The mean return and standard deviation of the optimized portfolio represents the frequency of the input data. If the input data is annual, then the results are annual return and risk (standard deviation). If the input data id monthly, then the results are monthly.
To annualize non annual results we need to multiply the return by the number of periods in a year (e.g. 12 for monthly) and multiply the standard deviation by the square root of of the number of periods in a year (e.g. SQRT(12) for monthly).
The results are based solely on the input data and so the assumption is that the same relationships between investments in the portfolio will be maintained in the future. To relax this assumption and apply predictive relationships for the portfolio in the future, we can modify the correlation matrix accordingly before the optimization process is executed.
The optimization process used an iterative process to test portfolio weighting scenarios in order to find the portfolio closest to the efficient frontier under the Sharpe ration (or Sortino ration under downside risk).
Monte Carlo simulation is employed to calculate the probability distribution and values for achieving the target return in the portfolio.
