/// <summary>
/// To calculate Burke ratio we take the difference between the portfolio
/// return and the risk free rate and we divide it by the square root of the
/// sum of the square of the drawdowns. To calculate the modified Burke ratio
/// we just multiply the Burke ratio by the square root of the number of datas.
/// （一种调整收益率的计算方式，调整是通过drawdown的平方和进行的）
/// </summary>
func BurkeRatio(Ra *utils.SlidingWindow, Rf float64, scale float64) (float64, error) {
var len = Ra.Count()
var in_drawdown = false
var peak = 1
var temp = 0.0
drawdown, err := utils.NewSlidingWindow(len)
if err != nil {
return math.NaN(), err
}
for i := 1; i < len; i++ {
if Ra.Data()[i] < 0 {
if !in_drawdown {
peak = i - 1
in_drawdown = true
}
} else {
if in_drawdown {
temp = 1.0
for j := peak + 1; j < i; j++ {
temp = temp * (1.0 + Ra.Data()[j])
}
drawdown.Add(temp - 1.0) //Source
in_drawdown = false
}
}
}
if in_drawdown {
temp = 1.0
for j := peak + 1; j < len; j++ {
temp = temp * (1.0 + Ra.Data()[j])
}
drawdown.Add(temp - 1.0) //Source
//drawdown.Add((temp - 1.0) * 100.0)
in_drawdown = false
}
//var Rp = Annualized(Ra, scale, true) - 1.0--->Source
Rp, err := Annualized(Ra, scale, true)
if err != nil {
return math.NaN(), err
}
var result float64
if drawdown.Count() != 0 {
pow_Sliding, err := utils.Power(drawdown, 2)
if err != nil {
return math.NaN(), err
}
Rf = Rf * scale
result = (Rp - Rf) / math.Sqrt(pow_Sliding.Sum())
} else {
result = 0
}
modified := true
if modified {
result = result * math.Sqrt(float64(len))
}
return result, 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>
/// 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>
/// 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>
/// downside risk (deviation, variance) of the return distribution
/// Downside deviation, semideviation, and semivariance are measures of downside
/// risk.
/// </summary>
// = "full"
// = false
//func DownsideDeviation(Ra *utils.SlidingWindow, MAR *utils.SlidingWindow, method string, potential bool) float64 {
func DownsideDeviation(Ra *utils.SlidingWindow, MAR *utils.SlidingWindow) (float64, error) {
if Ra == nil {
return math.NaN(), errors.New("In DownsideDeviation, Ra == nil")
}
if Ra.Count() <= 0 {
return math.NaN(), errors.New("In DownsideDeviation, Ra.Count() <= 0")
}
r, err := utils.NewSlidingWindow(Ra.Count())
if err != nil {
return math.NaN(), err
}
newMAR, err := utils.NewSlidingWindow(Ra.Count())
if err != nil {
return math.NaN(), err
}
len := 0.0
result := 0.0
for i := 0; i < Ra.Count(); i++ {
if Ra.Data()[i] < MAR.Data()[i] {
r.Add(Ra.Data()[i])
newMAR.Add(MAR.Data()[i])
}
}
potential := false
method := "subset"
if method == "full" {
len = float64(Ra.Count())
} else if method == "subset" {
len = float64(r.Count())
} else {
return math.NaN(), errors.New("In DownsideDeviation, method default !!!")
}
if newMAR.Count() <= 0 || r.Count() <= 0 || len <= 0 {
return math.NaN(), errors.New("In DownsideDeviation, newMAR.Count() <= 0 || r.Count() <= 0 || len <= 0")
}
if potential {
sub_Sliding, err := utils.Sub(newMAR, r)
if err != nil {
return math.NaN(), err
}
result = sub_Sliding.Sum() / len
} else {
sub_Sliding, err := utils.Sub(newMAR, r)
if err != nil {
return math.NaN(), err
}
pow_Sliding, err := utils.Power(sub_Sliding, 2.0)
if err != nil {
return math.NaN(), err
}
result = math.Sqrt(pow_Sliding.Sum() / len)
}
return result, 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
}