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Advanced Statistics: Legacy Metals

Advanced Statistics module contributed by Jules Ellis, C2 Member.

Jules has written a very helpful guide for these statistics.

MonthlyDaily (all)Daily (last 6 mo.)
ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-0.034
 SD0.007
 Sharpe ratio (Glass type estimate) -5.020
 Sharpe ratio (Hedges UMVUE)-4.005
 df4.000
 t-3.240
 p0.984
 Lowerbound of 95% confidence interval for Sharpe Ratio-9.423
 Upperbound of 95% confidence interval for Sharpe Ratio-0.384
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-8.119
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.109
Statistics related to Sortino ratio
 Sortino ratio-2.960
 Upside Potential Ratio0.139
 Upside part of mean0.002
 Downside part of mean-0.035
 Upside SD0.001
 Downside SD0.011
 N nonnegative terms1.000
 N negative terms4.000
Statistics related to linear regression on benchmark
 N of observations5.000
 Mean of predictor0.348
 Mean of criterion-0.034
 SD of predictor0.252
 SD of criterion0.007
 Covariance-0.000
 r-0.037
 b (slope, estimate of beta)-0.001
 a (intercept, estimate of alpha)-0.033
 Mean Square Error0.000
 DF error3.000
 t(b)-0.064
 p(b)0.523
 t(a)-2.539
 p(a)0.958
 Lowerbound of 95% confidence interval for beta-0.050
 Upperbound of 95% confidence interval for beta0.048
 Lowerbound of 95% confidence interval for alpha-0.075
 Upperbound of 95% confidence interval for alpha0.008
 Treynor index (mean / b)34.518
 Jensen alpha (a)-0.033
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.034
 SD0.007
 Sharpe ratio (Glass type estimate) -5.022
 Sharpe ratio (Hedges UMVUE)-4.007
 df4.000
 t-3.242
 p0.984
 Lowerbound of 95% confidence interval for Sharpe Ratio-9.426
 Upperbound of 95% confidence interval for Sharpe Ratio-0.385
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-8.121
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)0.108
Statistics related to Sortino ratio
 Sortino ratio-2.960
 Upside Potential Ratio0.139
 Upside part of mean0.002
 Downside part of mean-0.035
 Upside SD0.001
 Downside SD0.011
 N nonnegative terms1.000
 N negative terms4.000
Statistics related to linear regression on benchmark
 N of observations5.000
 Mean of predictor0.317
 Mean of criterion-0.034
 SD of predictor0.252
 SD of criterion0.007
 Covariance-0.000
 r-0.020
 b (slope, estimate of beta)-0.001
 a (intercept, estimate of alpha)-0.033
 Mean Square Error0.000
 DF error3.000
 t(b)-0.034
 p(b)0.513
 t(a)-2.589
 p(a)0.959
 Lowerbound of 95% confidence interval for beta-0.049
 Upperbound of 95% confidence interval for beta0.048
 Lowerbound of 95% confidence interval for alpha-0.075
 Upperbound of 95% confidence interval for alpha0.008
 Treynor index (mean / b)64.431
 Jensen alpha (a)-0.033
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.006
 Expected Shortfall on VaR0.007
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.005
 Expected Shortfall on VaR0.005
ORDER STATISTICS
Quartiles of return rates
 Number of observations5.000
 Minimum1.000
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.004
 Mean of quarter 11.000
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.004
 Inter Quartile Range0.000
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high1.000
 Percentage of outliers high0.200
 Mean of outliers high1.004
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 observations0.000
 MinimumNA
 Quartile 1NA
 MedianNA
 Quartile 3NA
 MaximumNA
 Mean of quarter 1NA
 Mean of quarter 2NA
 Mean of quarter 3NA
 Mean of quarter 4NA
 Inter Quartile Range0.000
 Number outliers low0.000
 Percentage of outliers lowNA
 Mean of outliers lowNA
 Number of outliers high0.000
 Percentage of outliers highNA
 Mean of outliers highNA
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)0.010
 Compounded annual return (geometric extrapolation)0.010
 Calmar ratio (compounded annual return / max draw down)NA
 Compounded annual return / average of 25% largest draw downsNA
 Compounded annual return / Expected Shortfall lognormal1.541
ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back)
RATIO STATISTICS
Ratio statistics of excess return rates
Statistics related to Sharpe ratio
 Mean-0.028
 SD0.114
 Sharpe ratio (Glass type estimate) -0.242
 Sharpe ratio (Hedges UMVUE)-0.241
 df146.000
 t-0.158
 p0.507
 Lowerbound of 95% confidence interval for Sharpe Ratio-3.240
 Upperbound of 95% confidence interval for Sharpe Ratio2.757
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-3.239
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.758
Statistics related to Sortino ratio
 Sortino ratio-0.419
 Upside Potential Ratio3.510
 Upside part of mean0.231
 Downside part of mean-0.259
 Upside SD0.092
 Downside SD0.066
 N nonnegative terms4.000
 N negative terms143.000
Statistics related to linear regression on benchmark
 N of observations147.000
 Mean of predictor0.418
 Mean of criterion-0.028
 SD of predictor0.205
 SD of criterion0.114
 Covariance-0.001
 r-0.058
 b (slope, estimate of beta)-0.032
 a (intercept, estimate of alpha)-0.014
 Mean Square Error0.013
 DF error145.000
 t(b)-0.699
 p(b)0.537
 t(a)-0.080
 p(a)0.504
 Lowerbound of 95% confidence interval for beta-0.123
 Upperbound of 95% confidence interval for beta0.059
 Lowerbound of 95% confidence interval for alpha-0.361
 Upperbound of 95% confidence interval for alpha0.333
 Treynor index (mean / b)0.856
 Jensen alpha (a)-0.014
Ratio statistics of excess log return rates
Statistics related to Sharpe ratio
 Mean-0.034
 SD0.113
 Sharpe ratio (Glass type estimate) -0.301
 Sharpe ratio (Hedges UMVUE)-0.299
 df146.000
 t-0.197
 p0.508
 Lowerbound of 95% confidence interval for Sharpe Ratio-3.299
 Upperbound of 95% confidence interval for Sharpe Ratio2.698
 Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation)-3.298
 Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation)2.699
Statistics related to Sortino ratio
 Sortino ratio-0.509
 Upside Potential Ratio3.402
 Upside part of mean0.227
 Downside part of mean-0.261
 Upside SD0.090
 Downside SD0.067
 N nonnegative terms4.000
 N negative terms143.000
Statistics related to linear regression on benchmark
 N of observations147.000
 Mean of predictor0.397
 Mean of criterion-0.034
 SD of predictor0.204
 SD of criterion0.113
 Covariance-0.001
 r-0.058
 b (slope, estimate of beta)-0.032
 a (intercept, estimate of alpha)-0.021
 Mean Square Error0.013
 DF error145.000
 t(b)-0.703
 p(b)0.537
 t(a)-0.122
 p(a)0.506
 Lowerbound of 95% confidence interval for beta-0.123
 Upperbound of 95% confidence interval for beta0.058
 Lowerbound of 95% confidence interval for alpha-0.364
 Upperbound of 95% confidence interval for alpha0.322
 Treynor index (mean / b)1.053
 Jensen alpha (a)-0.021
Risk estimates for a one-period unit investment (parametric)
assuming log normal returns and losses (using central moments from Sharpe statistics)
 VaR(95%)0.010
 Expected Shortfall on VaR0.013
assuming Pareto losses only (using partial moments from Sortino statistics)
 VaR(95%)0.003
 Expected Shortfall on VaR0.006
ORDER STATISTICS
Quartiles of return rates
 Number of observations147.000
 Minimum0.968
 Quartile 11.000
 Median1.000
 Quartile 31.000
 Maximum1.053
 Mean of quarter 10.998
 Mean of quarter 21.000
 Mean of quarter 31.000
 Mean of quarter 41.003
 Inter Quartile Range0.000
 Number outliers low7.000
 Percentage of outliers low0.048
 Mean of outliers low0.987
 Number of outliers high4.000
 Percentage of outliers high0.027
 Mean of outliers high1.025
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)0.163
 VaR(95%) (regression method)0.001
 Expected Shortfall (regression method)0.008
DRAW DOWN STATISTICS
Quartiles of draw downs
 Number of observations2.000
 Minimum0.017
 Quartile 10.031
 Median0.045
 Quartile 30.059
 Maximum0.073
 Mean of quarter 10.017
 Mean of quarter 2NA
 Mean of quarter 3NA
 Mean of quarter 40.073
 Inter Quartile Range0.028
 Number outliers low0.000
 Percentage of outliers low0.000
 Mean of outliers lowNA
 Number of outliers high0.000
 Percentage of outliers high0.000
 Mean of outliers highNA
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)0.010
 Compounded annual return (geometric extrapolation)0.010
 Calmar ratio (compounded annual return / max draw down)0.139
 Compounded annual return / average of 25% largest draw downs0.139
 Compounded annual return / Expected Shortfall lognormal0.810