Advanced Statistics: Small Cap Emerging Value timer
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 | -0.020 | ||||
| SD | 0.057 | ||||
| Sharpe ratio (Glass type estimate) | -0.359 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.353 | ||||
| df | 42.000 | ||||
| t | -0.680 | ||||
| p | 0.750 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.395 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.681 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.391 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.685 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.782 | ||||
| Upside Potential Ratio | 1.314 | ||||
| Upside part of mean | 0.034 | ||||
| Downside part of mean | -0.054 | ||||
| Upside SD | 0.050 | ||||
| Downside SD | 0.026 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 41.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 43.000 | ||||
| Mean of predictor | 0.452 | ||||
| Mean of criterion | -0.020 | ||||
| SD of predictor | 0.277 | ||||
| SD of criterion | 0.057 | ||||
| Covariance | -0.003 | ||||
| r | -0.166 | ||||
| b (slope, estimate of beta) | -0.034 | ||||
| a (intercept, estimate of alpha) | -0.005 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 41.000 | ||||
| t(b) | -1.079 | ||||
| p(b) | 0.856 | ||||
| t(a) | -0.151 | ||||
| p(a) | 0.560 | ||||
| Lowerbound of 95% confidence interval for beta | -0.097 | ||||
| Upperbound of 95% confidence interval for beta | 0.030 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.072 | ||||
| Upperbound of 95% confidence interval for alpha | 0.062 | ||||
| Treynor index (mean / b) | 0.599 | ||||
| Jensen alpha (a) | -0.005 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.022 | ||||
| SD | 0.055 | ||||
| Sharpe ratio (Glass type estimate) | -0.397 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.390 | ||||
| df | 42.000 | ||||
| t | -0.751 | ||||
| p | 0.772 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.433 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.644 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.429 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.649 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.826 | ||||
| Upside Potential Ratio | 1.248 | ||||
| Upside part of mean | 0.033 | ||||
| Downside part of mean | -0.055 | ||||
| Upside SD | 0.048 | ||||
| Downside SD | 0.026 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 41.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 43.000 | ||||
| Mean of predictor | 0.408 | ||||
| Mean of criterion | -0.022 | ||||
| SD of predictor | 0.263 | ||||
| SD of criterion | 0.055 | ||||
| Covariance | -0.002 | ||||
| r | -0.168 | ||||
| b (slope, estimate of beta) | -0.035 | ||||
| a (intercept, estimate of alpha) | -0.008 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 41.000 | ||||
| t(b) | -1.091 | ||||
| p(b) | 0.859 | ||||
| t(a) | -0.237 | ||||
| p(a) | 0.593 | ||||
| Lowerbound of 95% confidence interval for beta | -0.100 | ||||
| Upperbound of 95% confidence interval for beta | 0.030 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.071 | ||||
| Upperbound of 95% confidence interval for alpha | 0.056 | ||||
| Treynor index (mean / b) | 0.623 | ||||
| Jensen alpha (a) | -0.008 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.027 | ||||
| Expected Shortfall on VaR | 0.034 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.015 | ||||
| Expected Shortfall on VaR | 0.023 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 43.000 | ||||
| Minimum | 0.961 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.091 | ||||
| Mean of quarter 1 | 0.996 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.012 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.047 | ||||
| Mean of outliers low | 0.978 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.070 | ||||
| Mean of outliers high | 1.043 | ||||
| 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) | 1.521 | ||||
| VaR(95%) (regression method) | 0.002 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.006 | ||||
| Quartile 1 | 0.014 | ||||
| Median | 0.022 | ||||
| Quartile 3 | 0.031 | ||||
| Maximum | 0.039 | ||||
| Mean of quarter 1 | 0.006 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.039 | ||||
| Inter Quartile Range | 0.017 | ||||
| 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) | 0.023 | ||||
| Compounded annual return (geometric extrapolation) | 0.023 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.581 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.581 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.666 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.007 | ||||
| SD | 0.179 | ||||
| Sharpe ratio (Glass type estimate) | -0.036 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.036 | ||||
| df | 951.000 | ||||
| t | -0.069 | ||||
| p | 0.528 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.064 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.992 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.064 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.992 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.060 | ||||
| Upside Potential Ratio | 2.668 | ||||
| Upside part of mean | 0.288 | ||||
| Downside part of mean | -0.294 | ||||
| Upside SD | 0.143 | ||||
| Downside SD | 0.108 | ||||
| N nonnegative terms | 36.000 | ||||
| N negative terms | 916.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 952.000 | ||||
| Mean of predictor | 0.468 | ||||
| Mean of criterion | -0.007 | ||||
| SD of predictor | 0.340 | ||||
| SD of criterion | 0.179 | ||||
| Covariance | 0.000 | ||||
| r | 0.001 | ||||
| b (slope, estimate of beta) | 0.000 | ||||
| a (intercept, estimate of alpha) | -0.007 | ||||
| Mean Square Error | 0.032 | ||||
| DF error | 950.000 | ||||
| t(b) | 0.021 | ||||
| p(b) | 0.491 | ||||
| t(a) | -0.071 | ||||
| p(a) | 0.528 | ||||
| Lowerbound of 95% confidence interval for beta | -0.033 | ||||
| Upperbound of 95% confidence interval for beta | 0.034 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.192 | ||||
| Upperbound of 95% confidence interval for alpha | 0.179 | ||||
| Treynor index (mean / b) | -17.813 | ||||
| Jensen alpha (a) | -0.007 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.022 | ||||
| SD | 0.175 | ||||
| Sharpe ratio (Glass type estimate) | -0.126 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.126 | ||||
| df | 951.000 | ||||
| t | -0.240 | ||||
| p | 0.595 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.154 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.902 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.154 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.902 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.198 | ||||
| Upside Potential Ratio | 2.502 | ||||
| Upside part of mean | 0.278 | ||||
| Downside part of mean | -0.300 | ||||
| Upside SD | 0.135 | ||||
| Downside SD | 0.111 | ||||
| N nonnegative terms | 36.000 | ||||
| N negative terms | 916.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 952.000 | ||||
| Mean of predictor | 0.409 | ||||
| Mean of criterion | -0.022 | ||||
| SD of predictor | 0.346 | ||||
| SD of criterion | 0.175 | ||||
| Covariance | 0.000 | ||||
| r | 0.000 | ||||
| b (slope, estimate of beta) | 0.000 | ||||
| a (intercept, estimate of alpha) | -0.022 | ||||
| Mean Square Error | 0.031 | ||||
| DF error | 950.000 | ||||
| t(b) | 0.003 | ||||
| p(b) | 0.499 | ||||
| t(a) | -0.239 | ||||
| p(a) | 0.595 | ||||
| Lowerbound of 95% confidence interval for beta | -0.032 | ||||
| Upperbound of 95% confidence interval for beta | 0.032 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.203 | ||||
| Upperbound of 95% confidence interval for alpha | 0.159 | ||||
| Treynor index (mean / b) | -534.170 | ||||
| Jensen alpha (a) | -0.022 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.018 | ||||
| Expected Shortfall on VaR | 0.022 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.009 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 952.000 | ||||
| Minimum | 0.912 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.189 | ||||
| Mean of quarter 1 | 0.996 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.004 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 32.000 | ||||
| Percentage of outliers low | 0.034 | ||||
| Mean of outliers low | 0.971 | ||||
| Number of outliers high | 37.000 | ||||
| Percentage of outliers high | 0.039 | ||||
| Mean of outliers high | 1.028 | ||||
| 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) | -0.281 | ||||
| VaR(95%) (regression method) | -0.008 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.035 | ||||
| Quartile 1 | 0.043 | ||||
| Median | 0.062 | ||||
| Quartile 3 | 0.106 | ||||
| Maximum | 0.192 | ||||
| Mean of quarter 1 | 0.035 | ||||
| Mean of quarter 2 | 0.046 | ||||
| Mean of quarter 3 | 0.078 | ||||
| Mean of quarter 4 | 0.192 | ||||
| Inter Quartile Range | 0.063 | ||||
| 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) | 0.023 | ||||
| Compounded annual return (geometric extrapolation) | 0.022 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.116 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.116 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.004 | ||||
| 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 | 1.007 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.487 | ||||
| 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 | 0.886 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.493 | ||||
| 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) | -8745647818586232.000 | ||||
| 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) | -352436851092396114326376115339264.000 | ||||
| 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 | ||||