IS MEAN-VARIANCE OPTIMIZATION THE SAME AS MAXIMIZING THE SHARPE RATIO?

All calculations and information is from  ZOONOVA  First let’s look at a stock portfolio optimization calculation using a 15% minimum investment return as input. We will also calculate the Variance, Volatility, Sharpe Ratio, Efficient Frontier, and the Sharpe Ratio Frontier.

As you can see from the screen images 1 & 2, the Sharpe Ratio is determined by the minimum return selected by the user for the Portfolio Optimization calculation. Having a higher minimum return as input can lead to a lower Sharpe Ratio because of more volatility and risk associated with the return. You can actually see the Sharpe Ratio decrease in the graph as the portfolio volatility increases.

Under Portfolio Optimization there are a few Sharpe Ratio Calculations, one for the current portfolio return and the other against the CAPM RoR. There can also be a Sharpe Ratio calculation against a single stocks expected return and one using CVaR to calculate a Conditional Sharpe ratio. 

So if you want to maximize the Sharpe Ratio you have to select the minimum return that gives the highest Sharpe Ratio based on the calculated variance and volatility of the stock portfolio. This can be seen in the Sharpe Ratio ROI graph and the Efficient Frontier graph.