/// <summary>
/// Upside Potential Ratio,compared to Sortino, was a further improvement, extending the
/// measurement of only upside on the numerator, and only downside of the
/// denominator of the ratio equation.
/// （分子只考虑超过MAR部分，分母只考虑DownsideDeviation的下跌风险）
/// </summary>
func UpsidePotentialRatio(Ra *utils.SlidingWindow, MAR float64) (float64, error) {
//var r = Ra.Where<float64>(singleData => singleData > MAR).ToList<float64>();
r, err := utils.AboveValue(Ra, MAR)
if err != nil {
return math.NaN(), err
}
var length int
method := "subset"
switch method {
case "full":
length = Ra.Count()
break
case "subset":
length = r.Count()
break
default:
return math.NaN(), errors.New("In UpsidePotentialRatio, method is default !!!")
}
add_Sliding, err := utils.Add(-MAR, r)
if err != nil {
return math.NaN(), err
}
dd2Data, err := DownsideDeviation2(Ra, MAR)
if err != nil {
return math.NaN(), err
}
var result = (add_Sliding.Sum() / float64(length)) / dd2Data
return result, nil
}
/// <summary>
/// 峰度
/// </summary>
// = "sample"
func Kurtosis(Ra *utils.SlidingWindow) (float64, error) {
if Ra == nil || Ra.Count() <= 3 {
return math.NaN(), errors.New("In Kurtosis, Ra == nil || Ra.Count() <= 3")
}
n := float64(Ra.Count())
method := "sample_excess"
switch method {
case "sample_excess": //kurtosis = sum((x-mean(x))^4/var(x)^2)*n*(n+1)/((n-1)*(n-2)*(n-3)) - 3*(n-1)^2/((n-2)*(n-3))
var_data, err := Variance(Ra)
if err != nil {
return math.NaN(), err
}
add_Sliding, err := utils.Add(-Ra.Average(), Ra)
if err != nil {
return math.NaN(), err
}
pow_Sliding, err := utils.Power(add_Sliding, 4.0)
if err != nil {
return math.NaN(), err
}
multi_Sliding, err := utils.Multi(1.0/math.Pow(var_data, 2.0), pow_Sliding)
if err != nil {
return math.NaN(), err
}
return multi_Sliding.Sum()*n*(n+1.0)/((n-1.0)*(n-2.0)*(n-3.0)) - 3*(n-1.0)*(n-1.0)/((n-2.0)*(n-3.0)), nil
default:
return math.NaN(), errors.New("In Kurtosis, method is default")
}
return math.NaN(), nil
}
/// <summary>
/// Kappa is a generalized downside risk-adjusted performance measure.
/// To calculate it, we take the difference of the mean of the distribution
/// to the target and we divide it by the l-root of the lth lower partial
/// moment. To calculate the lth lower partial moment we take the subset of
/// returns below the target and we sum the differences of the target to
/// these returns. We then return return this sum divided by the length of
/// the whole distribution.
/// （非年化的超MAR平均收益率通过l阶根的低于MAR的收益率序列的l阶矩）
/// </summary>
func Kappa(Ra *utils.SlidingWindow, MAR float64, l float64) (float64, error) {
undervalues, err := utils.NewSlidingWindow(Ra.Count())
if err != nil {
return math.NaN(), err
}
for i := 0; i < Ra.Count(); i++ {
if Ra.Data()[i] < MAR {
undervalues.Add(Ra.Data()[i])
}
}
var n = float64(Ra.Count())
var m = float64(Ra.Average())
neg_Sliding, err := utils.Negative(undervalues)
if err != nil {
return math.NaN(), err
}
add_Sliding, err := utils.Add(MAR, neg_Sliding)
if err != nil {
return math.NaN(), err
}
pow_Sliding, err := utils.Power(add_Sliding, float64(l))
if err != nil {
return math.NaN(), err
}
var temp = pow_Sliding.Sum() / n
return (m - MAR) / math.Pow(temp, (1.0/float64(l))), nil
}
/// <summary>
/// 偏度
/// </summary>
// default = "moment"
func Skewness(Ra *utils.SlidingWindow) (float64, error) {
if Ra == nil || Ra.Count() <= 2 {
return math.NaN(), errors.New("In Skewness, Ra == nil || Ra.Count() <= 2")
}
n := float64(Ra.Count())
method := "moment"
switch method {
//"moment", "fisher", "sample"
case "moment": //skewness = sum((x-mean(x))^3/sqrt(var(x)*(n-1)/n)^3)/length(x)
var_data, err := Variance(Ra)
if err != nil {
return math.NaN(), err
}
add_Sliding, err := utils.Add(-Ra.Average(), Ra)
if err != nil {
return math.NaN(), err
}
pow_Sliding, err := utils.Power(add_Sliding, 3.0)
if err != nil {
return math.NaN(), err
}
multi_Sliding, err := utils.Multi(1.0/math.Pow(var_data*(n-1.0)/n, 1.5), pow_Sliding)
if err != nil {
return math.NaN(), err
}
return multi_Sliding.Sum() / n, nil
default:
return math.NaN(), errors.New("In Skewness, method is default")
}
return math.NaN(), nil
}
/// <summary>
/// 收益率序列的几何均值，非年化
/// </summary>
func MeanGeometric(Ra *utils.SlidingWindow) (float64, error) {
if Ra.Count() <= 0 {
return math.NaN(), errors.New("In MeanGeometric, Ra.Count() <= 0")
}
add_Sliding, _ := utils.Add(1, Ra)
log_Sliding, _ := utils.Log(add_Sliding)
return math.Exp(log_Sliding.Average()) - 1.0, nil
}
/// <summary>
/// To calculate Mean absolute deviation we take
/// the sum of the absolute value of the difference between the returns and the mean of the returns
/// and we divide it by the number of returns.
/// （描述收益率偏离均值得一个指标）
/// </summary>
func MeanAbsoluteDeviation(Ra *utils.SlidingWindow) (float64, error) {
if Ra.Count() <= 0 {
return math.NaN(), errors.New("In MeanAbsoluteDeviation, Ra.Count() <= 0")
}
add_Sliding, _ := utils.Add(-Ra.Average(), Ra)
ads_Sliding, _ := utils.Abs(add_Sliding)
return ads_Sliding.Sum() / float64(Ra.Count()), nil
}
/// <param name="returns"></param>
/// <returns></returns>
func Centered(returns *utils.SlidingWindow) (*utils.SlidingWindow, error) {
if returns == nil {
return nil, errors.New("Centered Sliding window is nil")
}
if returns.Count() == 0 {
return nil, errors.New("Centered Count is Zero !!!")
}
return utils.Add(-returns.Average(), returns)
}
/// <summary>
/// epsilon与R中不同,但似乎没有影响
/// Specific risk is the standard deviation of the error term in the
/// regression equation.
/// </summary>
func SpecificRisk(Ra *utils.SlidingWindow, Rb *utils.SlidingWindow, scale float64, Rf float64) (float64, error) {
//Period = Frequency(Ra)
alpha, err := Alpha2(Ra, Rb, Rf)
if err != nil {
return math.NaN(), err
}
beta, err := Beta2(Ra, Rb, Rf)
if err != nil {
return math.NaN(), err
}
add_Ra_Sliding, err := utils.Add(-Rf, Ra)
if err != nil {
return math.NaN(), err
}
add_Rb_Sliding, err := utils.Add(-Rf, Rb)
if err != nil {
return math.NaN(), err
}
multi_beta_Slidinig, err := utils.Multi(beta, add_Rb_Sliding)
if err != nil {
return math.NaN(), err
}
sub_Ra_Beta, err := utils.Sub(add_Ra_Sliding, multi_beta_Slidinig)
if err != nil {
return math.NaN(), err
}
epsilon, err := utils.Add(-alpha, sub_Ra_Beta)
if err != nil {
return math.NaN(), err
}
var_eps, err := Variance(epsilon)
if err != nil {
return math.NaN(), err
}
var result = math.Sqrt(var_eps*float64(epsilon.Count()-1)/float64(epsilon.Count())) * math.Sqrt(float64(scale))
return result, nil
}
func PainRatio(Ra *utils.SlidingWindow, Rf float64, scale float64) (float64, error) {
PI, err := PainIndex(Ra)
if err != nil {
return math.NaN(), err
}
n := Ra.Count()
add_Sliding, err := utils.Add(1.0, Ra)
if err != nil {
return math.NaN(), err
}
prod_Sliding, err := utils.Prod(add_Sliding)
if err != nil {
return math.NaN(), err
}
Rp := math.Pow(prod_Sliding, float64(scale)/float64(n)) - 1.0
Rf = Rf * scale
return (Rp - Rf) / PI, nil
}
/// <param name="returns"></param>
/// <param name="geometric"></param>
/// <returns></returns>
func Cumulative(returns *utils.SlidingWindow, geometric bool) (float64, error) {
if returns == nil {
return math.NaN(), errors.New("Cumulative Sliding window is Nil !!!")
}
if returns.Count() == 0 {
return math.NaN(), errors.New("Cumulative Count == 0 !!")
}
if !geometric {
return (returns.Sum()), nil
} else {
add_data, err := utils.Add(1.0, returns)
if err != nil {
return math.NaN(), err
}
prod_data, err := utils.Prod(add_data)
if err != nil {
return math.NaN(), err
}
return (prod_data - 1.0), nil
}
}
/// <param name="returns"></param>
/// <param name="scale"></param>
/// <param name="geometric"></param>
/// <returns></returns>
func Annualized(returns *utils.SlidingWindow, scale float64, geometric bool) (float64, error) {
if returns == nil {
return math.NaN(), errors.New("Returns Utils Sliding Window is nil")
}
if returns.Count() == 0 {
return math.NaN(), errors.New("Returns Windows content is Zero")
}
n := returns.Count()
if geometric {
add_Sliding, err := utils.Add(1.0, returns)
if err != nil {
return math.NaN(), err
}
prod_Data, err := utils.Prod(add_Sliding)
if err != nil {
return math.NaN(), err
}
return math.Pow(prod_Data, float64(scale)/float64(n)) - 1.0, nil
} else {
return returns.Average() * float64(scale), nil
}
}
/// <summary>
/// Upside Risk is the similar of semideviation taking the return above the
/// Minimum Acceptable Return instead of using the mean return or zero.
/// （一般来说，非对称类的比较，单求此统计量意义有限）
/// </summary>
func UpsideRisk(Ra *utils.SlidingWindow, MAR float64, stat string) (float64, error) {
r, err := utils.AboveValue(Ra, MAR)
if err != nil {
return math.NaN(), err
}
var length float64
method := "subset"
switch method {
case "full":
length = float64(Ra.Count())
break
case "subset":
length = float64(r.Count())
break
default:
return math.NaN(), errors.New("In Upside Risk, method is default !!!")
}
if length <= 0 {
return 0, nil
}
var result float64
switch stat {
case "risk":
add_Sliding, err := utils.Add(-MAR, r)
if err != nil {
return math.NaN(), err
}
pow_Sliding, err := utils.Power(add_Sliding, 2.0)
if err != nil {
return math.NaN(), err
}
multi_Sliding, err := utils.Multi(1.0/length, pow_Sliding)
if err != nil {
return math.NaN(), err
}
result = math.Sqrt(multi_Sliding.Sum())
break
case "variance":
add_Sliding, err := utils.Add(-MAR, r)
if err != nil {
return math.NaN(), err
}
pow_Sliding, err := utils.Power(add_Sliding, 2.0)
if err != nil {
return math.NaN(), err
}
multi_Sliding, err := utils.Multi(1.0/length, pow_Sliding)
if err != nil {
return math.NaN(), err
}
result = multi_Sliding.Sum()
break
case "potential":
add_Sliding, err := utils.Add(-MAR, r)
if err != nil {
return math.NaN(), err
}
multi_Slding, err := utils.Multi(1.0/length, add_Sliding)
if err != nil {
return math.NaN(), err
}
result = multi_Slding.Sum()
break
default:
return math.NaN(), errors.New("In UpSide Risk, method is default !!!")
}
return result, nil
}
/// <summary>
/// Appraisal ratio is the Jensen's alpha adjusted for specific risk. The numerator
/// is divided by specific risk instead of total risk.
/// </summary>
func AppraisalRatio(Ra *utils.SlidingWindow, Rb *utils.SlidingWindow, scale float64, Rf float64, method string) (float64, error) {
var result = 0.0
switch method {
case "appraisal":
be_data, err := Beta2(Ra, Rb, Rf)
if err != nil {
return math.NaN(), err
}
multi_Sliding, err := utils.Multi(be_data, Rb)
if err != nil {
return math.NaN(), err
}
sub_Sliding, err := utils.Sub(Ra, multi_Sliding)
if err != nil {
return math.NaN(), err
}
al_data, err := Alpha2(Ra, Rb, Rf)
if err != nil {
return math.NaN(), err
}
epsilon, err := utils.Add(-al_data, sub_Sliding)
if err != nil {
return math.NaN(), err
}
add_Sliding, err := utils.Add(-epsilon.Average(), epsilon)
if err != nil {
return math.NaN(), err
}
pow_Sliding, err := utils.Power(add_Sliding, 2)
if err != nil {
return math.NaN(), err
}
specifikRisk := math.Sqrt(pow_Sliding.Sum()/float64(epsilon.Count())) * math.Sqrt(float64(scale))
jsa_data, err := JensenAlpha2(Ra, Rb, Rf, scale)
if err != nil {
return math.NaN(), err
}
result = jsa_data / specifikRisk
break
case "modified":
jsa2_data, err := JensenAlpha2(Ra, Rb, Rf, scale)
if err != nil {
return math.NaN(), err
}
be2_data, err := Beta2(Ra, Rb, Rf)
if err != nil {
return math.NaN(), err
}
result = jsa2_data / be2_data
break
case "alternative":
jsa2_data, err := JensenAlpha2(Ra, Rb, Rf, scale)
if err != nil {
return math.NaN(), err
}
sr_data, err := SystematicRisk(Ra, Rb, scale, Rf)
if err != nil {
return math.NaN(), err
}
result = jsa2_data / sr_data
break
default:
return math.NaN(), errors.New("In AppraisalRatio, method is default !!!")
}
return result, nil
}
/// <param name="returns"></param>
/// <param name="Rf"></param>
/// <returns></returns>
func Excess2(returns *utils.SlidingWindow, Rf float64) (*utils.SlidingWindow, error) {
return utils.Add(-Rf, returns)
}