#ocekivani prinos i standardno odstupanje trzisnog portfolia i beta za sve instrumente
r<-c(0.08,0.1,0.12)
ro<-0.5
s<-c(0.1,0.14,0.12)
kovmat<-matrix(c(s[1]^2,ro*s[1]*s[2],ro*s[1]*s[3],ro*s[1]*s[2],s[2]^2,ro*s[2]*s[3],ro*s[1]*s[3],ro*s[2]*s[3],s[3]^2), ,ncol=3)
kovmatI<-solve(kovmat)
e<-as.matrix(c(1,1,1))
omega<-c(1/5,1/5,3/5)
rm<-t(r)%*%omega
sigmam<-t(omega)%*%kovmat%*%omega

beta1<-(omega[1]*s[1]^2+omega[2]*s[1]*s[2]*ro+omega[3]*s[1]*s[3]*ro)/sigmam
beta2<-(omega[2]*s[2]^2+omega[1]*s[1]*s[2]*ro+omega[3]*s[2]*s[3]*ro)/sigmam
beta3<-(omega[3]*s[3]^2+omega[1]*s[1]*s[3]*ro+omega[2]*s[2]*s[3]*ro)/sigmam
#provera
beta<-c(beta1,beta2,beta3)
sum(omega*beta) #treba da bude 1
#bezrizicna kamatna stopa
rf<-(r[1]-beta1*rm)/(1-beta1)