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MITOCW | watch?v=z2oQe6B1Qa4 The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. ANDREW LO: Well, let me pick up where we left off last time and give you just a very quick overview of where we're at now, because we're on the brink of a very important set of results that I think will change your perspective permanently on risk and expected return. Last time, remember, we looked at this trade-off between expected return and volatility. And we made the argument that when you combined a bunch of different securities that are not all perfectly correlated, what you get is this bullet-shaped curve in terms of the possible trade-offs between that expected return and riskiness of various different portfolios. So every single dot on this bullet-shaped curve corresponds to a specific portfolio, or weighting, or vector of portfolio weights, omega. So now what I want to ask you to do for the next lecture or two is to exhibit a little bit of a split personality kind of a perspective. I'm going to ask you to look at the geometry of risk and expected return, but at the same time, in the back of your brain, I want you to keep in mind the analytics of that set of geometries. In other words, I want you to keep in mind how we got this bullet-shaped curve. The way we got it was from taking different weighted averages of the securities that we have access to as investments. So every one of these points on the bullet corresponds to a specific weighting. As you change those weightings, you change the risk and return characteristics of your portfolio. So the example that I gave after showing you this curve where I argued that the upper branch of this bullet is where any rational person would want to be. And by rational, I've defined that as somebody who prefers more expected return to less, and somebody who prefers less risk to more, other things equal. So if you've got those kind of preferences, then you want to be in the Northeast. You want to be as north, sorry, Northwest as possible. And you would never want to be down in this lower branch when you could be in the upper branch because you'd have a higher expected return for the same level of risk. So after we developed this basic idea, I gave you this numerical example where you've got three stocks in your universe. General Motors, IBM, and Motorola. And these are the parameters that we've estimated using historical data. Now there's going to be a question, and we've already raised that question, of how stable are these parameters. Are they really parameters, or do they change over time. And I told you, in reality of course, they change over time. But for now, let's play the game and assume that they are constant over time, and see
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what we can do with those parameters.
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  • Spring '17
  • Jim Angel

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