Advanced Statistics: Sliced Bread Lite
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 | -0.134 | ||||
| SD | 0.186 | ||||
| Sharpe ratio (Glass type estimate) | -0.721 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.702 | ||||
| df | 30.000 | ||||
| t | -1.158 | ||||
| p | 0.872 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.948 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.518 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.935 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.530 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.939 | ||||
| Upside Potential Ratio | 0.742 | ||||
| Upside part of mean | 0.106 | ||||
| Downside part of mean | -0.240 | ||||
| Upside SD | 0.121 | ||||
| Downside SD | 0.143 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 28.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 31.000 | ||||
| Mean of predictor | 0.309 | ||||
| Mean of criterion | -0.134 | ||||
| SD of predictor | 0.244 | ||||
| SD of criterion | 0.186 | ||||
| Covariance | -0.013 | ||||
| r | -0.286 | ||||
| b (slope, estimate of beta) | -0.218 | ||||
| a (intercept, estimate of alpha) | -0.067 | ||||
| Mean Square Error | 0.033 | ||||
| DF error | 29.000 | ||||
| t(b) | -1.608 | ||||
| p(b) | 0.941 | ||||
| t(a) | -0.553 | ||||
| p(a) | 0.708 | ||||
| Lowerbound of 95% confidence interval for beta | -0.495 | ||||
| Upperbound of 95% confidence interval for beta | 0.059 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.313 | ||||
| Upperbound of 95% confidence interval for alpha | 0.179 | ||||
| Treynor index (mean / b) | 0.615 | ||||
| Jensen alpha (a) | -0.067 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.151 | ||||
| SD | 0.186 | ||||
| Sharpe ratio (Glass type estimate) | -0.813 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.792 | ||||
| df | 30.000 | ||||
| t | -1.306 | ||||
| p | 0.899 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.043 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.430 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.028 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.444 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.002 | ||||
| Upside Potential Ratio | 0.656 | ||||
| Upside part of mean | 0.099 | ||||
| Downside part of mean | -0.250 | ||||
| Upside SD | 0.112 | ||||
| Downside SD | 0.151 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 28.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 31.000 | ||||
| Mean of predictor | 0.278 | ||||
| Mean of criterion | -0.151 | ||||
| SD of predictor | 0.234 | ||||
| SD of criterion | 0.186 | ||||
| Covariance | -0.013 | ||||
| r | -0.296 | ||||
| b (slope, estimate of beta) | -0.235 | ||||
| a (intercept, estimate of alpha) | -0.086 | ||||
| Mean Square Error | 0.033 | ||||
| DF error | 29.000 | ||||
| t(b) | -1.669 | ||||
| p(b) | 0.947 | ||||
| t(a) | -0.720 | ||||
| p(a) | 0.761 | ||||
| Lowerbound of 95% confidence interval for beta | -0.524 | ||||
| Upperbound of 95% confidence interval for beta | 0.053 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.329 | ||||
| Upperbound of 95% confidence interval for alpha | 0.158 | ||||
| Treynor index (mean / b) | 0.642 | ||||
| Jensen alpha (a) | -0.086 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.096 | ||||
| Expected Shortfall on VaR | 0.116 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.065 | ||||
| Expected Shortfall on VaR | 0.119 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 31.000 | ||||
| Minimum | 0.858 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.173 | ||||
| Mean of quarter 1 | 0.935 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.036 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 7.000 | ||||
| Percentage of outliers low | 0.226 | ||||
| Mean of outliers low | 0.926 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.097 | ||||
| Mean of outliers high | 1.095 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -53.843 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -0.591 | ||||
| VaR(95%) (regression method) | 0.097 | ||||
| Expected Shortfall (regression method) | 0.120 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.283 | ||||
| Quartile 1 | 0.283 | ||||
| Median | 0.283 | ||||
| Quartile 3 | 0.283 | ||||
| Maximum | 0.283 | ||||
| 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 | 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) | -0.093 | ||||
| Compounded annual return (geometric extrapolation) | -0.101 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.359 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.877 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.144 | ||||
| SD | 0.114 | ||||
| Sharpe ratio (Glass type estimate) | -1.264 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.263 | ||||
| df | 891.000 | ||||
| t | -2.036 | ||||
| p | 0.979 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.483 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.045 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.482 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.045 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.689 | ||||
| Upside Potential Ratio | 3.662 | ||||
| Upside part of mean | 0.312 | ||||
| Downside part of mean | -0.457 | ||||
| Upside SD | 0.076 | ||||
| Downside SD | 0.085 | ||||
| N nonnegative terms | 94.000 | ||||
| N negative terms | 798.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 892.000 | ||||
| Mean of predictor | 0.319 | ||||
| Mean of criterion | -0.144 | ||||
| SD of predictor | 0.237 | ||||
| SD of criterion | 0.114 | ||||
| Covariance | 0.000 | ||||
| r | 0.012 | ||||
| b (slope, estimate of beta) | 0.006 | ||||
| a (intercept, estimate of alpha) | -0.146 | ||||
| Mean Square Error | 0.013 | ||||
| DF error | 890.000 | ||||
| t(b) | 0.354 | ||||
| p(b) | 0.362 | ||||
| t(a) | -2.055 | ||||
| p(a) | 0.980 | ||||
| Lowerbound of 95% confidence interval for beta | -0.026 | ||||
| Upperbound of 95% confidence interval for beta | 0.037 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.285 | ||||
| Upperbound of 95% confidence interval for alpha | -0.007 | ||||
| Treynor index (mean / b) | -25.287 | ||||
| Jensen alpha (a) | -0.146 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.151 | ||||
| SD | 0.114 | ||||
| Sharpe ratio (Glass type estimate) | -1.320 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.319 | ||||
| df | 891.000 | ||||
| t | -2.126 | ||||
| p | 0.983 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.539 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.101 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.538 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.100 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.743 | ||||
| Upside Potential Ratio | 3.583 | ||||
| Upside part of mean | 0.310 | ||||
| Downside part of mean | -0.460 | ||||
| Upside SD | 0.075 | ||||
| Downside SD | 0.086 | ||||
| N nonnegative terms | 94.000 | ||||
| N negative terms | 798.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 892.000 | ||||
| Mean of predictor | 0.291 | ||||
| Mean of criterion | -0.151 | ||||
| SD of predictor | 0.237 | ||||
| SD of criterion | 0.114 | ||||
| Covariance | 0.000 | ||||
| r | 0.012 | ||||
| b (slope, estimate of beta) | 0.006 | ||||
| a (intercept, estimate of alpha) | -0.152 | ||||
| Mean Square Error | 0.013 | ||||
| DF error | 890.000 | ||||
| t(b) | 0.363 | ||||
| p(b) | 0.358 | ||||
| t(a) | -2.144 | ||||
| p(a) | 0.984 | ||||
| Lowerbound of 95% confidence interval for beta | -0.026 | ||||
| Upperbound of 95% confidence interval for beta | 0.038 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.292 | ||||
| Upperbound of 95% confidence interval for alpha | -0.013 | ||||
| Treynor index (mean / b) | -25.671 | ||||
| Jensen alpha (a) | -0.152 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.010 | ||||
| Expected Shortfall on VaR | 0.013 | ||||
| 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 | 892.000 | ||||
| Minimum | 0.960 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.053 | ||||
| Mean of quarter 1 | 0.995 | ||||
| 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 | 159.000 | ||||
| Percentage of outliers low | 0.178 | ||||
| Mean of outliers low | 0.993 | ||||
| Number of outliers high | 120.000 | ||||
| Percentage of outliers high | 0.135 | ||||
| Mean of outliers high | 1.007 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.293 | ||||
| VaR(95%) (moments method) | 0.003 | ||||
| Expected Shortfall (moments method) | 0.006 | ||||
| Extreme Value Index (regression method) | -0.117 | ||||
| VaR(95%) (regression method) | 0.006 | ||||
| Expected Shortfall (regression method) | 0.011 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.288 | ||||
| Quartile 1 | 0.288 | ||||
| Median | 0.288 | ||||
| Quartile 3 | 0.288 | ||||
| Maximum | 0.288 | ||||
| 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 | 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) | -0.093 | ||||
| Compounded annual return (geometric extrapolation) | -0.101 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.351 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -7.756 | ||||
| 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 | -18.547 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.002 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 172.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 172.000 | ||||
| Mean of predictor | 0.635 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.291 | ||||
| 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) | -7936535306446244.000 | ||||
| Sharpe ratio (Hedges UMVUE) | -7901674975671223.000 | ||||
| df | 171.000 | ||||
| t | -5611977934314593.000 | ||||
| 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) | -8739115425704417.000 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -7064234525638030.000 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -18.547 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.002 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 172.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 172.000 | ||||
| Mean of predictor | 0.593 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.289 | ||||
| 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 | 170.000 | ||||
| t(b) | 0.000 | ||||
| p(b) | 0.500 | ||||
| t(a) | -5561565312878253.000 | ||||
| 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) | -609107397290696474299839088164864.000 | ||||
| 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 | 172.000 | ||||
| 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 | ||||
