Advanced Statistics: Mini N&R
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 | -0.016 | ||||
| SD | 0.117 | ||||
| Sharpe ratio (Glass type estimate) | -0.135 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.134 | ||||
| df | 71.000 | ||||
| t | -0.332 | ||||
| p | 0.630 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.935 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.665 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.935 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.666 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.270 | ||||
| Upside Potential Ratio | 1.311 | ||||
| Upside part of mean | 0.077 | ||||
| Downside part of mean | -0.093 | ||||
| Upside SD | 0.100 | ||||
| Downside SD | 0.059 | ||||
| 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 | 0.323 | ||||
| Mean of criterion | -0.016 | ||||
| SD of predictor | 0.223 | ||||
| SD of criterion | 0.117 | ||||
| Covariance | -0.003 | ||||
| r | -0.126 | ||||
| b (slope, estimate of beta) | -0.066 | ||||
| a (intercept, estimate of alpha) | 0.005 | ||||
| Mean Square Error | 0.014 | ||||
| DF error | 70.000 | ||||
| t(b) | -1.061 | ||||
| p(b) | 0.854 | ||||
| t(a) | 0.105 | ||||
| p(a) | 0.458 | ||||
| Lowerbound of 95% confidence interval for beta | -0.190 | ||||
| Upperbound of 95% confidence interval for beta | 0.058 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.098 | ||||
| Upperbound of 95% confidence interval for alpha | 0.109 | ||||
| Treynor index (mean / b) | 0.241 | ||||
| Jensen alpha (a) | 0.005 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.022 | ||||
| SD | 0.111 | ||||
| Sharpe ratio (Glass type estimate) | -0.198 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.196 | ||||
| df | 71.000 | ||||
| t | -0.486 | ||||
| p | 0.686 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.998 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.603 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.997 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.605 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.366 | ||||
| Upside Potential Ratio | 1.197 | ||||
| Upside part of mean | 0.072 | ||||
| Downside part of mean | -0.094 | ||||
| Upside SD | 0.093 | ||||
| Downside SD | 0.060 | ||||
| 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 | 0.296 | ||||
| Mean of criterion | -0.022 | ||||
| SD of predictor | 0.211 | ||||
| SD of criterion | 0.111 | ||||
| Covariance | -0.003 | ||||
| r | -0.125 | ||||
| b (slope, estimate of beta) | -0.066 | ||||
| a (intercept, estimate of alpha) | -0.003 | ||||
| Mean Square Error | 0.012 | ||||
| DF error | 70.000 | ||||
| t(b) | -1.055 | ||||
| p(b) | 0.852 | ||||
| t(a) | -0.053 | ||||
| p(a) | 0.521 | ||||
| Lowerbound of 95% confidence interval for beta | -0.191 | ||||
| Upperbound of 95% confidence interval for beta | 0.059 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.100 | ||||
| Upperbound of 95% confidence interval for alpha | 0.095 | ||||
| Treynor index (mean / b) | 0.335 | ||||
| Jensen alpha (a) | -0.003 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.053 | ||||
| Expected Shortfall on VaR | 0.066 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.025 | ||||
| Expected Shortfall on VaR | 0.048 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 72.000 | ||||
| Minimum | 0.927 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.196 | ||||
| Mean of quarter 1 | 0.983 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.027 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 8.000 | ||||
| Percentage of outliers low | 0.111 | ||||
| Mean of outliers low | 0.961 | ||||
| Number of outliers high | 7.000 | ||||
| Percentage of outliers high | 0.097 | ||||
| Mean of outliers high | 1.069 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -364.094 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -1.467 | ||||
| VaR(95%) (regression method) | 0.039 | ||||
| Expected Shortfall (regression method) | 0.054 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.058 | ||||
| Quartile 1 | 0.061 | ||||
| Median | 0.064 | ||||
| Quartile 3 | 0.111 | ||||
| Maximum | 0.159 | ||||
| Mean of quarter 1 | 0.058 | ||||
| Mean of quarter 2 | 0.064 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.159 | ||||
| Inter Quartile Range | 0.051 | ||||
| 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) | 0.139 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.139 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.337 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.006 | ||||
| SD | 0.239 | ||||
| Sharpe ratio (Glass type estimate) | 0.026 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.026 | ||||
| df | 1573.000 | ||||
| t | 0.064 | ||||
| p | 0.499 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.774 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.826 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.774 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.826 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.039 | ||||
| Upside Potential Ratio | 3.166 | ||||
| Upside part of mean | 0.499 | ||||
| Downside part of mean | -0.493 | ||||
| Upside SD | 0.180 | ||||
| Downside SD | 0.158 | ||||
| N nonnegative terms | 129.000 | ||||
| N negative terms | 1445.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1574.000 | ||||
| Mean of predictor | 0.350 | ||||
| Mean of criterion | 0.006 | ||||
| SD of predictor | 0.307 | ||||
| SD of criterion | 0.239 | ||||
| Covariance | -0.002 | ||||
| r | -0.025 | ||||
| b (slope, estimate of beta) | -0.019 | ||||
| a (intercept, estimate of alpha) | 0.013 | ||||
| Mean Square Error | 0.057 | ||||
| DF error | 1572.000 | ||||
| t(b) | -0.991 | ||||
| p(b) | 0.512 | ||||
| t(a) | 0.133 | ||||
| p(a) | 0.498 | ||||
| Lowerbound of 95% confidence interval for beta | -0.058 | ||||
| Upperbound of 95% confidence interval for beta | 0.019 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.179 | ||||
| Upperbound of 95% confidence interval for alpha | 0.205 | ||||
| Treynor index (mean / b) | -0.319 | ||||
| Jensen alpha (a) | 0.013 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.022 | ||||
| SD | 0.238 | ||||
| Sharpe ratio (Glass type estimate) | -0.093 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.093 | ||||
| df | 1573.000 | ||||
| t | -0.228 | ||||
| p | 0.504 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.893 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.707 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.893 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.707 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.134 | ||||
| Upside Potential Ratio | 2.926 | ||||
| Upside part of mean | 0.484 | ||||
| Downside part of mean | -0.506 | ||||
| Upside SD | 0.171 | ||||
| Downside SD | 0.165 | ||||
| N nonnegative terms | 129.000 | ||||
| N negative terms | 1445.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1574.000 | ||||
| Mean of predictor | 0.303 | ||||
| Mean of criterion | -0.022 | ||||
| SD of predictor | 0.308 | ||||
| SD of criterion | 0.238 | ||||
| Covariance | -0.002 | ||||
| r | -0.027 | ||||
| b (slope, estimate of beta) | -0.021 | ||||
| a (intercept, estimate of alpha) | -0.016 | ||||
| Mean Square Error | 0.057 | ||||
| DF error | 1572.000 | ||||
| t(b) | -1.056 | ||||
| p(b) | 0.513 | ||||
| t(a) | -0.163 | ||||
| p(a) | 0.502 | ||||
| Lowerbound of 95% confidence interval for beta | -0.059 | ||||
| Upperbound of 95% confidence interval for beta | 0.018 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.207 | ||||
| Upperbound of 95% confidence interval for alpha | 0.175 | ||||
| Treynor index (mean / b) | 1.075 | ||||
| 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%) | 0.024 | ||||
| Expected Shortfall on VaR | 0.030 | ||||
| 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 | 1574.000 | ||||
| Minimum | 0.855 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.195 | ||||
| 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 | 150.000 | ||||
| Percentage of outliers low | 0.095 | ||||
| Mean of outliers low | 0.982 | ||||
| Number of outliers high | 148.000 | ||||
| Percentage of outliers high | 0.094 | ||||
| Mean of outliers high | 1.020 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.006 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.004 | ||||
| Extreme Value Index (regression method) | 0.215 | ||||
| VaR(95%) (regression method) | 0.005 | ||||
| Expected Shortfall (regression method) | 0.018 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 11.000 | ||||
| Minimum | 0.005 | ||||
| Quartile 1 | 0.047 | ||||
| Median | 0.071 | ||||
| Quartile 3 | 0.130 | ||||
| Maximum | 0.268 | ||||
| Mean of quarter 1 | 0.021 | ||||
| Mean of quarter 2 | 0.063 | ||||
| Mean of quarter 3 | 0.099 | ||||
| Mean of quarter 4 | 0.192 | ||||
| Inter Quartile Range | 0.082 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.091 | ||||
| Mean of outliers high | 0.268 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.117 | ||||
| VaR(95%) (moments method) | 0.216 | ||||
| Expected Shortfall (moments method) | 0.278 | ||||
| Extreme Value Index (regression method) | 2.916 | ||||
| VaR(95%) (regression method) | 0.316 | ||||
| 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) | 0.083 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.115 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.740 | ||||
| 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 | 1.178 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.515 | ||||
| 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 | 1.041 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.523 | ||||
| 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) | -8733537310968639.000 | ||||
| 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) | -87378335895197307513039306620928.000 | ||||
| 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 | ||||