Advanced Statistics: BOB DYLAN SP500
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 | 0.125 | ||||
| SD | 0.175 | ||||
| Sharpe ratio (Glass type estimate) | 0.713 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.709 | ||||
| df | 129.000 | ||||
| t | 2.348 | ||||
| p | 0.372 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.110 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.314 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.108 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.311 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.345 | ||||
| Upside Potential Ratio | 2.462 | ||||
| Upside part of mean | 0.229 | ||||
| Downside part of mean | -0.104 | ||||
| Upside SD | 0.152 | ||||
| Downside SD | 0.093 | ||||
| N nonnegative terms | 56.000 | ||||
| N negative terms | 74.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 130.000 | ||||
| Mean of predictor | 0.139 | ||||
| Mean of criterion | 0.125 | ||||
| SD of predictor | 0.173 | ||||
| SD of criterion | 0.175 | ||||
| Covariance | 0.001 | ||||
| r | 0.029 | ||||
| b (slope, estimate of beta) | 0.029 | ||||
| a (intercept, estimate of alpha) | 0.121 | ||||
| Mean Square Error | 0.031 | ||||
| DF error | 128.000 | ||||
| t(b) | 0.323 | ||||
| p(b) | 0.486 | ||||
| t(a) | 2.206 | ||||
| p(a) | 0.404 | ||||
| Lowerbound of 95% confidence interval for beta | -0.148 | ||||
| Upperbound of 95% confidence interval for beta | 0.206 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.012 | ||||
| Upperbound of 95% confidence interval for alpha | 0.229 | ||||
| Treynor index (mean / b) | 4.331 | ||||
| Jensen alpha (a) | 0.121 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.109 | ||||
| SD | 0.171 | ||||
| Sharpe ratio (Glass type estimate) | 0.639 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.636 | ||||
| df | 129.000 | ||||
| t | 2.104 | ||||
| p | 0.385 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.038 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.239 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.035 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.236 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.090 | ||||
| Upside Potential Ratio | 2.169 | ||||
| Upside part of mean | 0.218 | ||||
| Downside part of mean | -0.108 | ||||
| Upside SD | 0.141 | ||||
| Downside SD | 0.100 | ||||
| N nonnegative terms | 56.000 | ||||
| N negative terms | 74.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 130.000 | ||||
| Mean of predictor | 0.124 | ||||
| Mean of criterion | 0.109 | ||||
| SD of predictor | 0.171 | ||||
| SD of criterion | 0.171 | ||||
| Covariance | 0.002 | ||||
| r | 0.057 | ||||
| b (slope, estimate of beta) | 0.058 | ||||
| a (intercept, estimate of alpha) | 0.102 | ||||
| Mean Square Error | 0.029 | ||||
| DF error | 128.000 | ||||
| t(b) | 0.651 | ||||
| p(b) | 0.471 | ||||
| t(a) | 1.921 | ||||
| p(a) | 0.416 | ||||
| Lowerbound of 95% confidence interval for beta | -0.117 | ||||
| Upperbound of 95% confidence interval for beta | 0.233 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.003 | ||||
| Upperbound of 95% confidence interval for alpha | 0.207 | ||||
| Treynor index (mean / b) | 1.899 | ||||
| Jensen alpha (a) | 0.102 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.070 | ||||
| Expected Shortfall on VaR | 0.088 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.021 | ||||
| Expected Shortfall on VaR | 0.046 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 130.000 | ||||
| Minimum | 0.792 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.027 | ||||
| Maximum | 1.270 | ||||
| Mean of quarter 1 | 0.974 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.010 | ||||
| Mean of quarter 4 | 1.072 | ||||
| Inter Quartile Range | 0.027 | ||||
| Number outliers low | 6.000 | ||||
| Percentage of outliers low | 0.046 | ||||
| Mean of outliers low | 0.896 | ||||
| Number of outliers high | 13.000 | ||||
| Percentage of outliers high | 0.100 | ||||
| Mean of outliers high | 1.124 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -5.093 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.001 | ||||
| Extreme Value Index (regression method) | 0.177 | ||||
| VaR(95%) (regression method) | 0.026 | ||||
| Expected Shortfall (regression method) | 0.058 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 9.000 | ||||
| Minimum | 0.005 | ||||
| Quartile 1 | 0.027 | ||||
| Median | 0.081 | ||||
| Quartile 3 | 0.107 | ||||
| Maximum | 0.258 | ||||
| Mean of quarter 1 | 0.014 | ||||
| Mean of quarter 2 | 0.060 | ||||
| Mean of quarter 3 | 0.095 | ||||
| Mean of quarter 4 | 0.184 | ||||
| Inter Quartile Range | 0.080 | ||||
| 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 | 0.111 | ||||
| Mean of outliers high | 0.258 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.406 | ||||
| VaR(95%) (moments method) | 0.206 | ||||
| Expected Shortfall (moments method) | 0.354 | ||||
| Extreme Value Index (regression method) | 5.166 | ||||
| VaR(95%) (regression method) | 1.146 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.394 | ||||
| Compounded annual return (geometric extrapolation) | 0.166 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.641 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.902 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.875 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.142 | ||||
| SD | 0.265 | ||||
| Sharpe ratio (Glass type estimate) | 0.536 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.536 | ||||
| df | 2854.000 | ||||
| t | 1.770 | ||||
| p | 0.038 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.058 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.130 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.058 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.130 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.927 | ||||
| Upside Potential Ratio | 3.822 | ||||
| Upside part of mean | 0.586 | ||||
| Downside part of mean | -0.444 | ||||
| Upside SD | 0.217 | ||||
| Downside SD | 0.153 | ||||
| N nonnegative terms | 309.000 | ||||
| N negative terms | 2546.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2855.000 | ||||
| Mean of predictor | 0.148 | ||||
| Mean of criterion | 0.142 | ||||
| SD of predictor | 0.198 | ||||
| SD of criterion | 0.265 | ||||
| Covariance | 0.012 | ||||
| r | 0.231 | ||||
| b (slope, estimate of beta) | 0.309 | ||||
| a (intercept, estimate of alpha) | 0.097 | ||||
| Mean Square Error | 0.067 | ||||
| DF error | 2853.000 | ||||
| t(b) | 12.658 | ||||
| p(b) | -0.000 | ||||
| t(a) | 1.234 | ||||
| p(a) | 0.109 | ||||
| Lowerbound of 95% confidence interval for beta | 0.261 | ||||
| Upperbound of 95% confidence interval for beta | 0.357 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.057 | ||||
| Upperbound of 95% confidence interval for alpha | 0.250 | ||||
| Treynor index (mean / b) | 0.461 | ||||
| Jensen alpha (a) | 0.097 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.108 | ||||
| SD | 0.258 | ||||
| Sharpe ratio (Glass type estimate) | 0.420 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.420 | ||||
| df | 2854.000 | ||||
| t | 1.387 | ||||
| p | 0.083 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.174 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.014 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.174 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.014 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.669 | ||||
| Upside Potential Ratio | 3.489 | ||||
| Upside part of mean | 0.565 | ||||
| Downside part of mean | -0.457 | ||||
| Upside SD | 0.201 | ||||
| Downside SD | 0.162 | ||||
| N nonnegative terms | 309.000 | ||||
| N negative terms | 2546.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2855.000 | ||||
| Mean of predictor | 0.128 | ||||
| Mean of criterion | 0.108 | ||||
| SD of predictor | 0.198 | ||||
| SD of criterion | 0.258 | ||||
| Covariance | 0.012 | ||||
| r | 0.231 | ||||
| b (slope, estimate of beta) | 0.300 | ||||
| a (intercept, estimate of alpha) | 0.070 | ||||
| Mean Square Error | 0.063 | ||||
| DF error | 2853.000 | ||||
| t(b) | 12.653 | ||||
| p(b) | -0.000 | ||||
| t(a) | 0.921 | ||||
| p(a) | 0.179 | ||||
| Lowerbound of 95% confidence interval for beta | 0.253 | ||||
| Upperbound of 95% confidence interval for beta | 0.346 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.079 | ||||
| Upperbound of 95% confidence interval for alpha | 0.219 | ||||
| Treynor index (mean / b) | 0.362 | ||||
| Jensen alpha (a) | 0.070 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.025 | ||||
| Expected Shortfall on VaR | 0.032 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.005 | ||||
| Expected Shortfall on VaR | 0.012 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 2855.000 | ||||
| Minimum | 0.803 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.344 | ||||
| Mean of quarter 1 | 0.994 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.009 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 346.000 | ||||
| Percentage of outliers low | 0.121 | ||||
| Mean of outliers low | 0.987 | ||||
| Number of outliers high | 419.000 | ||||
| Percentage of outliers high | 0.147 | ||||
| Mean of outliers high | 1.015 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.852 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.024 | ||||
| Extreme Value Index (regression method) | 0.247 | ||||
| VaR(95%) (regression method) | 0.005 | ||||
| Expected Shortfall (regression method) | 0.017 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 72.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.000 | ||||
| Median | 0.009 | ||||
| Quartile 3 | 0.053 | ||||
| Maximum | 0.272 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.003 | ||||
| Mean of quarter 3 | 0.022 | ||||
| Mean of quarter 4 | 0.126 | ||||
| Inter Quartile Range | 0.053 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 7.000 | ||||
| Percentage of outliers high | 0.097 | ||||
| Mean of outliers high | 0.195 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.016 | ||||
| VaR(95%) (moments method) | 0.121 | ||||
| Expected Shortfall (moments method) | 0.161 | ||||
| Extreme Value Index (regression method) | 0.128 | ||||
| VaR(95%) (regression method) | 0.104 | ||||
| Expected Shortfall (regression method) | 0.142 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.391 | ||||
| Compounded annual return (geometric extrapolation) | 0.165 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.606 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.303 | ||||
| Compounded annual return / Expected Shortfall lognormal | 5.159 | ||||
| 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 | 0.991 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.391 | ||||
| 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 | 0.913 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.392 | ||||
| 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) | -8709390529065093.000 | ||||
| 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) | 1487298049470235141524476628303872.000 | ||||
| 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 | ||||