# Portfolio Optimization

## Description

In this exercise we will perform both security selection and asset allocation. From this, we will derive the Efficient Frontier and Capital Market Line.

## Directions

1. Find the portfolio composed of Apple, Google and Microsoft that maximize the portfolio's Sharpe ratio. Assume no short selling is allowed. Plot the portfolio's expected return against its standard deviation on the Risk-Reward chart.

2. Find the portfolio composed of Apple, Google and Microsoft that minimizes the portfolio's variance. Assume no short selling is allowed. Plot the portfolio's expected return against its standard deviation on the Risk-Reward chart. Do you want to invest on the efficient frontier below the minimum variance portfolio?

3. Find the portfolio composed of Apple, Google, Microsoft and the risk-free bond that maximizes the portfolio's Sharpe ratio given the investment weight in the risk-free bond is 25%. Assume no short selling is allowed. Plot the portfolio's expected return against its standard deviation on the Risk-Reward chart.

4. Repeat (3) using investment weights of 50%, 75% and 100% in the risk-free bond. Plot these portfolio's expected returns against their standard deviations on the Risk-Reward chart. Note that the Capital Market Line (CML) is the straight line from the risk-free rate through the market portfolio you found in (1), as drawn below.

## Questions

1. Do you want to invest on the efficient frontier below the minimum variance portfolio? Why or why not?
2. How do the Sharpe ratios of the portfolios on the CML compare?
3. Given your conclusion from (2), is there a "best" portfolio on the CML in terms of Sharpe ratio?
4. If you were risk-averse, where would you invest in the CML? What if you wanted high-expected returns?
5. How can you achieve a portfolio with an expected return higher than the stock market portfolio (i.e. the portfolio with a 100% investment weight in equities).