Based on your financial expertise, provide your response or viewpoint on the given financial question or topic. The response format is open.

Optimal Asset Allocation
There are some good answers about the benefits of diversification, but I'm going to go into what is going on mathematically with what you are attempting. I was always under the assumption that as long as two securities are less than perfectly correlated (i.e. 1), that the standard deviation/risk would be less than if I had put 100% into either of the securities. While there does exist a minimum variance portfolio that is a combination of the two with lower vol than 100% of either individually, this portfolio is not necessarily the portfolio with highest utility under your metric.  Your metric includes returns not just volatility/variance so the different returns bias the result away from the min-vol portfolio. Using the utility function: E[x] - .5*A*sig^2 results in the highest utility of 100% VTSAX. So here the Sharpe ratio (risk adjusted return) of the U.S. portfolio is so much higher than the international portfolio over the period tracked that the loss of returns from adding more international stocks outweigh the lower risk that you would get from both just adding the lower vol international stocks and the diversification effects from having a correlation less than one. The key point in the above is "over the period tracked".  When you do this type of analysis you implicitly assume that the returns/risk observed in the past will be similar to the returns/risk in the future.   Certainly, if you had invested 100% in the U.S. recently you would have done better than investing in a mix of US/Intl.  However, while the risk and correlations of assets can be (somewhat) stable over time relative returns can vary wildly! This uncertainty of future returns is why most people use a diversified portfolio of assets.  What is the exact right amount is a very hard question though.