Advanced Statistics: Green Dog
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 | 0.313 | ||||
SD | 0.678 | ||||
Sharpe ratio (Glass type estimate) | 0.462 | ||||
Sharpe ratio (Hedges UMVUE) | 0.452 | ||||
df | 37.000 | ||||
t | 0.821 | ||||
p | 0.208 | ||||
Lowerbound of 95% confidence interval for Sharpe Ratio | -0.648 | ||||
Upperbound of 95% confidence interval for Sharpe Ratio | 1.565 | ||||
Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.654 | ||||
Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.558 | ||||
Statistics related to Sortino ratio | |||||
Sortino ratio | 0.803 | ||||
Upside Potential Ratio | 2.314 | ||||
Upside part of mean | 0.902 | ||||
Downside part of mean | -0.589 | ||||
Upside SD | 0.551 | ||||
Downside SD | 0.390 | ||||
N nonnegative terms | 18.000 | ||||
N negative terms | 20.000 | ||||
Statistics related to linear regression on benchmark | |||||
N of observations | 38.000 | ||||
Mean of predictor | 0.173 | ||||
Mean of criterion | 0.313 | ||||
SD of predictor | 0.135 | ||||
SD of criterion | 0.678 | ||||
Covariance | 0.018 | ||||
r | 0.198 | ||||
b (slope, estimate of beta) | 0.999 | ||||
a (intercept, estimate of alpha) | 0.140 | ||||
Mean Square Error | 0.454 | ||||
DF error | 36.000 | ||||
t(b) | 1.214 | ||||
p(b) | 0.116 | ||||
t(a) | 0.347 | ||||
p(a) | 0.365 | ||||
Lowerbound of 95% confidence interval for beta | -0.670 | ||||
Upperbound of 95% confidence interval for beta | 2.668 | ||||
Lowerbound of 95% confidence interval for alpha | -0.679 | ||||
Upperbound of 95% confidence interval for alpha | 0.960 | ||||
Treynor index (mean / b) | 0.313 | ||||
Jensen alpha (a) | 0.140 | ||||
Ratio statistics of excess log return rates | |||||
Statistics related to Sharpe ratio | |||||
Mean | 0.097 | ||||
SD | 0.663 | ||||
Sharpe ratio (Glass type estimate) | 0.147 | ||||
Sharpe ratio (Hedges UMVUE) | 0.144 | ||||
df | 37.000 | ||||
t | 0.262 | ||||
p | 0.398 | ||||
Lowerbound of 95% confidence interval for Sharpe Ratio | -0.956 | ||||
Upperbound of 95% confidence interval for Sharpe Ratio | 1.248 | ||||
Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.958 | ||||
Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.246 | ||||
Statistics related to Sortino ratio | |||||
Sortino ratio | 0.207 | ||||
Upside Potential Ratio | 1.662 | ||||
Upside part of mean | 0.781 | ||||
Downside part of mean | -0.684 | ||||
Upside SD | 0.456 | ||||
Downside SD | 0.470 | ||||
N nonnegative terms | 18.000 | ||||
N negative terms | 20.000 | ||||
Statistics related to linear regression on benchmark | |||||
N of observations | 38.000 | ||||
Mean of predictor | 0.162 | ||||
Mean of criterion | 0.097 | ||||
SD of predictor | 0.134 | ||||
SD of criterion | 0.663 | ||||
Covariance | 0.018 | ||||
r | 0.203 | ||||
b (slope, estimate of beta) | 1.003 | ||||
a (intercept, estimate of alpha) | -0.065 | ||||
Mean Square Error | 0.433 | ||||
DF error | 36.000 | ||||
t(b) | 1.244 | ||||
p(b) | 0.111 | ||||
t(a) | -0.166 | ||||
p(a) | 0.566 | ||||
Lowerbound of 95% confidence interval for beta | -0.632 | ||||
Upperbound of 95% confidence interval for beta | 2.639 | ||||
Lowerbound of 95% confidence interval for alpha | -0.860 | ||||
Upperbound of 95% confidence interval for alpha | 0.730 | ||||
Treynor index (mean / b) | 0.097 | ||||
Jensen alpha (a) | -0.065 | ||||
Risk estimates for a one-period unit investment (parametric) | |||||
assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
VaR(95%) | 0.264 | ||||
Expected Shortfall on VaR | 0.319 | ||||
assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
VaR(95%) | 0.116 | ||||
Expected Shortfall on VaR | 0.236 | ||||
ORDER STATISTICS | |||||
Quartiles of return rates | |||||
Number of observations | 38.000 | ||||
Minimum | 0.569 | ||||
Quartile 1 | 1.000 | ||||
Median | 1.000 | ||||
Quartile 3 | 1.094 | ||||
Maximum | 1.647 | ||||
Mean of quarter 1 | 0.821 | ||||
Mean of quarter 2 | 1.000 | ||||
Mean of quarter 3 | 1.034 | ||||
Mean of quarter 4 | 1.261 | ||||
Inter Quartile Range | 0.094 | ||||
Number outliers low | 6.000 | ||||
Percentage of outliers low | 0.158 | ||||
Mean of outliers low | 0.741 | ||||
Number of outliers high | 4.000 | ||||
Percentage of outliers high | 0.105 | ||||
Mean of outliers high | 1.442 | ||||
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) | -0.394 | ||||
VaR(95%) (regression method) | 0.254 | ||||
Expected Shortfall (regression method) | 0.333 | ||||
DRAW DOWN STATISTICS | |||||
Quartiles of draw downs | |||||
Number of observations | 2.000 | ||||
Minimum | 0.221 | ||||
Quartile 1 | 0.352 | ||||
Median | 0.483 | ||||
Quartile 3 | 0.613 | ||||
Maximum | 0.744 | ||||
Mean of quarter 1 | 0.221 | ||||
Mean of quarter 2 | NA | ||||
Mean of quarter 3 | NA | ||||
Mean of quarter 4 | 0.744 | ||||
Inter Quartile Range | 0.261 | ||||
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) | 0.178 | ||||
Compounded annual return (geometric extrapolation) | 0.152 | ||||
Calmar ratio (compounded annual return / max draw down) | 0.204 | ||||
Compounded annual return / average of 25% largest draw downs | 0.204 | ||||
Compounded annual return / Expected Shortfall lognormal | 0.476 | ||||
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
RATIO STATISTICS | |||||
Ratio statistics of excess return rates | |||||
Statistics related to Sharpe ratio | |||||
Mean | 0.244 | ||||
SD | 0.575 | ||||
Sharpe ratio (Glass type estimate) | 0.424 | ||||
Sharpe ratio (Hedges UMVUE) | 0.423 | ||||
df | 850.000 | ||||
t | 0.764 | ||||
p | 0.223 | ||||
Lowerbound of 95% confidence interval for Sharpe Ratio | -0.664 | ||||
Upperbound of 95% confidence interval for Sharpe Ratio | 1.511 | ||||
Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.664 | ||||
Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.511 | ||||
Statistics related to Sortino ratio | |||||
Sortino ratio | 0.735 | ||||
Upside Potential Ratio | 6.244 | ||||
Upside part of mean | 2.070 | ||||
Downside part of mean | -1.826 | ||||
Upside SD | 0.470 | ||||
Downside SD | 0.331 | ||||
N nonnegative terms | 303.000 | ||||
N negative terms | 548.000 | ||||
Statistics related to linear regression on benchmark | |||||
N of observations | 851.000 | ||||
Mean of predictor | 0.188 | ||||
Mean of criterion | 0.244 | ||||
SD of predictor | 0.163 | ||||
SD of criterion | 0.575 | ||||
Covariance | 0.007 | ||||
r | 0.073 | ||||
b (slope, estimate of beta) | 0.258 | ||||
a (intercept, estimate of alpha) | 0.195 | ||||
Mean Square Error | 0.329 | ||||
DF error | 849.000 | ||||
t(b) | 2.130 | ||||
p(b) | 0.017 | ||||
t(a) | 0.611 | ||||
p(a) | 0.271 | ||||
Lowerbound of 95% confidence interval for beta | 0.020 | ||||
Upperbound of 95% confidence interval for beta | 0.495 | ||||
Lowerbound of 95% confidence interval for alpha | -0.432 | ||||
Upperbound of 95% confidence interval for alpha | 0.822 | ||||
Treynor index (mean / b) | 0.946 | ||||
Jensen alpha (a) | 0.195 | ||||
Ratio statistics of excess log return rates | |||||
Statistics related to Sharpe ratio | |||||
Mean | 0.094 | ||||
SD | 0.537 | ||||
Sharpe ratio (Glass type estimate) | 0.175 | ||||
Sharpe ratio (Hedges UMVUE) | 0.175 | ||||
df | 850.000 | ||||
t | 0.315 | ||||
p | 0.376 | ||||
Lowerbound of 95% confidence interval for Sharpe Ratio | -0.913 | ||||
Upperbound of 95% confidence interval for Sharpe Ratio | 1.262 | ||||
Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.913 | ||||
Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.262 | ||||
Statistics related to Sortino ratio | |||||
Sortino ratio | 0.266 | ||||
Upside Potential Ratio | 5.605 | ||||
Upside part of mean | 1.979 | ||||
Downside part of mean | -1.886 | ||||
Upside SD | 0.405 | ||||
Downside SD | 0.353 | ||||
N nonnegative terms | 303.000 | ||||
N negative terms | 548.000 | ||||
Statistics related to linear regression on benchmark | |||||
N of observations | 851.000 | ||||
Mean of predictor | 0.175 | ||||
Mean of criterion | 0.094 | ||||
SD of predictor | 0.163 | ||||
SD of criterion | 0.537 | ||||
Covariance | 0.006 | ||||
r | 0.073 | ||||
b (slope, estimate of beta) | 0.241 | ||||
a (intercept, estimate of alpha) | 0.052 | ||||
Mean Square Error | 0.288 | ||||
DF error | 849.000 | ||||
t(b) | 2.137 | ||||
p(b) | 0.016 | ||||
t(a) | 0.174 | ||||
p(a) | 0.431 | ||||
Lowerbound of 95% confidence interval for beta | 0.020 | ||||
Upperbound of 95% confidence interval for beta | 0.462 | ||||
Lowerbound of 95% confidence interval for alpha | -0.533 | ||||
Upperbound of 95% confidence interval for alpha | 0.637 | ||||
Treynor index (mean / b) | 0.390 | ||||
Jensen alpha (a) | 0.052 | ||||
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%) | 0.018 | ||||
Expected Shortfall on VaR | 0.040 | ||||
ORDER STATISTICS | |||||
Quartiles of return rates | |||||
Number of observations | 851.000 | ||||
Minimum | 0.743 | ||||
Quartile 1 | 0.997 | ||||
Median | 1.000 | ||||
Quartile 3 | 1.006 | ||||
Maximum | 1.591 | ||||
Mean of quarter 1 | 0.973 | ||||
Mean of quarter 2 | 1.000 | ||||
Mean of quarter 3 | 1.001 | ||||
Mean of quarter 4 | 1.030 | ||||
Inter Quartile Range | 0.010 | ||||
Number outliers low | 105.000 | ||||
Percentage of outliers low | 0.123 | ||||
Mean of outliers low | 0.954 | ||||
Number of outliers high | 104.000 | ||||
Percentage of outliers high | 0.122 | ||||
Mean of outliers high | 1.049 | ||||
Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
Extreme Value Index (moments method) | 0.553 | ||||
VaR(95%) (moments method) | 0.017 | ||||
Expected Shortfall (moments method) | 0.046 | ||||
Extreme Value Index (regression method) | 0.258 | ||||
VaR(95%) (regression method) | 0.026 | ||||
Expected Shortfall (regression method) | 0.048 | ||||
DRAW DOWN STATISTICS | |||||
Quartiles of draw downs | |||||
Number of observations | 27.000 | ||||
Minimum | 0.000 | ||||
Quartile 1 | 0.018 | ||||
Median | 0.029 | ||||
Quartile 3 | 0.050 | ||||
Maximum | 0.786 | ||||
Mean of quarter 1 | 0.007 | ||||
Mean of quarter 2 | 0.025 | ||||
Mean of quarter 3 | 0.040 | ||||
Mean of quarter 4 | 0.222 | ||||
Inter Quartile Range | 0.032 | ||||
Number outliers low | 0.000 | ||||
Percentage of outliers low | 0.000 | ||||
Mean of outliers low | NA | ||||
Number of outliers high | 3.000 | ||||
Percentage of outliers high | 0.111 | ||||
Mean of outliers high | 0.427 | ||||
Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
Extreme Value Index (moments method) | 0.872 | ||||
VaR(95%) (moments method) | 0.227 | ||||
Expected Shortfall (moments method) | 1.880 | ||||
Extreme Value Index (regression method) | 1.631 | ||||
VaR(95%) (regression method) | 0.233 | ||||
Expected Shortfall (regression method) | NA | ||||
COMBINED STATISTICS | |||||
Annualized return (arithmetic extrapolation) | 0.174 | ||||
Compounded annual return (geometric extrapolation) | 0.148 | ||||
Calmar ratio (compounded annual return / max draw down) | 0.188 | ||||
Compounded annual return / average of 25% largest draw downs | 0.667 | ||||
Compounded annual return / Expected Shortfall lognormal | 2.248 | ||||
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) | -972.869 | ||||
Sharpe ratio (Hedges UMVUE) | -967.245 | ||||
df | 130.000 | ||||
t | -687.922 | ||||
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) | -1084.848 | ||||
Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -849.642 | ||||
Statistics related to Sortino ratio | |||||
Sortino ratio | -16.184 | ||||
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 | 0.411 | ||||
Mean of criterion | -0.044 | ||||
SD of predictor | 0.274 | ||||
SD of criterion | 0.000 | ||||
Covariance | 0.000 | ||||
r | 0.175 | ||||
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) | 2.018 | ||||
p(b) | 0.389 | ||||
t(a) | -693.204 | ||||
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) | -1523.594 | ||||
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) | -972.803 | ||||
Sharpe ratio (Hedges UMVUE) | -967.179 | ||||
df | 130.000 | ||||
t | -687.875 | ||||
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) | -1084.774 | ||||
Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -849.584 | ||||
Statistics related to Sortino ratio | |||||
Sortino ratio | -16.184 | ||||
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 | 0.373 | ||||
Mean of criterion | -0.044 | ||||
SD of predictor | 0.276 | ||||
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 | 129.000 | ||||
t(b) | 1.971 | ||||
p(b) | 0.392 | ||||
t(a) | -693.210 | ||||
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) | -1573.335 | ||||
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 | 1.000 | ||||
Percentage of outliers high | 0.008 | ||||
Mean of outliers high | 1.000 | ||||
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 | 0.368 |