source('exercise_3.R') ## read in the data from the book (it was used in another exercise)

ms = apply(SR[, 2:5], 2, mean) # the m measurement
sigma_i = apply(SR[, 2:5], 2, sd)
sigma_M = sd(SR$market)
beta = c(0.9, 1.02, 1.40, 0.68)

ns = 5.84 + beta * 13.83

sigma_m2 = sigma_i^2
sigma_n2 = beta^2 * sigma_M^2
sigma_mn = 25 * sigma_i^2

x = (sigma_n2 - sigma_mn)/(2*(sigma_m2 - 2*sigma_mn + sigma_n2))
print(x)

print(x * ms + (1-x) * ns)