P = data.frame(stock=c('A', 'B', 'C'),
               beta=c(1.10, 0.8, 1.0),
               sd_of_error=c(0.07, 0.023, 0.01),
               weight=c(.2, .5, .3))
print(P)

r_M = 0.12
s_M = 0.18
r_f = 0.05

r_p = r_f + sum(P$weight * P$beta) * ( r_M - r_f )
print(r_p)


## Part (b):
##
pb = sum(P$weight * P$beta)
ve2 = sum( P$weight^2 * P$sd_of_error^2 )
print(sqrt(ve2))
vp = pb^2 * s_M^2 + ve2
print(c(vp, sqrt(vp)))