Advanced Statistics: STP 100
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 | -0.058 | ||||
| SD | 0.042 | ||||
| Sharpe ratio (Glass type estimate) | -1.372 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.340 | ||||
| df | 32.000 | ||||
| t | -2.276 | ||||
| p | 0.985 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.591 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.134 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.567 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.113 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.392 | ||||
| Upside Potential Ratio | 0.321 | ||||
| Upside part of mean | 0.013 | ||||
| Downside part of mean | -0.071 | ||||
| Upside SD | 0.016 | ||||
| Downside SD | 0.041 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 31.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 33.000 | ||||
| Mean of predictor | 0.192 | ||||
| Mean of criterion | -0.058 | ||||
| SD of predictor | 0.206 | ||||
| SD of criterion | 0.042 | ||||
| Covariance | -0.001 | ||||
| r | -0.172 | ||||
| b (slope, estimate of beta) | -0.035 | ||||
| a (intercept, estimate of alpha) | -0.051 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 31.000 | ||||
| t(b) | -0.972 | ||||
| p(b) | 0.831 | ||||
| t(a) | -1.939 | ||||
| p(a) | 0.969 | ||||
| Lowerbound of 95% confidence interval for beta | -0.109 | ||||
| Upperbound of 95% confidence interval for beta | 0.038 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.105 | ||||
| Upperbound of 95% confidence interval for alpha | 0.003 | ||||
| Treynor index (mean / b) | 1.647 | ||||
| Jensen alpha (a) | -0.051 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.059 | ||||
| SD | 0.043 | ||||
| Sharpe ratio (Glass type estimate) | -1.367 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.334 | ||||
| df | 32.000 | ||||
| t | -2.266 | ||||
| p | 0.985 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.585 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.129 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.561 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.108 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.380 | ||||
| Upside Potential Ratio | 0.309 | ||||
| Upside part of mean | 0.013 | ||||
| Downside part of mean | -0.072 | ||||
| Upside SD | 0.016 | ||||
| Downside SD | 0.042 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 31.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 33.000 | ||||
| Mean of predictor | 0.170 | ||||
| Mean of criterion | -0.059 | ||||
| SD of predictor | 0.203 | ||||
| SD of criterion | 0.043 | ||||
| Covariance | -0.001 | ||||
| r | -0.167 | ||||
| b (slope, estimate of beta) | -0.035 | ||||
| a (intercept, estimate of alpha) | -0.053 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 31.000 | ||||
| t(b) | -0.944 | ||||
| p(b) | 0.824 | ||||
| t(a) | -1.973 | ||||
| p(a) | 0.971 | ||||
| Lowerbound of 95% confidence interval for beta | -0.111 | ||||
| Upperbound of 95% confidence interval for beta | 0.041 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.107 | ||||
| Upperbound of 95% confidence interval for alpha | 0.002 | ||||
| Treynor index (mean / b) | 1.660 | ||||
| Jensen alpha (a) | -0.053 | ||||
| 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%) | 0.020 | ||||
| Expected Shortfall on VaR | 0.036 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 33.000 | ||||
| Minimum | 0.943 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.028 | ||||
| Mean of quarter 1 | 0.991 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.006 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 6.000 | ||||
| Percentage of outliers low | 0.182 | ||||
| Mean of outliers low | 0.986 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.182 | ||||
| Mean of outliers high | 1.008 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -6.468 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.002 | ||||
| Extreme Value Index (regression method) | 0.573 | ||||
| VaR(95%) (regression method) | 0.019 | ||||
| Expected Shortfall (regression method) | 0.084 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.061 | ||||
| Quartile 1 | 0.061 | ||||
| Median | 0.061 | ||||
| Quartile 3 | 0.061 | ||||
| Maximum | 0.061 | ||||
| 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) | -0.014 | ||||
| Compounded annual return (geometric extrapolation) | -0.014 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.236 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.482 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.058 | ||||
| SD | 0.043 | ||||
| Sharpe ratio (Glass type estimate) | -1.352 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.351 | ||||
| df | 947.000 | ||||
| t | -2.244 | ||||
| p | 0.987 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.534 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.169 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.533 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.168 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.829 | ||||
| Upside Potential Ratio | 2.783 | ||||
| Upside part of mean | 0.088 | ||||
| Downside part of mean | -0.145 | ||||
| Upside SD | 0.029 | ||||
| Downside SD | 0.031 | ||||
| N nonnegative terms | 68.000 | ||||
| N negative terms | 880.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 948.000 | ||||
| Mean of predictor | 0.205 | ||||
| Mean of criterion | -0.058 | ||||
| SD of predictor | 0.202 | ||||
| SD of criterion | 0.043 | ||||
| Covariance | -0.001 | ||||
| r | -0.106 | ||||
| b (slope, estimate of beta) | -0.022 | ||||
| a (intercept, estimate of alpha) | -0.053 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 946.000 | ||||
| t(b) | -3.276 | ||||
| p(b) | 0.999 | ||||
| t(a) | -2.073 | ||||
| p(a) | 0.981 | ||||
| Lowerbound of 95% confidence interval for beta | -0.036 | ||||
| Upperbound of 95% confidence interval for beta | -0.009 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.103 | ||||
| Upperbound of 95% confidence interval for alpha | -0.003 | ||||
| Treynor index (mean / b) | 2.578 | ||||
| Jensen alpha (a) | -0.053 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.058 | ||||
| SD | 0.043 | ||||
| Sharpe ratio (Glass type estimate) | -1.372 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.371 | ||||
| df | 947.000 | ||||
| t | -2.278 | ||||
| p | 0.989 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.554 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.190 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.553 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.189 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.845 | ||||
| Upside Potential Ratio | 2.750 | ||||
| Upside part of mean | 0.087 | ||||
| Downside part of mean | -0.146 | ||||
| Upside SD | 0.029 | ||||
| Downside SD | 0.032 | ||||
| N nonnegative terms | 68.000 | ||||
| N negative terms | 880.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 948.000 | ||||
| Mean of predictor | 0.184 | ||||
| Mean of criterion | -0.058 | ||||
| SD of predictor | 0.202 | ||||
| SD of criterion | 0.043 | ||||
| Covariance | -0.001 | ||||
| r | -0.106 | ||||
| b (slope, estimate of beta) | -0.022 | ||||
| a (intercept, estimate of alpha) | -0.054 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 946.000 | ||||
| t(b) | -3.285 | ||||
| p(b) | 0.999 | ||||
| t(a) | -2.125 | ||||
| p(a) | 0.983 | ||||
| Lowerbound of 95% confidence interval for beta | -0.036 | ||||
| Upperbound of 95% confidence interval for beta | -0.009 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.105 | ||||
| Upperbound of 95% confidence interval for alpha | -0.004 | ||||
| Treynor index (mean / b) | 2.613 | ||||
| Jensen alpha (a) | -0.054 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.005 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.001 | ||||
| Expected Shortfall on VaR | 0.003 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 948.000 | ||||
| Minimum | 0.977 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.021 | ||||
| Mean of quarter 1 | 0.999 | ||||
| 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 | 89.000 | ||||
| Percentage of outliers low | 0.094 | ||||
| Mean of outliers low | 0.997 | ||||
| Number of outliers high | 81.000 | ||||
| Percentage of outliers high | 0.085 | ||||
| Mean of outliers high | 1.003 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.384 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.003 | ||||
| Extreme Value Index (regression method) | 0.335 | ||||
| VaR(95%) (regression method) | 0.001 | ||||
| Expected Shortfall (regression method) | 0.004 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.048 | ||||
| Quartile 1 | 0.055 | ||||
| Median | 0.063 | ||||
| Quartile 3 | 0.070 | ||||
| Maximum | 0.078 | ||||
| Mean of quarter 1 | 0.048 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.078 | ||||
| Inter Quartile Range | 0.015 | ||||
| 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) | -0.014 | ||||
| Compounded annual return (geometric extrapolation) | -0.014 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.184 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.184 | ||||
| Compounded annual return / Expected Shortfall lognormal | -2.935 | ||||
| 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) | -749.169 | ||||
| Sharpe ratio (Hedges UMVUE) | -745.879 | ||||
| df | 171.000 | ||||
| t | -529.743 | ||||
| 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) | -824.977 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -666.780 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -18.542 | ||||
| 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 | 0.688 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.251 | ||||
| SD of criterion | 0.000 | ||||
| Covariance | -0.000 | ||||
| r | -0.171 | ||||
| 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) | -2.264 | ||||
| p(b) | 0.586 | ||||
| t(a) | -529.996 | ||||
| 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) | 1100.955 | ||||
| Jensen alpha (a) | -0.044 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.000 | ||||
| Sharpe ratio (Glass type estimate) | -749.106 | ||||
| Sharpe ratio (Hedges UMVUE) | -745.815 | ||||
| df | 171.000 | ||||
| t | -529.698 | ||||
| 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) | -824.908 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -666.723 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -18.542 | ||||
| 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 | 0.656 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.251 | ||||
| SD of criterion | 0.000 | ||||
| Covariance | -0.000 | ||||
| r | -0.169 | ||||
| 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) | -2.236 | ||||
| p(b) | 0.585 | ||||
| t(a) | -530.278 | ||||
| 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) | 1111.814 | ||||
| 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 | 1.000 | ||||
| Percentage of outliers low | 0.006 | ||||
| Mean of outliers low | 1.000 | ||||
| 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 | 1.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.000 | ||||
| Median | 0.000 | ||||
| Quartile 3 | 0.000 | ||||
| Maximum | 0.000 | ||||
| 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) | -0.000 | ||||
| Compounded annual return (geometric extrapolation) | -0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | -2.000 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.618 | ||||
