#Example 5.6 --- no riskless asset  return <- c(5, 20, 50)/100 +  .05      #return vol     <- c(12, 40, 110)/100          #volatility corr   = matrix(c(1, 0.7, 0.4, 0.7, 1, 0.5, 0.4, 0.5, 1),byrow=T, ncol=3)                       						#correlation  cova  = diag(vol) %*% corr %*% diag(vol) #covariance matrix one = c(1,1,1)  A = one %*% solve(cova, return) B = return %*% solve(cova, return) C = one %*% solve(cova, one) D = B*C - A^2  g = solve(cova,  B*one - A * return)/D h = solve(cova, -A*one + C * return)/D  g%*%cova%*%g 2*h%*%cova%*%g h%*%cova%*%h  mu = 0.05 round(c(1.5052, -0.4244, -0.0807) + mu *c(-4.7307,  3.7627,  0.9680),4)  V = round(0.0287 -0.5100*mu + 3.6442 * mu^2, 6) sqrt(V)  mu = .1848 round(c(1.5052, -0.4244, -0.0807) + mu *c(-4.7307,  3.7627,  0.9680),4)  V = round(0.0287 -0.5100*mu + 3.6442 * mu^2, 6) sqrt(V)  mu = .1848 mu = A/C - D/C^2 /(mu - A/C) round(c(1.5052, -0.4244, -0.0807) + mu *c(-4.7307,  3.7627,  0.9680),4)  V = round(0.0287 -0.5100*mu + 3.6442 * mu^2, 6) sqrt(V)  t(c(0.6310, 0.2709, 0.0982)) %*% cova %*% c(1.2963, -0.2583, -0.0380)   t(c(0.6310, 0.2709, 0.0982)) %*% cova %*% c(0.6310, 0.2709, 0.0982)   t(c(1.2963, -0.2583, -0.0380)) %*% cova %*% c(1.2963, -0.2583, -0.0380)    ############################ mu = .1848 V= (C^2*(mu - E)^2 + D)/C^3/(mu - E)^2  sqrt(V)