Question

I am comparing an equally weighted portfolio vs an optimal portfolio with the same data. The Equally weighted porfolio has a higher sharpe ratio but lower $ return, while the optimal portfolio has a lower sharpe ratio and a higher return.

My questions is

Is this possible or does the higher sharpe ratio always have to the highest $ return

Was it better to diversify and why?

Answer 1

Sharpe ratio is the amount of excess return per unit standard deviation of the portfolio. So, if a portfolio has a higher sharpe ratio then it returns more value per unit of risk. It may be the case that the dollar return is less as compared to another portfolio with a lower sharpe ratio which though has a higher risk but higher return.

Yes, it is to diversify as it reduces the unsystematic risk present in the individual securities and thus increases the sharpe ratio.