Advanced Statistics: Lunar Cycles
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 | -0.074 | ||||
| SD | 0.039 | ||||
| Sharpe ratio (Glass type estimate) | -1.921 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.889 | ||||
| df | 45.000 | ||||
| t | -3.761 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.988 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.835 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.963 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.814 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.694 | ||||
| Upside Potential Ratio | 0.002 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.075 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.044 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 45.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 46.000 | ||||
| Mean of predictor | 0.473 | ||||
| Mean of criterion | -0.074 | ||||
| SD of predictor | 0.275 | ||||
| SD of criterion | 0.039 | ||||
| Covariance | -0.000 | ||||
| r | -0.025 | ||||
| b (slope, estimate of beta) | -0.003 | ||||
| a (intercept, estimate of alpha) | -0.073 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 44.000 | ||||
| t(b) | -0.164 | ||||
| p(b) | 0.565 | ||||
| t(a) | -3.252 | ||||
| p(a) | 0.999 | ||||
| Lowerbound of 95% confidence interval for beta | -0.046 | ||||
| Upperbound of 95% confidence interval for beta | 0.039 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.118 | ||||
| Upperbound of 95% confidence interval for alpha | -0.028 | ||||
| Treynor index (mean / b) | 21.389 | ||||
| Jensen alpha (a) | -0.073 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.075 | ||||
| SD | 0.040 | ||||
| Sharpe ratio (Glass type estimate) | -1.881 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.850 | ||||
| df | 45.000 | ||||
| t | -3.683 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.946 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.799 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.921 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.778 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.667 | ||||
| Upside Potential Ratio | 0.002 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.075 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.045 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 45.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 46.000 | ||||
| Mean of predictor | 0.428 | ||||
| Mean of criterion | -0.075 | ||||
| SD of predictor | 0.262 | ||||
| SD of criterion | 0.040 | ||||
| Covariance | -0.000 | ||||
| r | -0.033 | ||||
| b (slope, estimate of beta) | -0.005 | ||||
| a (intercept, estimate of alpha) | -0.073 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 44.000 | ||||
| t(b) | -0.220 | ||||
| p(b) | 0.587 | ||||
| t(a) | -3.194 | ||||
| p(a) | 0.999 | ||||
| Lowerbound of 95% confidence interval for beta | -0.051 | ||||
| Upperbound of 95% confidence interval for beta | 0.041 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.119 | ||||
| Upperbound of 95% confidence interval for alpha | -0.027 | ||||
| Treynor index (mean / b) | 14.852 | ||||
| Jensen alpha (a) | -0.073 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.025 | ||||
| Expected Shortfall on VaR | 0.030 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.021 | ||||
| Expected Shortfall on VaR | 0.038 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 46.000 | ||||
| Minimum | 0.932 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.004 | ||||
| Mean of quarter 1 | 0.990 | ||||
| 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 | 4.000 | ||||
| Percentage of outliers low | 0.087 | ||||
| Mean of outliers low | 0.970 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.022 | ||||
| Mean of outliers high | 1.004 | ||||
| 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) | 0.360 | ||||
| VaR(95%) (regression method) | 0.019 | ||||
| Expected Shortfall (regression method) | 0.064 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.113 | ||||
| Quartile 1 | 0.113 | ||||
| Median | 0.113 | ||||
| Quartile 3 | 0.113 | ||||
| Maximum | 0.113 | ||||
| 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) | -0.029 | ||||
| Compounded annual return (geometric extrapolation) | -0.031 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.273 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.037 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.074 | ||||
| SD | 0.056 | ||||
| Sharpe ratio (Glass type estimate) | -1.318 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.317 | ||||
| df | 1007.000 | ||||
| t | -2.585 | ||||
| p | 0.552 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.318 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.316 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.318 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.316 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.691 | ||||
| Upside Potential Ratio | 1.776 | ||||
| Upside part of mean | 0.077 | ||||
| Downside part of mean | -0.151 | ||||
| Upside SD | 0.035 | ||||
| Downside SD | 0.044 | ||||
| N nonnegative terms | 28.000 | ||||
| N negative terms | 980.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1008.000 | ||||
| Mean of predictor | 0.514 | ||||
| Mean of criterion | -0.074 | ||||
| SD of predictor | 0.326 | ||||
| SD of criterion | 0.056 | ||||
| Covariance | 0.000 | ||||
| r | 0.006 | ||||
| b (slope, estimate of beta) | 0.001 | ||||
| a (intercept, estimate of alpha) | -0.074 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 1006.000 | ||||
| t(b) | 0.192 | ||||
| p(b) | 0.497 | ||||
| t(a) | -2.590 | ||||
| p(a) | 0.541 | ||||
| Lowerbound of 95% confidence interval for beta | -0.010 | ||||
| Upperbound of 95% confidence interval for beta | 0.012 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.130 | ||||
| Upperbound of 95% confidence interval for alpha | -0.018 | ||||
| Treynor index (mean / b) | -70.916 | ||||
| Jensen alpha (a) | -0.074 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.075 | ||||
| SD | 0.056 | ||||
| Sharpe ratio (Glass type estimate) | -1.342 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.341 | ||||
| df | 1007.000 | ||||
| t | -2.631 | ||||
| p | 0.553 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.342 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.340 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.342 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.340 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.706 | ||||
| Upside Potential Ratio | 1.741 | ||||
| Upside part of mean | 0.077 | ||||
| Downside part of mean | -0.152 | ||||
| Upside SD | 0.035 | ||||
| Downside SD | 0.044 | ||||
| N nonnegative terms | 28.000 | ||||
| N negative terms | 980.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1008.000 | ||||
| Mean of predictor | 0.460 | ||||
| Mean of criterion | -0.075 | ||||
| SD of predictor | 0.328 | ||||
| SD of criterion | 0.056 | ||||
| Covariance | 0.000 | ||||
| r | 0.005 | ||||
| b (slope, estimate of beta) | 0.001 | ||||
| a (intercept, estimate of alpha) | -0.076 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 1006.000 | ||||
| t(b) | 0.165 | ||||
| p(b) | 0.497 | ||||
| t(a) | -2.635 | ||||
| p(a) | 0.541 | ||||
| Lowerbound of 95% confidence interval for beta | -0.010 | ||||
| Upperbound of 95% confidence interval for beta | 0.011 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.132 | ||||
| Upperbound of 95% confidence interval for alpha | -0.019 | ||||
| Treynor index (mean / b) | -84.481 | ||||
| Jensen alpha (a) | -0.076 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.006 | ||||
| Expected Shortfall on VaR | 0.007 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.004 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1008.000 | ||||
| Minimum | 0.963 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.033 | ||||
| Mean of quarter 1 | 0.998 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.001 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 44.000 | ||||
| Percentage of outliers low | 0.044 | ||||
| Mean of outliers low | 0.991 | ||||
| Number of outliers high | 29.000 | ||||
| Percentage of outliers high | 0.029 | ||||
| Mean of outliers high | 1.010 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.257 | ||||
| VaR(95%) (moments method) | -0.000 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -0.058 | ||||
| VaR(95%) (regression method) | -0.000 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.015 | ||||
| Quartile 1 | 0.044 | ||||
| Median | 0.073 | ||||
| Quartile 3 | 0.102 | ||||
| Maximum | 0.130 | ||||
| Mean of quarter 1 | 0.015 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.130 | ||||
| Inter Quartile Range | 0.058 | ||||
| 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) | -0.029 | ||||
| Compounded annual return (geometric extrapolation) | -0.031 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.235 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.235 | ||||
| Compounded annual return / Expected Shortfall lognormal | -4.141 | ||||
| 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 | 1.193 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.505 | ||||
| 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 | 1.062 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.509 | ||||
| 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) | -8726935956943485.000 | ||||
| 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) | 469698078787548017939096627314688.000 | ||||
| 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 | ||||