# Simulating random portfolios to illustrate the 'efficient frontier' of returns

## Question

Suppose you're given an array of equities and asked to **simulate random portfolios to visualize the 'efficient frontier'**.

The efficient frontier shows the set of 'optimal' portfolios that offer the **highest expected return for a defined level of risk**, where standard deviation is used as a proxy for risk.

In order to build the simulation and illustrate the efficient frontier, you can follow the steps below:

- Calculate periodic returns of the stocks in your portfolio
- Write function(s) to simulate randomized runs of your portfolio (randomly assigning weights). - You'll probably want to calculate a covariance matrix for the equities as well as the mean historical returns as general inputs
- Plot the output of the annualized portfolio returns generated from your simulation function(s), as well as the portfolio standard deviation (volatility) in a scatter plot -- the left outer curve on this plot will illustrate the 'efficient frontier' where maximum expected returns for a given risk level exist

To help get you started, you can reference this Google Colab notebook with the historical returns for a portfolio of the following equities:

```
['AAPL','FB', 'C', 'DIS']
```