Merge pull request CamDavidsonPilon#347 from rsvp/devis-277-Ch6-portfolio-opt

Fix CamDavidsonPilon#277 Ch6 portfolio optimization equation

Author: CamDavidsonPilon

Chapter6_Priorities/Ch6_Priors_PyMC2.ipynb

@@ -1378,7 +1378,7 @@
     "\n",
     "With this Bayesian analysis of the stock market, we can throw it into a Mean-Variance optimizer (which I cannot stress enough to not use with frequentist point estimates) and find the minimum. This optimizer balances the tradeoff between a high return and high variance.\n",
     "\n",
-    "$$ w_{opt} = \\min_{w} \\frac{1}{N}\\left( \\sum_{i=0}^N \\mu_i^T w - \\frac{\\lambda}{2}w^T\\Sigma_i w \\right)$$\n",
+    "$$ w_{opt} = \\max_{w} \\frac{1}{N}\\left( \\sum_{i=0}^N \\mu_i^T w - \\frac{\\lambda}{2}w^T\\Sigma_i w \\right)$$\n",
     "\n",
     "where $\\mu_i$ and $\\Sigma_i$ are the $i$th posterior estimate of the mean returns and the covariance matrix. This is another example of loss function optimization."
    ]

Chapter6_Priorities/Ch6_Priors_PyMC3.ipynb

@@ -1378,7 +1378,7 @@
     "\n",
     "With this Bayesian analysis of the stock market, we can throw it into a Mean-Variance optimizer (which I cannot stress enough, do not use with frequentist point estimates) and find the minimum. This optimizer balances the tradeoff between a high return and high variance.\n",
     "\n",
-    "$$ w_{opt} = \\min_{w} \\frac{1}{N}\\left( \\sum_{i=0}^N \\mu_i^T w - \\frac{\\lambda}{2}w^T\\Sigma_i w \\right)$$\n",
+    "$$ w_{opt} = \\max_{w} \\frac{1}{N}\\left( \\sum_{i=0}^N \\mu_i^T w - \\frac{\\lambda}{2}w^T\\Sigma_i w \\right)$$\n",
     "\n",
     "where $\\mu_i$ and $\\Sigma_i$ are the $i$th posterior estimate of the mean returns and the covariance matrix. This is another example of loss function optimization."
    ]