6 – L3 08 The Efficient Frontier V3

Okay. So far you’ve learned about the importance of diversification and how to calculate portfolio mean and variance. You may wonder, what are the best ways to assign to each stock in your portfolio. Before we dive into portfolio optimization, let’s take a look at the set of all possible portfolios. This will lead us to an important concept, the efficient frontier. Before we start, let’s quickly recap. The expected return of a portfolio, equals the weighted sum of each stock’s expected returns. The variance of a portfolio, equals the sum of the pairwise covariances weighted by the products of the weights. Okay. I think we’re ready to go. Let’s first take a look at a simple example with five stocks. Stocks A, B, C, D and E with given annual mean returns and covariances. One day your manager gives you $10,000 and tells you to invest in these five stocks whichever way you want. But taking only long not short positions. What would you do with this money? Of course, you would want to impress your manager and create a portfolio with the highest returns and the lowest risk. Is this possible? How would you do it? You’ve given the task some thought and decided to just create a few portfolios with randomly assigned weights. For the first portfolio, you give each stock an equal weight of 20

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