Advanced Statistics: Ahmad
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 | -0.024 | ||||
| SD | 0.068 | ||||
| Sharpe ratio (Glass type estimate) | -0.349 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.341 | ||||
| df | 32.000 | ||||
| t | -0.579 | ||||
| p | 0.717 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.531 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.839 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.526 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.844 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.566 | ||||
| Upside Potential Ratio | 0.932 | ||||
| Upside part of mean | 0.039 | ||||
| Downside part of mean | -0.063 | ||||
| Upside SD | 0.053 | ||||
| Downside SD | 0.042 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 30.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 33.000 | ||||
| Mean of predictor | 0.597 | ||||
| Mean of criterion | -0.024 | ||||
| SD of predictor | 0.330 | ||||
| SD of criterion | 0.068 | ||||
| Covariance | 0.002 | ||||
| r | 0.092 | ||||
| b (slope, estimate of beta) | 0.019 | ||||
| a (intercept, estimate of alpha) | -0.035 | ||||
| Mean Square Error | 0.005 | ||||
| DF error | 31.000 | ||||
| t(b) | 0.517 | ||||
| p(b) | 0.305 | ||||
| t(a) | -0.748 | ||||
| p(a) | 0.770 | ||||
| Lowerbound of 95% confidence interval for beta | -0.056 | ||||
| Upperbound of 95% confidence interval for beta | 0.095 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.132 | ||||
| Upperbound of 95% confidence interval for alpha | 0.061 | ||||
| Treynor index (mean / b) | -1.245 | ||||
| Jensen alpha (a) | -0.035 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.026 | ||||
| SD | 0.067 | ||||
| Sharpe ratio (Glass type estimate) | -0.387 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.377 | ||||
| df | 32.000 | ||||
| t | -0.641 | ||||
| p | 0.737 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.569 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.802 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.563 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.808 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.600 | ||||
| Upside Potential Ratio | 0.873 | ||||
| Upside part of mean | 0.038 | ||||
| Downside part of mean | -0.064 | ||||
| Upside SD | 0.051 | ||||
| Downside SD | 0.043 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 30.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 33.000 | ||||
| Mean of predictor | 0.534 | ||||
| Mean of criterion | -0.026 | ||||
| SD of predictor | 0.309 | ||||
| SD of criterion | 0.067 | ||||
| Covariance | 0.002 | ||||
| r | 0.105 | ||||
| b (slope, estimate of beta) | 0.023 | ||||
| a (intercept, estimate of alpha) | -0.038 | ||||
| Mean Square Error | 0.005 | ||||
| DF error | 31.000 | ||||
| t(b) | 0.589 | ||||
| p(b) | 0.280 | ||||
| t(a) | -0.832 | ||||
| p(a) | 0.794 | ||||
| Lowerbound of 95% confidence interval for beta | -0.056 | ||||
| Upperbound of 95% confidence interval for beta | 0.102 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.132 | ||||
| Upperbound of 95% confidence interval for alpha | 0.055 | ||||
| Treynor index (mean / b) | -1.134 | ||||
| Jensen alpha (a) | -0.038 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.034 | ||||
| Expected Shortfall on VaR | 0.041 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.017 | ||||
| Expected Shortfall on VaR | 0.033 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 33.000 | ||||
| Minimum | 0.937 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.089 | ||||
| Mean of quarter 1 | 0.993 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.015 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.030 | ||||
| Mean of outliers low | 0.937 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.091 | ||||
| Mean of outliers high | 1.040 | ||||
| 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 | 1.000 | ||||
| Minimum | 0.063 | ||||
| Quartile 1 | 0.063 | ||||
| Median | 0.063 | ||||
| Quartile 3 | 0.063 | ||||
| Maximum | 0.063 | ||||
| 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) | 0.018 | ||||
| Compounded annual return (geometric extrapolation) | 0.018 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.287 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.440 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.023 | ||||
| SD | 0.078 | ||||
| Sharpe ratio (Glass type estimate) | -0.296 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.296 | ||||
| df | 724.000 | ||||
| t | -0.492 | ||||
| p | 0.689 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.474 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.882 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.474 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.883 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.451 | ||||
| Upside Potential Ratio | 3.015 | ||||
| Upside part of mean | 0.154 | ||||
| Downside part of mean | -0.177 | ||||
| Upside SD | 0.059 | ||||
| Downside SD | 0.051 | ||||
| N nonnegative terms | 32.000 | ||||
| N negative terms | 693.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 725.000 | ||||
| Mean of predictor | 0.635 | ||||
| Mean of criterion | -0.023 | ||||
| SD of predictor | 0.343 | ||||
| SD of criterion | 0.078 | ||||
| Covariance | 0.003 | ||||
| r | 0.097 | ||||
| b (slope, estimate of beta) | 0.022 | ||||
| a (intercept, estimate of alpha) | -0.037 | ||||
| Mean Square Error | 0.006 | ||||
| DF error | 723.000 | ||||
| t(b) | 2.608 | ||||
| p(b) | 0.005 | ||||
| t(a) | -0.788 | ||||
| p(a) | 0.785 | ||||
| Lowerbound of 95% confidence interval for beta | 0.005 | ||||
| Upperbound of 95% confidence interval for beta | 0.039 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.129 | ||||
| Upperbound of 95% confidence interval for alpha | 0.055 | ||||
| Treynor index (mean / b) | -1.051 | ||||
| Jensen alpha (a) | -0.037 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.026 | ||||
| SD | 0.078 | ||||
| Sharpe ratio (Glass type estimate) | -0.336 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.335 | ||||
| df | 724.000 | ||||
| t | -0.558 | ||||
| p | 0.712 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.514 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.843 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.514 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.843 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.504 | ||||
| Upside Potential Ratio | 2.947 | ||||
| Upside part of mean | 0.153 | ||||
| Downside part of mean | -0.179 | ||||
| Upside SD | 0.058 | ||||
| Downside SD | 0.052 | ||||
| N nonnegative terms | 32.000 | ||||
| N negative terms | 693.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 725.000 | ||||
| Mean of predictor | 0.575 | ||||
| Mean of criterion | -0.026 | ||||
| SD of predictor | 0.349 | ||||
| SD of criterion | 0.078 | ||||
| Covariance | 0.003 | ||||
| r | 0.096 | ||||
| b (slope, estimate of beta) | 0.021 | ||||
| a (intercept, estimate of alpha) | -0.038 | ||||
| Mean Square Error | 0.006 | ||||
| DF error | 723.000 | ||||
| t(b) | 2.585 | ||||
| p(b) | 0.005 | ||||
| t(a) | -0.819 | ||||
| p(a) | 0.794 | ||||
| Lowerbound of 95% confidence interval for beta | 0.005 | ||||
| Upperbound of 95% confidence interval for beta | 0.038 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.130 | ||||
| Upperbound of 95% confidence interval for alpha | 0.054 | ||||
| Treynor index (mean / b) | -1.225 | ||||
| Jensen alpha (a) | -0.038 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.008 | ||||
| Expected Shortfall on VaR | 0.010 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.005 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 725.000 | ||||
| Minimum | 0.967 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.038 | ||||
| Mean of quarter 1 | 0.998 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.002 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 30.000 | ||||
| Percentage of outliers low | 0.041 | ||||
| Mean of outliers low | 0.988 | ||||
| Number of outliers high | 32.000 | ||||
| Percentage of outliers high | 0.044 | ||||
| Mean of outliers high | 1.014 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.243 | ||||
| VaR(95%) (moments method) | -0.000 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -0.451 | ||||
| VaR(95%) (regression method) | -0.001 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.071 | ||||
| Quartile 1 | 0.075 | ||||
| Median | 0.078 | ||||
| Quartile 3 | 0.081 | ||||
| Maximum | 0.085 | ||||
| Mean of quarter 1 | 0.071 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.085 | ||||
| Inter Quartile Range | 0.007 | ||||
| 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) | 0.018 | ||||
| Compounded annual return (geometric extrapolation) | 0.018 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.213 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.213 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.814 | ||||
| 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 | 1.041 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.481 | ||||
| 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 | 0.923 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.484 | ||||
| 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) | -8738973496772666.000 | ||||
| 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) | -154712747549566630121046947135488.000 | ||||
| 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 | ||||