Cyclical vs. Defensive Sector Alpha

study(title="Cyclical vs. Defensive Sector Alpha", shorttitle="Cyclical vs. Defensive Sector Alpha (%)")

////SHOWS MEAN US CYCLICAL vs. DEFENSIVE MARKET SECTOR EXCESS RETURNS
//Alpha is a measure of the active return on an investment, the performance of that investment compared to a suitable market index, in %
//alpha < 0: the investment has earned too little for its risk (or, was too risky for the return)
//alpha = 0: the investment has earned a return adequate for the risk taken
//alpha > 0: the investment has a return in excess of the reward for the assumed risk
//https://en.wikipedia.org/wiki/Alpha_(finance)

//Beta Calculation
sym = "SPY", res=period, src = close, length = input(title = "Beta Window", defval=300, minval=1)
ovr = security(sym, res, src)

sym2 = "XLF"
ovr2 = security(sym2, res, src)

sym3 = "XLK"
ovr3 = security(sym3, res, src)

sym4 = "XLI"
ovr4 = security(sym4, res, src)

sym5 = "XLB"
ovr5 = security(sym5, res, src)

sym6 = "XLV"
ovr6 = security(sym6, res, src)

sym7 = "XLU"
ovr7 = security(sym7, res, src)

sym8 = "XLE"
ovr8 = security(sym8, res, src)

sym9 = "XLP"
ovr9 = security(sym9, res, src)

sym10 = "XLY"
ovr10 = security(sym10, res, src)

//////////////////////////////////////////    FINANCIALS

retxlf = log(ovr2) - log(ovr2[1])
retb = log(ovr) - log(ovr[1])
secd = stdev(retxlf, length), mktd = stdev(retb, length)
Betaxlf = correlation(retxlf, retb, length) * secd / mktd

//Alpha Calculation
y = input(title="alpha period", type=integer, defval=90, minval=1, maxval=1000)
retxlf2 = log(ovr2) - log(ovr2[y])
retb2 = log(ovr) - log(ovr[y])
alphaxlf = retxlf2 - retb2*Betaxlf
//plot(alphaxlf*100, color=green, style=line, transp=40, title='Fin')

//////////////////////////////////////////    TECHNOLOGY

retxlk = log(ovr3) - log(ovr3[1])
secdxlk = stdev(retxlk, length)
Betaxlk = correlation(retxlk, retb, length) * secdxlk / mktd

//Alpha Calculation

retxlk3 = log(ovr3) - log(ovr3[y])
alphaxlk = retxlk3 - retb2*Betaxlk
//plot(alphaxlk*100, color=blue, style=line, transp=40, title='Tech')

//////////////////////////////////////////    INDUSTRIALS

retxli = log(ovr4) - log(ovr4[1])
secdxli = stdev(retxli, length)
Betaxli = correlation(retxli, retb, length) * secdxli / mktd

//Alpha Calculation

retxli3 = log(ovr4) - log(ovr4[y])
alphaxli = retxli3 - retb2*Betaxli
//plot(alphaxli*100, color=aqua, style=line, transp=40, title='Indu')


//////////////////////////////////////////    MATERIALS

retxlb = log(ovr5) - log(ovr5[1])
secdxlb = stdev(retxlb, length)
Betaxlb = correlation(retxlb, retb, length) * secdxlb / mktd

//Alpha Calculation

retxlb2 = log(ovr5) - log(ovr5[y])
alphaxlb = retxlb2 - retb2*Betaxlb
//plot(alphaxlb*100, color=green, style=line, transp=0, title='Mats')

//////////////////////////////////////////    HEALTHCARE

retxlv = log(ovr6) - log(ovr6[1])
secdxlv = stdev(retxlv, length)
Betaxlv = correlation(retxlv, retb, length) * secdxlv / mktd

//Alpha Calculation

retxlv2 = log(ovr6) - log(ovr6[y])
alphaxlv = retxlv2 - retb2*Betaxlv
//plot(alphaxlv*100, color=red, style=line, transp=40, title='HlthCare')


//////////////////////////////////////////    UTILITIES

retxlu = log(ovr7) - log(ovr7[1])
secdxlu = stdev(retxlu, length)
Betaxlu = correlation(retxlu, retb, length) * secdxlu / mktd

//Alpha Calculation

retxlu2 = log(ovr7) - log(ovr7[y])
alphaxlu = retxlu2 - retb2*Betaxlu
//plot(alphaxlu*100, color=orange, style=line, transp=60, title='Utlt')

//////////////////////////////////////////    ENERGY

retxle = log(ovr8) - log(ovr8[1])
secdxle = stdev(retxle, length)
Betaxle = correlation(retxle, retb, length) * secdxle / mktd

//Alpha Calculation

retxle2 = log(ovr8) - log(ovr8[y])
alphaxle = retxle2 - retb2*Betaxle
//plot(alphaxle*100, color=orange, style=line, transp=0, title='Nrg')

//////////////////////////////////////////    CONSUMER STAPLES

retxlp = log(ovr9) - log(ovr9[1])
secdxlp = stdev(retxlp, length)
Betaxlp = correlation(retxlp, retb, length) * secdxlp / mktd

//Alpha Calculation

retxlp2 = log(ovr9) - log(ovr9[y])
alphaxlp = retxlp2 - retb2*Betaxlp
//plot(alphaxlp*100, color=maroon, style=line, transp=40, title='Stpl')


//////////////////////////////////////////    CONSUMER DISCRETIONARY

retxly = log(ovr10) - log(ovr10[1])
secdxly = stdev(retxly, length)
Betaxly = correlation(retxly, retb, length) * secdxly / mktd

//Alpha Calculation

retxly2 = log(ovr10) - log(ovr10[y])
alphaxly = retxly2 - retb2*Betaxly
//plot(alphaxly*100, color=olive, style=line, transp=10, linewidth=1, title='Disc')



non=(alphaxlu+alphaxlp+alphaxlv+alphaxle)*100/4
cycl=(alphaxlk+alphaxlf+alphaxly+alphaxli+alphaxlb)*100/5
//bgcolor (sma(med,9) > 0 ? green : red, transp=70)
plot(non, color=red, style=line, transp=40, linewidth=1)
plot(cycl, color=black, style=line, transp=40, linewidth=1)
hline(0, linewidth=1)