Portfolio Metrics

// This source code is subject to the terms of the Mozilla Public License 2.0 at https://mozilla.org/MPL/2.0/
// © luminaryfi


//@version=4
study("Portfolio Metrics", precision=6, overlay=false)
sym = input('SPX', title="benchmark index:", options=['SPX','NDX','DJI'])
length = input(title="input length:", defval=252)
type = input('returns', title="returns", options=['returns','logarithmic returns'])
rf = input('DTB3', title="select risk-free rate:", options=['DTB3'])
disp = input('all', title='display', options=['all','alpha','beta','correlation','maxdd','maxg','stdev','variance','rsquared','group-coefficients','group-profit.loss','group-stats'])
bmla = security(sym, timeframe.period, close, lookahead=barmerge.lookahead_on)
rfla = security(rf, timeframe.period, close, lookahead=barmerge.lookahead_on)
     // SPX = s+p 500
     // NDX = nasdaq 100
     // DJI = dow jones 30
     // DTB3 = 3-month treasury bill: secondary market rate
     // DGS2 = 2-Year treasury bond: constant maturity rate
     // DGS5 = 5-Year treasury bond: constant maturity rate
     // DGS10 = 10-Year treasury bond: constant maturity rate
     // DGS30 = 30-Year treasury bond: constant maturity rate
     // beta = portfolio beta or 'β coefficient'
     // stdev = portfolio standard deviation or 'σ'
     // variance = portfolio variance or 'σ²'



rtp = type=='returns' ? close/close[1]-1 :
      type=='logarithmic returns' ? log(close/close[1]) : close

rtbi = type=='returns' ? bmla/bmla[1]-1 : 
       type=='logarithmic returns' ? log(bmla/bmla[1]) : bmla 
  

rplo = lowest(rtp,length)
rbilo = lowest(rtbi,length)
     // lowest return of portfolio
     // lowest return of market

rphi = highest(rtp,length)
rbihi = highest(rtp,length)
     // highest return of portfolio
     // highest return of market

rpm = sma(rtp,length)
rbim = sma(rtbi,length)
     // mean of portfolio returns
     // mean of market returns

rpdd = rpm - rplo
rbdd = rbim - rbilo
     // mean - lowest of portfolio returns
     // mean - lowest of market returns

rpmg = (rpm - (-rphi))
rbmg = (rbim - (-rbihi))
     // mean + highest of portfolio returns
     // mean + highest of market returns


psigma = stdev(rtp,length)
bsigma = stdev(rtbi,length)
corr = correlation(rtp,rtbi,length)
vari = pow(psigma,2)
rsq = pow(corr,2)
     // psigma = portfolio/stock standard deviation
     // bsigma = benchmark/market standard deviation
     // variance = portfolio(standard deviation^2)
     // r-squared = correlation^2 (power of determination)


    
stdiv = psigma/ bsigma
beta = corr* stdiv
rpre = rtbi - rfla
rskb = beta*rpre
capm = rfla + rskb
alpha = rtp - capm
     // rskb = portfolio beta * risk premium
     // alphp = risk-free lookahead + rskb
     // alpha = portfolio return - capm

correlation = corr
stdev = psigma
mean = rpm
maxdd = rpdd
maxg = rpmg
variance = vari
rsquared= rsq
     // variable switch


plot(disp=='alpha' or disp=='group-coefficients' or disp=='all'?alpha:na, color=#9d8c2f, linewidth=2, title='α')
plot(disp=='beta' or disp=='group-coefficients' or disp=='all'?beta:na, color=#707070, linewidth=2, title='β')
plot(disp=='maxdd' or disp=='group-profit.loss'or disp=='all'?maxdd:na, color=#8b0000, linewidth=2, title='max.drawdown')
plot(disp=='maxg' or disp=='group-profit.loss' or disp=='all'?maxg:na, color=#008b00, linewidth=2, title='max.gain')
plot(disp=='stdev' or disp=='group-stats' or disp=='all'?stdev:na, color=#f57f17, linewidth=2, title='σ')
plot(disp=='variance' or disp=='group-stats' or disp=='all'?variance:na, color=#e65100, linewidth=2, title='σ²')
plot(disp=='correlation' or disp=='group-stats' or disp=='all'?correlation:na, color=#663bb7, linewidth=2, title='ρ')
plot(disp=='rsquared' or disp=='group-stats' or disp=='all'?rsquared:na, color=#46287d, linewidth=2, title='ρ²')


hline(2.000, color=color.white, linestyle=hline.style_dotted, linewidth=1)
hline(1.750, color=color.white, linestyle=hline.style_dotted, linewidth=1)
hline(1.500, color=color.white, linestyle=hline.style_dotted, linewidth=1)
hline(1.250, color=color.white, linestyle=hline.style_dotted, linewidth=1)
hline(1.000, color=color.white, linestyle=hline.style_dotted, linewidth=1)
hline(0.750, color=color.white, linestyle=hline.style_dotted, linewidth=1)
hline(0.500, color=color.white, linestyle=hline.style_dotted, linewidth=1)
hline(0.250, color=color.white, linestyle=hline.style_dotted, linewidth=1)
hline(0.000, color=color.white, linestyle=hline.style_dotted, linewidth=1)
hline(-0.250, color=color.white, linestyle=hline.style_dotted, linewidth=1)
hline(-0.500, color=color.white, linestyle=hline.style_dotted, linewidth=1)