Advanced Statistics: Sleep Well
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 | -0.031 | ||||
| SD | 0.164 | ||||
| Sharpe ratio (Glass type estimate) | -0.191 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.190 | ||||
| df | 99.000 | ||||
| t | -0.552 | ||||
| p | 0.709 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.870 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.489 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.869 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.490 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.310 | ||||
| Upside Potential Ratio | 0.631 | ||||
| Upside part of mean | 0.064 | ||||
| Downside part of mean | -0.095 | ||||
| Upside SD | 0.128 | ||||
| Downside SD | 0.101 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 95.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 100.000 | ||||
| Mean of predictor | 0.105 | ||||
| Mean of criterion | -0.031 | ||||
| SD of predictor | 0.243 | ||||
| SD of criterion | 0.164 | ||||
| Covariance | 0.005 | ||||
| r | 0.126 | ||||
| b (slope, estimate of beta) | 0.084 | ||||
| a (intercept, estimate of alpha) | -0.040 | ||||
| Mean Square Error | 0.027 | ||||
| DF error | 98.000 | ||||
| t(b) | 1.254 | ||||
| p(b) | 0.106 | ||||
| t(a) | -0.705 | ||||
| p(a) | 0.759 | ||||
| Lowerbound of 95% confidence interval for beta | -0.049 | ||||
| Upperbound of 95% confidence interval for beta | 0.218 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.153 | ||||
| Upperbound of 95% confidence interval for alpha | 0.073 | ||||
| Treynor index (mean / b) | -0.370 | ||||
| Jensen alpha (a) | -0.040 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.162 | ||||
| Sharpe ratio (Glass type estimate) | -0.272 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.270 | ||||
| df | 99.000 | ||||
| t | -0.786 | ||||
| p | 0.783 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.952 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.408 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.950 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.410 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.380 | ||||
| Upside Potential Ratio | 0.486 | ||||
| Upside part of mean | 0.056 | ||||
| Downside part of mean | -0.101 | ||||
| Upside SD | 0.113 | ||||
| Downside SD | 0.116 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 95.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 100.000 | ||||
| Mean of predictor | 0.076 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.243 | ||||
| SD of criterion | 0.162 | ||||
| Covariance | 0.006 | ||||
| r | 0.162 | ||||
| b (slope, estimate of beta) | 0.109 | ||||
| a (intercept, estimate of alpha) | -0.052 | ||||
| Mean Square Error | 0.026 | ||||
| DF error | 98.000 | ||||
| t(b) | 1.629 | ||||
| p(b) | 0.053 | ||||
| t(a) | -0.936 | ||||
| p(a) | 0.824 | ||||
| Lowerbound of 95% confidence interval for beta | -0.024 | ||||
| Upperbound of 95% confidence interval for beta | 0.241 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.164 | ||||
| Upperbound of 95% confidence interval for alpha | 0.059 | ||||
| Treynor index (mean / b) | -0.407 | ||||
| Jensen alpha (a) | -0.052 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.078 | ||||
| Expected Shortfall on VaR | 0.095 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.027 | ||||
| Expected Shortfall on VaR | 0.057 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 100.000 | ||||
| Minimum | 0.726 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.307 | ||||
| Mean of quarter 1 | 0.982 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.022 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 16.000 | ||||
| Percentage of outliers low | 0.160 | ||||
| Mean of outliers low | 0.972 | ||||
| Number of outliers high | 15.000 | ||||
| Percentage of outliers high | 0.150 | ||||
| Mean of outliers high | 1.037 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -4.037 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | 0.000 | ||||
| Extreme Value Index (regression method) | 0.545 | ||||
| VaR(95%) (regression method) | 0.010 | ||||
| Expected Shortfall (regression method) | 0.049 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.041 | ||||
| Quartile 1 | 0.117 | ||||
| Median | 0.192 | ||||
| Quartile 3 | 0.268 | ||||
| Maximum | 0.344 | ||||
| Mean of quarter 1 | 0.041 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.344 | ||||
| Inter Quartile Range | 0.152 | ||||
| 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) | -0.000 | ||||
| Compounded annual return (geometric extrapolation) | -0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.001 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.001 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.002 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.089 | ||||
| SD | 0.532 | ||||
| Sharpe ratio (Glass type estimate) | 0.168 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.168 | ||||
| df | 2189.000 | ||||
| t | 0.486 | ||||
| p | 0.313 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.510 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.846 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.510 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.846 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.285 | ||||
| Upside Potential Ratio | 1.738 | ||||
| Upside part of mean | 0.544 | ||||
| Downside part of mean | -0.455 | ||||
| Upside SD | 0.430 | ||||
| Downside SD | 0.313 | ||||
| N nonnegative terms | 126.000 | ||||
| N negative terms | 2064.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2190.000 | ||||
| Mean of predictor | 0.295 | ||||
| Mean of criterion | 0.089 | ||||
| SD of predictor | 0.574 | ||||
| SD of criterion | 0.532 | ||||
| Covariance | 0.105 | ||||
| r | 0.344 | ||||
| b (slope, estimate of beta) | 0.319 | ||||
| a (intercept, estimate of alpha) | -0.005 | ||||
| Mean Square Error | 0.249 | ||||
| DF error | 2188.000 | ||||
| t(b) | 17.164 | ||||
| p(b) | 0.000 | ||||
| t(a) | -0.028 | ||||
| p(a) | 0.511 | ||||
| Lowerbound of 95% confidence interval for beta | 0.283 | ||||
| Upperbound of 95% confidence interval for beta | 0.355 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.344 | ||||
| Upperbound of 95% confidence interval for alpha | 0.334 | ||||
| Treynor index (mean / b) | 0.280 | ||||
| Jensen alpha (a) | -0.005 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.516 | ||||
| Sharpe ratio (Glass type estimate) | -0.086 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.086 | ||||
| df | 2189.000 | ||||
| t | -0.248 | ||||
| p | 0.598 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.764 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.592 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.764 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.592 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.118 | ||||
| Upside Potential Ratio | 1.258 | ||||
| Upside part of mean | 0.473 | ||||
| Downside part of mean | -0.517 | ||||
| Upside SD | 0.353 | ||||
| Downside SD | 0.376 | ||||
| N nonnegative terms | 126.000 | ||||
| N negative terms | 2064.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2190.000 | ||||
| Mean of predictor | 0.134 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.568 | ||||
| SD of criterion | 0.516 | ||||
| Covariance | 0.102 | ||||
| r | 0.349 | ||||
| b (slope, estimate of beta) | 0.317 | ||||
| a (intercept, estimate of alpha) | -0.087 | ||||
| Mean Square Error | 0.234 | ||||
| DF error | 2188.000 | ||||
| t(b) | 17.430 | ||||
| p(b) | 0.000 | ||||
| t(a) | -0.518 | ||||
| p(a) | 0.698 | ||||
| Lowerbound of 95% confidence interval for beta | 0.282 | ||||
| Upperbound of 95% confidence interval for beta | 0.353 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.415 | ||||
| Upperbound of 95% confidence interval for alpha | 0.242 | ||||
| Treynor index (mean / b) | -0.139 | ||||
| Jensen alpha (a) | -0.087 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.051 | ||||
| Expected Shortfall on VaR | 0.064 | ||||
| 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 | 2190.000 | ||||
| Minimum | 0.653 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.544 | ||||
| Mean of quarter 1 | 0.994 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.008 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 172.000 | ||||
| Percentage of outliers low | 0.079 | ||||
| Mean of outliers low | 0.980 | ||||
| Number of outliers high | 189.000 | ||||
| Percentage of outliers high | 0.086 | ||||
| Mean of outliers high | 1.024 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.476 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| 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 | 10.000 | ||||
| Minimum | 0.008 | ||||
| Quartile 1 | 0.111 | ||||
| Median | 0.321 | ||||
| Quartile 3 | 0.346 | ||||
| Maximum | 0.381 | ||||
| Mean of quarter 1 | 0.026 | ||||
| Mean of quarter 2 | 0.316 | ||||
| Mean of quarter 3 | 0.336 | ||||
| Mean of quarter 4 | 0.361 | ||||
| Inter Quartile Range | 0.235 | ||||
| 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) | -1.134 | ||||
| VaR(95%) (moments method) | 0.379 | ||||
| Expected Shortfall (moments method) | 0.383 | ||||
| Extreme Value Index (regression method) | 0.318 | ||||
| VaR(95%) (regression method) | 0.386 | ||||
| Expected Shortfall (regression method) | 0.430 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.000 | ||||
| Compounded annual return (geometric extrapolation) | -0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.001 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.001 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.003 | ||||
| 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 | 1.915 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.874 | ||||
| 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 | 1.591 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.770 | ||||
| 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) | -8728446793158445.000 | ||||
| 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) | -998544567910349130416120794185728.000 | ||||
| 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 | ||||