#  Create a 3 by 3 covariance matrix to play with the accuracy of
#  first order approximations.

C  = matrix( c(3., 1., 1., 1., 3., 1., 1., 1., 3.), nrow = 3, ncol = 3)
mu = c( 2., 1., 0.)
w  = c( .5, .5, 0.)
sigsq_P = w %*% ( C %*% w )
cat("portfolio variance is", sigsq_P, "\n")
mu_P = mu %*% w
cat("portfolio expected return is", mu_P, "\n")

dw       = c(.01, 0., -.01)
dsig_pred = w %*% ( C %*% dw )
dsig_true = (w+dw) %*% ( C %*% (w+dw) ) - sigsq_P
cat("predicted change in variance is ", dsig_pred, ", actual change is ", dsig_true, "\n")