Week 2 Notes - Chapter 8: Portfolio Theory and the Capital...

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Chapter 8: Portfolio Theory and the Capital Asset Pricing Model Markowitz showed exactly how an investor could reduce the standard deviation of portfolio returns by choosing stocks that do not move exactly together. Stock returns conform to a normal distribution. When measured over a short time interval, the past rates of return on any stock conform fairly closely to a normal distribution. Normal distributions can be completely defined by the Expected Return (average) and Standard Deviation . If returns are normally distributed, expected returns and standard deviation are the only two measure that an investor need consider. Combing Stocks into Portfolios Suppose you want to invest in the shares of Campbell Soup or Boeing. Campbell Soup offers an expected return of 3.1% and Boeing offers and expected return of 9.5%. The Standard deviation of returns I 15.8% for Campbell Soup and 23.7 for Boeing. There is no reason to just hold one stock. Eg if you invested 60% In Campbell and 40% in Boeing the expected return is about 5.7% - a weighted average of the evpected returns. Thanks to diversification the portfolio risk is less than the average of the risks of the separate stocks. The curved line above shows the expected return and risk that you could achieve by using different combinations of the two stocks in your portfolio. The optimal combination of depends on how much risk you wish to take. The gains from diversification depend on how highly the stocks are correlated. If two stocks moved in the exact same way (ie. p= +1) there would be no gains from diversification. You can see this by the straight line between the 100% invested in Boeing and 100% invested in Campbell Soup. The red line shows a case in which the returns on the two stocks are perfectly negatively correlated (p= -1). If this were true the portfolio would have no risk. In practice however you are not just limited to investing in just two stocks – can combine many different stocks to replicate market returns. The graph below shows the combination of risk and return offered by a different individual security.
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By holding different proportions of the different securities you can obtain and even wider selection of risk and return; anywhere in the shaded area above. The “best” area is in the top left hand corner, where you can have high return and low risk. The most realistic area is to go up and to the left - the portfolios that lie on the solid line – Efficient Portfolios . They offer the highest expected return for any given level of risk. Portfolio A in the graph above offers the highest expected return: it is invested in only one stock – the most risky one. Portfolio C on the other hand offers the minimum risk – it holds portfolios with the lowest standard deviations. This portfolio can also hold an individual risky security. Why? This stock is uncorrelated with the other stocks in the portfolio and thus provides
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This note was uploaded on 08/20/2011 for the course ECON 101 taught by Professor Mrsmith during the Two '11 term at University of Sydney.

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Week 2 Notes - Chapter 8: Portfolio Theory and the Capital...

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