Advanced Statistics: Secure Profits
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 | -0.029 | ||||
| SD | 0.105 | ||||
| Sharpe ratio (Glass type estimate) | -0.279 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.275 | ||||
| df | 51.000 | ||||
| t | -0.580 | ||||
| p | 0.718 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.221 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.666 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.218 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.668 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.415 | ||||
| Upside Potential Ratio | 1.197 | ||||
| Upside part of mean | 0.084 | ||||
| Downside part of mean | -0.113 | ||||
| Upside SD | 0.077 | ||||
| Downside SD | 0.070 | ||||
| N nonnegative terms | 7.000 | ||||
| N negative terms | 45.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 52.000 | ||||
| Mean of predictor | 0.376 | ||||
| Mean of criterion | -0.029 | ||||
| SD of predictor | 0.276 | ||||
| SD of criterion | 0.105 | ||||
| Covariance | 0.002 | ||||
| r | 0.055 | ||||
| b (slope, estimate of beta) | 0.021 | ||||
| a (intercept, estimate of alpha) | -0.037 | ||||
| Mean Square Error | 0.011 | ||||
| DF error | 50.000 | ||||
| t(b) | 0.386 | ||||
| p(b) | 0.351 | ||||
| t(a) | -0.677 | ||||
| p(a) | 0.749 | ||||
| Lowerbound of 95% confidence interval for beta | -0.087 | ||||
| Upperbound of 95% confidence interval for beta | 0.128 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.147 | ||||
| Upperbound of 95% confidence interval for alpha | 0.073 | ||||
| Treynor index (mean / b) | -1.413 | ||||
| Jensen alpha (a) | -0.037 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.034 | ||||
| SD | 0.104 | ||||
| Sharpe ratio (Glass type estimate) | -0.331 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.327 | ||||
| df | 51.000 | ||||
| t | -0.690 | ||||
| p | 0.753 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.274 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.614 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.270 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.617 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.474 | ||||
| Upside Potential Ratio | 1.117 | ||||
| Upside part of mean | 0.081 | ||||
| Downside part of mean | -0.116 | ||||
| Upside SD | 0.074 | ||||
| Downside SD | 0.073 | ||||
| N nonnegative terms | 7.000 | ||||
| N negative terms | 45.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 52.000 | ||||
| Mean of predictor | 0.334 | ||||
| Mean of criterion | -0.034 | ||||
| SD of predictor | 0.266 | ||||
| SD of criterion | 0.104 | ||||
| Covariance | 0.002 | ||||
| r | 0.057 | ||||
| b (slope, estimate of beta) | 0.022 | ||||
| a (intercept, estimate of alpha) | -0.042 | ||||
| Mean Square Error | 0.011 | ||||
| DF error | 50.000 | ||||
| t(b) | 0.405 | ||||
| p(b) | 0.344 | ||||
| t(a) | -0.782 | ||||
| p(a) | 0.781 | ||||
| Lowerbound of 95% confidence interval for beta | -0.088 | ||||
| Upperbound of 95% confidence interval for beta | 0.133 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.150 | ||||
| Upperbound of 95% confidence interval for alpha | 0.066 | ||||
| Treynor index (mean / b) | -1.543 | ||||
| Jensen alpha (a) | -0.042 | ||||
| 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 | 0.063 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.030 | ||||
| Expected Shortfall on VaR | 0.057 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 52.000 | ||||
| Minimum | 0.914 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.099 | ||||
| Mean of quarter 1 | 0.975 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.030 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 9.000 | ||||
| Percentage of outliers low | 0.173 | ||||
| Mean of outliers low | 0.964 | ||||
| Number of outliers high | 7.000 | ||||
| Percentage of outliers high | 0.135 | ||||
| Mean of outliers high | 1.056 | ||||
| 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) | -0.317 | ||||
| VaR(95%) (regression method) | 0.043 | ||||
| Expected Shortfall (regression method) | 0.063 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.015 | ||||
| Quartile 1 | 0.022 | ||||
| Median | 0.029 | ||||
| Quartile 3 | 0.094 | ||||
| Maximum | 0.160 | ||||
| Mean of quarter 1 | 0.015 | ||||
| Mean of quarter 2 | 0.029 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.160 | ||||
| Inter Quartile Range | 0.072 | ||||
| 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) | 0.010 | ||||
| Compounded annual return (geometric extrapolation) | 0.010 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.060 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.060 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.153 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.026 | ||||
| SD | 0.134 | ||||
| Sharpe ratio (Glass type estimate) | -0.190 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.190 | ||||
| df | 1140.000 | ||||
| t | -0.397 | ||||
| p | 0.506 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.130 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.749 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.129 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.749 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.274 | ||||
| Upside Potential Ratio | 4.481 | ||||
| Upside part of mean | 0.417 | ||||
| Downside part of mean | -0.442 | ||||
| Upside SD | 0.097 | ||||
| Downside SD | 0.093 | ||||
| N nonnegative terms | 167.000 | ||||
| N negative terms | 974.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1141.000 | ||||
| Mean of predictor | 0.398 | ||||
| Mean of criterion | -0.026 | ||||
| SD of predictor | 0.290 | ||||
| SD of criterion | 0.134 | ||||
| Covariance | 0.002 | ||||
| r | 0.040 | ||||
| b (slope, estimate of beta) | 0.018 | ||||
| a (intercept, estimate of alpha) | -0.033 | ||||
| Mean Square Error | 0.018 | ||||
| DF error | 1139.000 | ||||
| t(b) | 1.338 | ||||
| p(b) | 0.475 | ||||
| t(a) | -0.509 | ||||
| p(a) | 0.510 | ||||
| Lowerbound of 95% confidence interval for beta | -0.009 | ||||
| Upperbound of 95% confidence interval for beta | 0.045 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.159 | ||||
| Upperbound of 95% confidence interval for alpha | 0.094 | ||||
| Treynor index (mean / b) | -1.394 | ||||
| Jensen alpha (a) | -0.033 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.035 | ||||
| SD | 0.134 | ||||
| Sharpe ratio (Glass type estimate) | -0.257 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.257 | ||||
| df | 1140.000 | ||||
| t | -0.537 | ||||
| p | 0.508 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.197 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.682 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.197 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.682 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.365 | ||||
| Upside Potential Ratio | 4.362 | ||||
| Upside part of mean | 0.412 | ||||
| Downside part of mean | -0.447 | ||||
| Upside SD | 0.095 | ||||
| Downside SD | 0.094 | ||||
| N nonnegative terms | 167.000 | ||||
| N negative terms | 974.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1141.000 | ||||
| Mean of predictor | 0.356 | ||||
| Mean of criterion | -0.035 | ||||
| SD of predictor | 0.291 | ||||
| SD of criterion | 0.134 | ||||
| Covariance | 0.002 | ||||
| r | 0.040 | ||||
| b (slope, estimate of beta) | 0.019 | ||||
| a (intercept, estimate of alpha) | -0.041 | ||||
| Mean Square Error | 0.018 | ||||
| DF error | 1139.000 | ||||
| t(b) | 1.359 | ||||
| p(b) | 0.474 | ||||
| t(a) | -0.638 | ||||
| p(a) | 0.512 | ||||
| Lowerbound of 95% confidence interval for beta | -0.008 | ||||
| Upperbound of 95% confidence interval for beta | 0.045 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.167 | ||||
| Upperbound of 95% confidence interval for alpha | 0.085 | ||||
| Treynor index (mean / b) | -1.860 | ||||
| Jensen alpha (a) | -0.041 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.014 | ||||
| Expected Shortfall on VaR | 0.017 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.005 | ||||
| Expected Shortfall on VaR | 0.011 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1141.000 | ||||
| Minimum | 0.931 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.070 | ||||
| Mean of quarter 1 | 0.994 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.006 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 157.000 | ||||
| Percentage of outliers low | 0.138 | ||||
| Mean of outliers low | 0.989 | ||||
| Number of outliers high | 173.000 | ||||
| Percentage of outliers high | 0.152 | ||||
| Mean of outliers high | 1.011 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.172 | ||||
| VaR(95%) (moments method) | 0.003 | ||||
| Expected Shortfall (moments method) | 0.005 | ||||
| Extreme Value Index (regression method) | 0.026 | ||||
| VaR(95%) (regression method) | 0.007 | ||||
| Expected Shortfall (regression method) | 0.013 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 12.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.006 | ||||
| Median | 0.012 | ||||
| Quartile 3 | 0.044 | ||||
| Maximum | 0.286 | ||||
| Mean of quarter 1 | 0.003 | ||||
| Mean of quarter 2 | 0.007 | ||||
| Mean of quarter 3 | 0.033 | ||||
| Mean of quarter 4 | 0.127 | ||||
| Inter Quartile Range | 0.038 | ||||
| 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 | 0.083 | ||||
| Mean of outliers high | 0.286 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.863 | ||||
| VaR(95%) (moments method) | 0.138 | ||||
| Expected Shortfall (moments method) | 1.035 | ||||
| Extreme Value Index (regression method) | 4.869 | ||||
| VaR(95%) (regression method) | 0.441 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.010 | ||||
| Compounded annual return (geometric extrapolation) | 0.010 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.033 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.075 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.560 | ||||
| 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 | 1.117 | ||||
| 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 | 1.006 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.468 | ||||
| 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) | -8722573045777824.000 | ||||
| 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) | -163067372182906166923594290954240.000 | ||||
| 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 | ||||