Fund key figures for comparison with a benchmark
The key figures in this category are either time series or refer to an evaluation date.
Time_series.InformationRatio[Consolidation;Periods;Date;Safe_Returns;Logarithmic_Returns]→Number
Consolidation (figure[1]): The parameter specifies the consolidation of the time series in days, where "30" means month, "7" weeks and everything else means the number of trading days between two points.
Periods (figure [252]): The number of points in the time series over which the calculation is to be performed.
Date (date).
Sicherer_Zins (Secure interest rate of the currency).
Logarithmic_Returns (Boolean[False]).
Result: The InformationRatio function returns the information ratio. This ratio is the quotient of Jensen alpha and the tracking error, i.e. it can be seen as an extension of the Sharpe ratio, and provides an indication of how (with what outperformance) a deviation from the benchmark is rewarded.
Time_series.JensenRegressionAlpha[underlying_securities_time_series;periods;date;safe_interest;logarithmic_returns]→number
Base paper time series (time series).
Periods (figure [252]): The number of points in the time series over which the calculation is to be performed.
Date (date).
Sicherer_Zins (Secure interest rate of the currency).
Logarithmic_Returns (Boolean[False]).
Result: The JensenRegressionAlpha function returns the Jensen alpha. This key figure can be used as an assessment measure for the performance of the management (of a fund) in relation to the risk-adjusted benchmark return. The rule is that a positive alpha implies outperformance.
TimeSeries.JensenRegressionBeta[underlying_securities_time_series;Periods;Date;Safe_interest;Logarithmic_returns]→number
Base paper time series (time series).
Periods (figure [252]): The number of points in the time series over which the calculation is to be performed.
Date (date).
Sicherer_Zins (Secure interest rate of the currency).
Logarithmic_Returns (Boolean[False]).
Result: The JensenRegressionBeta function returns the Jensen beta. This key figure can be interpreted as a measure of risk and measures the dependency of the risk-adjusted return on securities on the risk-adjusted benchmark return.
Time_series.modigli_measure[Consolidation;Periods;Date;Safe_interest;Logarithmic_returns]→number
Consolidation (figure[1]): The parameter specifies the consolidation of the time series in days, where "30" means month, "7" weeks and everything else means the number of trading days between two points.
Periods (figure [252]): The number of points in the time series over which the calculation is to be performed.
Date (date).
Sicherer_Zins (Secure interest rate of the currency).
Logarithmic_Returns (Boolean[False]).
Result: The Modigliani measure function returns the Modigliani measure. This key figure is the product of the excess return compared to a risk-free investment and the quotient of the volatilities of the benchmark and the security, i.e. it measures the excess return achieved relative to a benchmark as a percentage.
TimeSeries.NegativeReturnElasticity[UnderlyingSecuritiesTimeSeries;Periods;Date;Logarithmic_Returns]→Number
Base paper time series (time series).
Periods (figure [252]): The number of points in the time series over which the calculation is to be performed.
Date (date).
Sicherer_Zins (Secure interest rate of the currency).
Logarithmic_Returns (Boolean[False]).
Result: The NegativeReturnElasticity function provides the negative elasticity, i.e. the dependency of security performance on the underlying security performance in a falling market phase.
Time_series.outperformance[underlying_securities_time_series;Periods;Log_returns]→Time_series
Base paper time series (time series).
Periods (figure [252]): The number of points in the time series over which the calculation is to be performed.
Logarithmic_Returns (Boolean[False]).
Result: The Outperformance function returns the outperformance. This is defined as the (percentage) increase or decrease in income over a period of n periods (i.e. depending on the consolidation).
TimeSeries.PositiveReturnElasticity[underlying_securities_time_series;periods;date;logarithmic_returns]→number
Base paper time series (time series).
Periods (figure [252]): The number of points in the time series over which the calculation is to be performed.
Date (date).
Logarithmic_Returns (Boolean[False]).
Result: The PositiveReturnElasticity function provides the positive elasticity, i.e. the dependency of security performance on the underlying security performance in a rising market phase.
Time_series.ProbabilityOfOutperformance[underlying_securities_time_series;periods;log_returns]→Time_series
Base paper time series.
Periods (figure [252]): The number of points in the time series over which the calculation is to be performed.
Logarithmic_Returns (Boolean[False]).
Result: The ProbabilityOfOutperformance function provides the probability of outperformance. It is defined as the quotient of the number of periods with positive outperformance and the number of observation periods n in a period of n periods (i.e. depending on the consolidation).
Fund.SharpeRatio[date;years;risk-free_return]→number
Date (date).
Years (number).
Risk-free_interest_rate (safe_interest_rate of the currency).
Result: The SharpeRatio function returns Sharpe ratios. The key figure is the ratio of excess return compared to a risk-free investment and volatility, i.e. it measures the excess return achieved per unit of risk.
Time_series.SharpeRatioEx[Consolidation;Periods;Date;Safe_Returns;Logarithmic_Returns]→number
Consolidation (figure[1]): The parameter specifies the consolidation of the time series in days, where "30" means month, "7" weeks and everything else means the number of trading days between two points.
Periods (figure [252]): The number of points in the time series over which the volatility is to be calculated.
Date (date).
Sicherer_Zins (Secure interest rate of the currency).
Logarithmic_Returns (Boolean[False]).
Result: The SharpeRatioEx function returns the Sharpe ratio with an extended parameterization. The Sharpe ratio is the ratio of the excess return over a risk-free investment and volatility, i.e. it measures the excess return achieved per unit of risk.
TimeSeries.StabilityOfOutperformance[UnderlyingSecuritiesTimeSeries;Periods;Logarithmic_Returns]→TimeSeries
Base paper time series.
Periods (figure [252]): The number of points in the time series over which the calculation is to be performed.
Logarithmic_Returns (Boolean[False]).
Result: The StabilityOfOutperformance function provides the stability of the outperformance. It is defined as the annualized standard deviation over n sample periods of the outperformance time series in a period of n periods (i.e. depending on the consolidation).
Time_series.trackingerror[Underlying_securities_time_series;Periods;Logarithmic_returns]→Time_series
Base paper time series (time series).
Periods (figure [252]): The number of points in the time series over which the calculation is to be performed.
Logarithmic_Returns (Boolean[False]).
Result: The tracking error function returns the tracking error. It is defined as the annualized standard deviation over n sample periods of the difference time series of security performance and underlying security performance.
Fund.TreynorRatio[date;years;risk-free_interest]→number
Date (date).
Years (number).
Risk-free_interest_rate (safe_interest_rate of the currency).
Result: The TreynorRatio function returns the Treynor ratio. This key figure is the quotient of the additional return compared to a risk-free investment and the Jensen beta.
Time_series.TreynorRatioEx[Consolidation;Periods;Date;Safe_Returns;Logarithmic_Returns]→Number
Consolidation (figure[1]): The parameter specifies the consolidation of the time series in days, where "30" means month, "7" weeks and everything else means the number of trading days between two points.
Periods (figure [252]): The number of points in the time series over which the calculation is to be performed.
Date (date).
Sicherer_Zins (Secure interest rate of the currency).
Logarithmic_Returns (Boolean[False]).
Result: The TreynorRatioEx function returns the Treynor ratio with extended parameterization. The Treynor ratio is the ratio of the excess return over a risk-free investment and the Jensen beta.