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 | -0.078 | ||||
| SD | 0.084 | ||||
| Sharpe ratio (Glass type estimate) | -0.925 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.913 | ||||
| df | 58.000 | ||||
| t | -2.050 | ||||
| p | 0.978 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.820 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.021 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.812 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.013 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.085 | ||||
| Upside Potential Ratio | 0.413 | ||||
| Upside part of mean | 0.030 | ||||
| Downside part of mean | -0.107 | ||||
| Upside SD | 0.048 | ||||
| Downside SD | 0.071 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 56.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 59.000 | ||||
| Mean of predictor | 0.437 | ||||
| Mean of criterion | -0.078 | ||||
| SD of predictor | 0.231 | ||||
| SD of criterion | 0.084 | ||||
| Covariance | -0.002 | ||||
| r | -0.117 | ||||
| b (slope, estimate of beta) | -0.042 | ||||
| a (intercept, estimate of alpha) | -0.059 | ||||
| Mean Square Error | 0.007 | ||||
| DF error | 57.000 | ||||
| t(b) | -0.888 | ||||
| p(b) | 0.811 | ||||
| t(a) | -1.366 | ||||
| p(a) | 0.911 | ||||
| Lowerbound of 95% confidence interval for beta | -0.138 | ||||
| Upperbound of 95% confidence interval for beta | 0.053 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.146 | ||||
| Upperbound of 95% confidence interval for alpha | 0.028 | ||||
| Treynor index (mean / b) | 1.833 | ||||
| Jensen alpha (a) | -0.059 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.081 | ||||
| SD | 0.085 | ||||
| Sharpe ratio (Glass type estimate) | -0.955 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.942 | ||||
| df | 58.000 | ||||
| t | -2.117 | ||||
| p | 0.981 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.852 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.050 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.843 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.042 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.091 | ||||
| Upside Potential Ratio | 0.382 | ||||
| Upside part of mean | 0.028 | ||||
| Downside part of mean | -0.109 | ||||
| Upside SD | 0.046 | ||||
| Downside SD | 0.074 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 56.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 59.000 | ||||
| Mean of predictor | 0.403 | ||||
| Mean of criterion | -0.081 | ||||
| SD of predictor | 0.225 | ||||
| SD of criterion | 0.085 | ||||
| Covariance | -0.002 | ||||
| r | -0.116 | ||||
| b (slope, estimate of beta) | -0.044 | ||||
| a (intercept, estimate of alpha) | -0.063 | ||||
| Mean Square Error | 0.007 | ||||
| DF error | 57.000 | ||||
| t(b) | -0.881 | ||||
| p(b) | 0.809 | ||||
| t(a) | -1.465 | ||||
| p(a) | 0.926 | ||||
| Lowerbound of 95% confidence interval for beta | -0.143 | ||||
| Upperbound of 95% confidence interval for beta | 0.056 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.150 | ||||
| Upperbound of 95% confidence interval for alpha | 0.023 | ||||
| Treynor index (mean / b) | 1.851 | ||||
| Jensen alpha (a) | -0.063 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.046 | ||||
| Expected Shortfall on VaR | 0.056 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.030 | ||||
| Expected Shortfall on VaR | 0.058 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 59.000 | ||||
| Minimum | 0.898 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.099 | ||||
| Mean of quarter 1 | 0.979 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.010 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 8.000 | ||||
| Percentage of outliers low | 0.136 | ||||
| Mean of outliers low | 0.960 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.102 | ||||
| Mean of outliers high | 1.026 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -68.121 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -0.100 | ||||
| VaR(95%) (regression method) | 0.029 | ||||
| Expected Shortfall (regression method) | 0.059 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.064 | ||||
| Quartile 1 | 0.102 | ||||
| Median | 0.139 | ||||
| Quartile 3 | 0.177 | ||||
| Maximum | 0.215 | ||||
| Mean of quarter 1 | 0.064 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.215 | ||||
| Inter Quartile Range | 0.075 | ||||
| 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) | -0.034 | ||||
| Compounded annual return (geometric extrapolation) | -0.036 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.169 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.169 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.653 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.043 | ||||
| SD | 0.278 | ||||
| Sharpe ratio (Glass type estimate) | -0.153 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.153 | ||||
| df | 1299.000 | ||||
| t | -0.341 | ||||
| p | 0.506 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.033 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.727 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.033 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.727 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.235 | ||||
| Upside Potential Ratio | 2.683 | ||||
| Upside part of mean | 0.487 | ||||
| Downside part of mean | -0.530 | ||||
| Upside SD | 0.211 | ||||
| Downside SD | 0.182 | ||||
| N nonnegative terms | 87.000 | ||||
| N negative terms | 1213.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1300.000 | ||||
| Mean of predictor | 0.486 | ||||
| Mean of criterion | -0.043 | ||||
| SD of predictor | 0.359 | ||||
| SD of criterion | 0.278 | ||||
| Covariance | -0.013 | ||||
| r | -0.127 | ||||
| b (slope, estimate of beta) | -0.099 | ||||
| a (intercept, estimate of alpha) | 0.005 | ||||
| Mean Square Error | 0.076 | ||||
| DF error | 1298.000 | ||||
| t(b) | -4.631 | ||||
| p(b) | 0.564 | ||||
| t(a) | 0.044 | ||||
| p(a) | 0.499 | ||||
| Lowerbound of 95% confidence interval for beta | -0.141 | ||||
| Upperbound of 95% confidence interval for beta | -0.057 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.239 | ||||
| Upperbound of 95% confidence interval for alpha | 0.250 | ||||
| Treynor index (mean / b) | 0.431 | ||||
| Jensen alpha (a) | 0.005 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.081 | ||||
| SD | 0.275 | ||||
| Sharpe ratio (Glass type estimate) | -0.293 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.293 | ||||
| df | 1299.000 | ||||
| t | -0.653 | ||||
| p | 0.512 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.173 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.587 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.173 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.587 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.419 | ||||
| Upside Potential Ratio | 2.425 | ||||
| Upside part of mean | 0.467 | ||||
| Downside part of mean | -0.548 | ||||
| Upside SD | 0.196 | ||||
| Downside SD | 0.193 | ||||
| N nonnegative terms | 87.000 | ||||
| N negative terms | 1213.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1300.000 | ||||
| Mean of predictor | 0.422 | ||||
| Mean of criterion | -0.081 | ||||
| SD of predictor | 0.358 | ||||
| SD of criterion | 0.275 | ||||
| Covariance | -0.013 | ||||
| r | -0.127 | ||||
| b (slope, estimate of beta) | -0.098 | ||||
| a (intercept, estimate of alpha) | -0.039 | ||||
| Mean Square Error | 0.075 | ||||
| DF error | 1298.000 | ||||
| t(b) | -4.620 | ||||
| p(b) | 0.564 | ||||
| t(a) | -0.321 | ||||
| p(a) | 0.504 | ||||
| Lowerbound of 95% confidence interval for beta | -0.139 | ||||
| Upperbound of 95% confidence interval for beta | -0.056 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.280 | ||||
| Upperbound of 95% confidence interval for alpha | 0.202 | ||||
| Treynor index (mean / b) | 0.825 | ||||
| Jensen alpha (a) | -0.039 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.028 | ||||
| Expected Shortfall on VaR | 0.035 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.007 | ||||
| Expected Shortfall on VaR | 0.015 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1300.000 | ||||
| Minimum | 0.800 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.246 | ||||
| Mean of quarter 1 | 0.993 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.007 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 111.000 | ||||
| Percentage of outliers low | 0.085 | ||||
| Mean of outliers low | 0.978 | ||||
| Number of outliers high | 106.000 | ||||
| Percentage of outliers high | 0.082 | ||||
| Mean of outliers high | 1.023 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.139 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.005 | ||||
| Extreme Value Index (regression method) | 0.314 | ||||
| VaR(95%) (regression method) | 0.005 | ||||
| Expected Shortfall (regression method) | 0.025 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.284 | ||||
| Quartile 1 | 0.284 | ||||
| Median | 0.284 | ||||
| Quartile 3 | 0.284 | ||||
| Maximum | 0.284 | ||||
| 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) | -0.034 | ||||
| Compounded annual return (geometric extrapolation) | -0.036 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.127 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.036 | ||||
| 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 | 1.352 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.355 | ||||
| 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 | 1.286 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.355 | ||||
| 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) | -8586277253784857.000 | ||||
| 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) | -94049922565840839364207324430336.000 | ||||
| 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 | ||||