034 | ||||
| Maximum | 1.184 | ||||
| Mean of quarter 1 | 0.966 | ||||
| Mean of quarter 2 | 1.002 | ||||
| Mean of quarter 3 | 1.022 | ||||
| Mean of quarter 4 | 1.062 | ||||
| Inter Quartile Range | 0.036 | ||||
| Number outliers low | 4.000 | ||||
| Percentage of outliers low | 0.049 | ||||
| Mean of outliers low | 0.895 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.037 | ||||
| Mean of outliers high | 1.140 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.491 | ||||
| VaR(95%) (moments method) | 0.018 | ||||
| Expected Shortfall (moments method) | 0.045 | ||||
| Extreme Value Index (regression method) | 0.534 | ||||
| VaR(95%) (regression method) | 0.036 | ||||
| Expected Shortfall (regression method) | 0.102 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 10.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.010 | ||||
| Median | 0.029 | ||||
| Quartile 3 | 0.084 | ||||
| Maximum | 0.231 | ||||
| Mean of quarter 1 | 0.004 | ||||
| Mean of quarter 2 | 0.018 | ||||
| Mean of quarter 3 | 0.053 | ||||
| Mean of quarter 4 | 0.158 | ||||
| Inter Quartile Range | 0.073 | ||||
| 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 | 0.100 | ||||
| Mean of outliers high | 0.231 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -5.669 | ||||
| VaR(95%) (moments method) | 0.168 | ||||
| Expected Shortfall (moments method) | 0.168 | ||||
| Extreme Value Index (regression method) | -0.767 | ||||
| VaR(95%) (regression method) | 0.257 | ||||
| Expected Shortfall (regression method) | 0.285 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.240 | ||||
| Compounded annual return (geometric extrapolation) | 0.153 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.662 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.967 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.900 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.114 | ||||
| SD | 0.189 | ||||
| Sharpe ratio (Glass type estimate) | 0.605 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.605 | ||||
| df | 1806.000 | ||||
| t | 1.589 | ||||
| p | 0.481 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.142 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.351 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.142 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.351 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.988 | ||||
| Upside Potential Ratio | 5.340 | ||||
| Upside part of mean | 0.618 | ||||
| Downside part of mean | -0.504 | ||||
| Upside SD | 0.150 | ||||
| Downside SD | 0.116 | ||||
| N nonnegative terms | 389.000 | ||||
| N negative terms | 1418.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1807.000 | ||||
| Mean of predictor | 0.207 | ||||
| Mean of criterion | 0.114 | ||||
| SD of predictor | 0.208 | ||||
| SD of criterion | 0.189 | ||||
| Covariance | 0.005 | ||||
| r | 0.135 | ||||
| b (slope, estimate of beta) | 0.123 | ||||
| a (intercept, estimate of alpha) | 0.089 | ||||
| Mean Square Error | 0.035 | ||||
| DF error | 1805.000 | ||||
| t(b) | 5.796 | ||||
| p(b) | 0.414 | ||||
| t(a) | 1.245 | ||||
| p(a) | 0.481 | ||||
| Lowerbound of 95% confidence interval for beta | 0.081 | ||||
| Upperbound of 95% confidence interval for beta | 0.164 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.051 | ||||
| Upperbound of 95% confidence interval for alpha | 0.229 | ||||
| Treynor index (mean / b) | 0.933 | ||||
| Jensen alpha (a) | 0.089 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.097 | ||||
| SD | 0.187 | ||||
| Sharpe ratio (Glass type estimate) | 0.518 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.518 | ||||
| df | 1806.000 | ||||
| t | 1.360 | ||||
| p | 0.484 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.229 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.264 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.229 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.264 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.808 | ||||
| Upside Potential Ratio | 5.075 | ||||
| Upside part of mean | 0.608 | ||||
| Downside part of mean | -0.511 | ||||
| Upside SD | 0.144 | ||||
| Downside SD | 0.120 | ||||
| N nonnegative terms | 389.000 | ||||
| N negative terms | 1418.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1807.000 | ||||
| Mean of predictor | 0.185 | ||||
| Mean of criterion | 0.097 | ||||
| SD of predictor | 0.210 | ||||
| SD of criterion | 0.187 | ||||
| Covariance | 0.005 | ||||
| r | 0.135 | ||||
| b (slope, estimate of beta) | 0.121 | ||||
| a (intercept, estimate of alpha) | 0.074 | ||||
| Mean Square Error | 0.034 | ||||
| DF error | 1805.000 | ||||
| t(b) | 5.807 | ||||
| p(b) | 0.414 | ||||
| t(a) | 1.054 | ||||
| p(a) | 0.484 | ||||
| Lowerbound of 95% confidence interval for beta | 0.080 | ||||
| Upperbound of 95% confidence interval for beta | 0.161 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.064 | ||||
| Upperbound of 95% confidence interval for alpha | 0.213 | ||||
| Treynor index (mean / b) | 0.802 | ||||
| Jensen alpha (a) | 0.074 | ||||
| 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%) | 0.006 | ||||
| Expected Shortfall on VaR | 0.013 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1807.000 | ||||
| Minimum | 0.851 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.176 | ||||
| Mean of quarter 1 | 0.993 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.010 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 328.000 | ||||
| Percentage of outliers low | 0.182 | ||||
| Mean of outliers low | 0.990 | ||||
| Number of outliers high | 399.000 | ||||
| Percentage of outliers high | 0.221 | ||||
| Mean of outliers high | 1.011 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.411 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | 0.009 | ||||
| Extreme Value Index (regression method) | 0.246 | ||||
| VaR(95%) (regression method) | 0.007 | ||||
| Expected Shortfall (regression method) | 0.016 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 45.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.006 | ||||
| Median | 0.013 | ||||
| Quartile 3 | 0.040 | ||||
| Maximum | 0.285 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.010 | ||||
| Mean of quarter 3 | 0.028 | ||||
| Mean of quarter 4 | 0.133 | ||||
| Inter Quartile Range | 0.034 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.133 | ||||
| Mean of outliers high | 0.192 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.261 | ||||
| VaR(95%) (moments method) | 0.119 | ||||
| Expected Shortfall (moments method) | 0.201 | ||||
| Extreme Value Index (regression method) | -0.275 | ||||
| VaR(95%) (regression method) | 0.152 | ||||
| Expected Shortfall (regression method) | 0.195 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.238 | ||||
| Compounded annual return (geometric extrapolation) | 0.151 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.530 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.134 | ||||
| Compounded annual return / Expected Shortfall lognormal | 6.528 | ||||
| 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 | 0.901 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.467 | ||||
| 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 | 0.789 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.474 | ||||
| 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) | -8753239312499153.000 | ||||
| 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) | -26068333461179128238651678585257984.000 | ||||
| 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 | ||||