Advanced Statistics: KC Covered Call Fund
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 | -0.063 | ||||
| SD | 0.079 | ||||
| Sharpe ratio (Glass type estimate) | -0.796 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.788 | ||||
| df | 71.000 | ||||
| t | -1.950 | ||||
| p | 0.972 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.604 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.017 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.598 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.023 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.911 | ||||
| Upside Potential Ratio | 0.430 | ||||
| Upside part of mean | 0.030 | ||||
| Downside part of mean | -0.092 | ||||
| Upside SD | 0.041 | ||||
| Downside SD | 0.069 | ||||
| N nonnegative terms | 6.000 | ||||
| N negative terms | 66.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 72.000 | ||||
| Mean of predictor | 0.321 | ||||
| Mean of criterion | -0.063 | ||||
| SD of predictor | 0.248 | ||||
| SD of criterion | 0.079 | ||||
| Covariance | 0.006 | ||||
| r | 0.302 | ||||
| b (slope, estimate of beta) | 0.096 | ||||
| a (intercept, estimate of alpha) | -0.093 | ||||
| Mean Square Error | 0.006 | ||||
| DF error | 70.000 | ||||
| t(b) | 2.651 | ||||
| p(b) | 0.005 | ||||
| t(a) | -2.836 | ||||
| p(a) | 0.997 | ||||
| Lowerbound of 95% confidence interval for beta | 0.024 | ||||
| Upperbound of 95% confidence interval for beta | 0.168 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.159 | ||||
| Upperbound of 95% confidence interval for alpha | -0.028 | ||||
| Treynor index (mean / b) | -0.653 | ||||
| Jensen alpha (a) | -0.093 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.066 | ||||
| SD | 0.082 | ||||
| Sharpe ratio (Glass type estimate) | -0.805 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.797 | ||||
| df | 71.000 | ||||
| t | -1.972 | ||||
| p | 0.974 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.614 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.008 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.608 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.014 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.897 | ||||
| Upside Potential Ratio | 0.391 | ||||
| Upside part of mean | 0.029 | ||||
| Downside part of mean | -0.094 | ||||
| Upside SD | 0.039 | ||||
| Downside SD | 0.073 | ||||
| N nonnegative terms | 6.000 | ||||
| N negative terms | 66.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 72.000 | ||||
| Mean of predictor | 0.288 | ||||
| Mean of criterion | -0.066 | ||||
| SD of predictor | 0.241 | ||||
| SD of criterion | 0.082 | ||||
| Covariance | 0.006 | ||||
| r | 0.314 | ||||
| b (slope, estimate of beta) | 0.106 | ||||
| a (intercept, estimate of alpha) | -0.096 | ||||
| Mean Square Error | 0.006 | ||||
| DF error | 70.000 | ||||
| t(b) | 2.765 | ||||
| p(b) | 0.004 | ||||
| t(a) | -2.856 | ||||
| p(a) | 0.997 | ||||
| Lowerbound of 95% confidence interval for beta | 0.030 | ||||
| Upperbound of 95% confidence interval for beta | 0.183 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.164 | ||||
| Upperbound of 95% confidence interval for alpha | -0.029 | ||||
| Treynor index (mean / b) | -0.617 | ||||
| Jensen alpha (a) | -0.096 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.043 | ||||
| Expected Shortfall on VaR | 0.053 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.025 | ||||
| Expected Shortfall on VaR | 0.051 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 72.000 | ||||
| Minimum | 0.853 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.096 | ||||
| Mean of quarter 1 | 0.983 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.011 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 11.000 | ||||
| Percentage of outliers low | 0.153 | ||||
| Mean of outliers low | 0.972 | ||||
| Number of outliers high | 9.000 | ||||
| Percentage of outliers high | 0.125 | ||||
| Mean of outliers high | 1.023 | ||||
| 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) | 0.160 | ||||
| VaR(95%) (regression method) | 0.015 | ||||
| Expected Shortfall (regression method) | 0.032 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.175 | ||||
| Quartile 1 | 0.175 | ||||
| Median | 0.175 | ||||
| Quartile 3 | 0.175 | ||||
| Maximum | 0.175 | ||||
| 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) | -0.020 | ||||
| Compounded annual return (geometric extrapolation) | -0.021 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.123 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.408 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.059 | ||||
| SD | 0.113 | ||||
| Sharpe ratio (Glass type estimate) | -0.525 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.525 | ||||
| df | 1574.000 | ||||
| t | -1.287 | ||||
| p | 0.516 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.324 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.275 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.324 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.275 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.725 | ||||
| Upside Potential Ratio | 2.956 | ||||
| Upside part of mean | 0.242 | ||||
| Downside part of mean | -0.301 | ||||
| Upside SD | 0.078 | ||||
| Downside SD | 0.082 | ||||
| N nonnegative terms | 162.000 | ||||
| N negative terms | 1413.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1575.000 | ||||
| Mean of predictor | 0.352 | ||||
| Mean of criterion | -0.059 | ||||
| SD of predictor | 0.375 | ||||
| SD of criterion | 0.113 | ||||
| Covariance | 0.013 | ||||
| r | 0.308 | ||||
| b (slope, estimate of beta) | 0.093 | ||||
| a (intercept, estimate of alpha) | -0.092 | ||||
| Mean Square Error | 0.012 | ||||
| DF error | 1573.000 | ||||
| t(b) | 12.853 | ||||
| p(b) | 0.307 | ||||
| t(a) | -2.095 | ||||
| p(a) | 0.534 | ||||
| Lowerbound of 95% confidence interval for beta | 0.079 | ||||
| Upperbound of 95% confidence interval for beta | 0.107 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.178 | ||||
| Upperbound of 95% confidence interval for alpha | -0.006 | ||||
| Treynor index (mean / b) | -0.638 | ||||
| Jensen alpha (a) | -0.092 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.066 | ||||
| SD | 0.113 | ||||
| Sharpe ratio (Glass type estimate) | -0.581 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.580 | ||||
| df | 1574.000 | ||||
| t | -1.423 | ||||
| p | 0.518 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.380 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.219 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.380 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.219 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.786 | ||||
| Upside Potential Ratio | 2.860 | ||||
| Upside part of mean | 0.239 | ||||
| Downside part of mean | -0.304 | ||||
| Upside SD | 0.076 | ||||
| Downside SD | 0.083 | ||||
| N nonnegative terms | 162.000 | ||||
| N negative terms | 1413.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1575.000 | ||||
| Mean of predictor | 0.282 | ||||
| Mean of criterion | -0.066 | ||||
| SD of predictor | 0.375 | ||||
| SD of criterion | 0.113 | ||||
| Covariance | 0.013 | ||||
| r | 0.305 | ||||
| b (slope, estimate of beta) | 0.092 | ||||
| a (intercept, estimate of alpha) | -0.092 | ||||
| Mean Square Error | 0.012 | ||||
| DF error | 1573.000 | ||||
| t(b) | 12.710 | ||||
| p(b) | 0.309 | ||||
| t(a) | -2.082 | ||||
| p(a) | 0.533 | ||||
| Lowerbound of 95% confidence interval for beta | 0.078 | ||||
| Upperbound of 95% confidence interval for beta | 0.106 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.178 | ||||
| Upperbound of 95% confidence interval for alpha | -0.005 | ||||
| Treynor index (mean / b) | -0.713 | ||||
| Jensen alpha (a) | -0.092 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.012 | ||||
| Expected Shortfall on VaR | 0.015 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.008 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1575.000 | ||||
| Minimum | 0.920 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.080 | ||||
| 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 | 167.000 | ||||
| Percentage of outliers low | 0.106 | ||||
| Mean of outliers low | 0.991 | ||||
| Number of outliers high | 167.000 | ||||
| Percentage of outliers high | 0.106 | ||||
| Mean of outliers high | 1.009 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.452 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.006 | ||||
| Extreme Value Index (regression method) | 0.292 | ||||
| VaR(95%) (regression method) | 0.004 | ||||
| Expected Shortfall (regression method) | 0.011 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.011 | ||||
| Quartile 1 | 0.053 | ||||
| Median | 0.095 | ||||
| Quartile 3 | 0.137 | ||||
| Maximum | 0.179 | ||||
| Mean of quarter 1 | 0.011 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.179 | ||||
| Inter Quartile Range | 0.084 | ||||
| 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) | -0.020 | ||||
| Compounded annual return (geometric extrapolation) | -0.021 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.120 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.120 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.470 | ||||
| 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 | 0.851 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.447 | ||||
| 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 | 0.750 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.450 | ||||
| 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) | -8753140552686081.000 | ||||
| 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) | -225925065782360704744777456812032.000 | ||||
| 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 | ||||