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 | 0.021 | ||||
| SD | 0.075 | ||||
| Sharpe ratio (Glass type estimate) | 0.276 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.260 | ||||
| df | 14.000 | ||||
| t | 0.308 | ||||
| p | 0.459 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.485 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.027 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.495 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.016 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.522 | ||||
| Upside Potential Ratio | 2.202 | ||||
| Upside part of mean | 0.087 | ||||
| Downside part of mean | -0.066 | ||||
| Upside SD | 0.061 | ||||
| Downside SD | 0.039 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 12.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 15.000 | ||||
| Mean of predictor | 0.103 | ||||
| Mean of criterion | 0.021 | ||||
| SD of predictor | 0.213 | ||||
| SD of criterion | 0.075 | ||||
| Covariance | 0.002 | ||||
| r | 0.147 | ||||
| b (slope, estimate of beta) | 0.051 | ||||
| a (intercept, estimate of alpha) | 0.015 | ||||
| Mean Square Error | 0.006 | ||||
| DF error | 13.000 | ||||
| t(b) | 0.535 | ||||
| p(b) | 0.407 | ||||
| t(a) | 0.221 | ||||
| p(a) | 0.461 | ||||
| Lowerbound of 95% confidence interval for beta | -0.156 | ||||
| Upperbound of 95% confidence interval for beta | 0.259 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.134 | ||||
| Upperbound of 95% confidence interval for alpha | 0.165 | ||||
| Treynor index (mean / b) | 0.400 | ||||
| Jensen alpha (a) | 0.015 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.018 | ||||
| SD | 0.074 | ||||
| Sharpe ratio (Glass type estimate) | 0.243 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.230 | ||||
| df | 14.000 | ||||
| t | 0.272 | ||||
| p | 0.464 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.516 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.994 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.525 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.985 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.447 | ||||
| Upside Potential Ratio | 2.114 | ||||
| Upside part of mean | 0.085 | ||||
| Downside part of mean | -0.067 | ||||
| Upside SD | 0.059 | ||||
| Downside SD | 0.040 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 12.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 15.000 | ||||
| Mean of predictor | 0.081 | ||||
| Mean of criterion | 0.018 | ||||
| SD of predictor | 0.212 | ||||
| SD of criterion | 0.074 | ||||
| Covariance | 0.002 | ||||
| r | 0.154 | ||||
| b (slope, estimate of beta) | 0.054 | ||||
| a (intercept, estimate of alpha) | 0.014 | ||||
| Mean Square Error | 0.006 | ||||
| DF error | 13.000 | ||||
| t(b) | 0.564 | ||||
| p(b) | 0.402 | ||||
| t(a) | 0.200 | ||||
| p(a) | 0.465 | ||||
| Lowerbound of 95% confidence interval for beta | -0.152 | ||||
| Upperbound of 95% confidence interval for beta | 0.259 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.133 | ||||
| Upperbound of 95% confidence interval for alpha | 0.160 | ||||
| Treynor index (mean / b) | 0.335 | ||||
| Jensen alpha (a) | 0.014 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.033 | ||||
| Expected Shortfall on VaR | 0.041 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.017 | ||||
| Expected Shortfall on VaR | 0.031 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 15.000 | ||||
| Minimum | 0.961 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.060 | ||||
| Mean of quarter 1 | 0.990 | ||||
| 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 | 1.000 | ||||
| Percentage of outliers low | 0.067 | ||||
| Mean of outliers low | 0.961 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.200 | ||||
| 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 | 0.039 | ||||
| Quartile 1 | 0.039 | ||||
| Median | 0.039 | ||||
| Quartile 3 | 0.039 | ||||
| Maximum | 0.039 | ||||
| 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) | 0.064 | ||||
| Compounded annual return (geometric extrapolation) | 0.064 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.653 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.542 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.050 | ||||
| SD | 0.256 | ||||
| Sharpe ratio (Glass type estimate) | 0.193 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.193 | ||||
| df | 434.000 | ||||
| t | 0.217 | ||||
| p | 0.414 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.550 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.936 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.550 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.936 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.300 | ||||
| Upside Potential Ratio | 4.285 | ||||
| Upside part of mean | 0.708 | ||||
| Downside part of mean | -0.658 | ||||
| Upside SD | 0.196 | ||||
| Downside SD | 0.165 | ||||
| N nonnegative terms | 35.000 | ||||
| N negative terms | 400.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 435.000 | ||||
| Mean of predictor | 0.145 | ||||
| Mean of criterion | 0.050 | ||||
| SD of predictor | 0.235 | ||||
| SD of criterion | 0.256 | ||||
| Covariance | 0.001 | ||||
| r | 0.012 | ||||
| b (slope, estimate of beta) | 0.013 | ||||
| a (intercept, estimate of alpha) | 0.048 | ||||
| Mean Square Error | 0.066 | ||||
| DF error | 433.000 | ||||
| t(b) | 0.242 | ||||
| p(b) | 0.405 | ||||
| t(a) | 0.209 | ||||
| p(a) | 0.417 | ||||
| Lowerbound of 95% confidence interval for beta | -0.090 | ||||
| Upperbound of 95% confidence interval for beta | 0.116 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.401 | ||||
| Upperbound of 95% confidence interval for alpha | 0.496 | ||||
| Treynor index (mean / b) | 3.920 | ||||
| Jensen alpha (a) | 0.048 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.017 | ||||
| SD | 0.254 | ||||
| Sharpe ratio (Glass type estimate) | 0.068 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.068 | ||||
| df | 434.000 | ||||
| t | 0.076 | ||||
| p | 0.470 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.675 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.811 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.675 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.811 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.101 | ||||
| Upside Potential Ratio | 4.046 | ||||
| Upside part of mean | 0.689 | ||||
| Downside part of mean | -0.672 | ||||
| Upside SD | 0.188 | ||||
| Downside SD | 0.170 | ||||
| N nonnegative terms | 35.000 | ||||
| N negative terms | 400.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 435.000 | ||||
| Mean of predictor | 0.118 | ||||
| Mean of criterion | 0.017 | ||||
| SD of predictor | 0.235 | ||||
| SD of criterion | 0.254 | ||||
| Covariance | 0.001 | ||||
| r | 0.011 | ||||
| b (slope, estimate of beta) | 0.012 | ||||
| a (intercept, estimate of alpha) | 0.016 | ||||
| Mean Square Error | 0.065 | ||||
| DF error | 433.000 | ||||
| t(b) | 0.226 | ||||
| p(b) | 0.411 | ||||
| t(a) | 0.070 | ||||
| p(a) | 0.472 | ||||
| Lowerbound of 95% confidence interval for beta | -0.090 | ||||
| Upperbound of 95% confidence interval for beta | 0.114 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.429 | ||||
| Upperbound of 95% confidence interval for alpha | 0.460 | ||||
| Treynor index (mean / b) | 1.466 | ||||
| Jensen alpha (a) | 0.016 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.022 | ||||
| Expected Shortfall on VaR | 0.028 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.006 | ||||
| Expected Shortfall on VaR | 0.014 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 435.000 | ||||
| Minimum | 0.912 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.137 | ||||
| Mean of quarter 1 | 0.993 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.008 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 35.000 | ||||
| Percentage of outliers low | 0.080 | ||||
| Mean of outliers low | 0.978 | ||||
| Number of outliers high | 35.000 | ||||
| Percentage of outliers high | 0.080 | ||||
| Mean of outliers high | 1.026 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.073 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.002 | ||||
| Extreme Value Index (regression method) | -0.073 | ||||
| VaR(95%) (regression method) | 0.006 | ||||
| Expected Shortfall (regression method) | 0.018 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.037 | ||||
| Quartile 1 | 0.057 | ||||
| Median | 0.078 | ||||
| Quartile 3 | 0.135 | ||||
| Maximum | 0.192 | ||||
| Mean of quarter 1 | 0.037 | ||||
| Mean of quarter 2 | 0.078 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.192 | ||||
| Inter Quartile Range | 0.077 | ||||
| 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) | 0.064 | ||||
| Compounded annual return (geometric extrapolation) | 0.063 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.329 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.329 | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.272 | ||||
| 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 | -18.547 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.002 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 172.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 172.000 | ||||
| Mean of predictor | 0.366 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.194 | ||||
| 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) | -7936535306446244.000 | ||||
| Sharpe ratio (Hedges UMVUE) | -7901674975671223.000 | ||||
| df | 171.000 | ||||
| t | -5611977934314593.000 | ||||
| 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) | -8739115425704417.000 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -7064234525638030.000 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -18.547 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.002 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 172.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 172.000 | ||||
| Mean of predictor | 0.347 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.193 | ||||
| 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 | 170.000 | ||||
| t(b) | 0.000 | ||||
| p(b) | 0.500 | ||||
| t(a) | -5569360174268599.000 | ||||
| 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) | -11419288798791572278228245544960.000 | ||||
| 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 | 172.000 | ||||
| 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 | ||||
