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Lecture12_student - More on CAPM The math behind...

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Unformatted text preview: More on CAPM The math behind diversification and risk CAPM The last lecture and todays deal with CAPM What is CAPM? Capital Asset Pricing Model Wikipedia defines it as a model that is used to determine a theoretically appropriate required rate of return of an asset, if that asset is to be added to an already well-diversified portfolio, given that asset's non-diversifiable risk Today, we address how we derive CAPM Recall stock portfolios Stock portfolios have two or more stocks In many examples, we will only have two stocks Calculations become more cumbersome with three or more stocks The math Throughout the quarter, I typically have gone through examples that are different from the textbook Today, I will go through a complicated example in the book Supertech and Slowpoke Supertech and Slowpoke Supertech Returns closely follow what the market does When times are very good, the stock gets a very high return When times are very bad, the stock loses money Slowpoke Returns do not coincide with the market as a whole This stock does well in times of recession During normal times, this stock loses money Expected returns under different market conditions Supertech Returns (R AT ) Slowpoke Returns (R BT ) Depression 20% 5% Recession 10% 20% Normal 30% 12% Boom 50% 9% Simple case here We assume that each state of the world occurs with equal probability This will make the calculations easier to do in this first example In reality, the distributions are typically not such that each outcome occurs with equal probability Calculating standard deviation of a stocks returns There are five steps involved in calculating the standard deviation of the returns of each stock Step 1: Calculate the expected return of the stock Step 2: Find the difference between expected return and actual return for the stock Step 3: Take the square of each number Step 4: Calculate the average squared deviation (this is variance) Step 5: Take the square root of the variance Step 1: Calculate the expected return of the stock Supertech (0.2 + 0.1 + 0.3 + 0.5) / 4 = 0.175 = 17.5% Slowpoke (0.05 + 0.2 0.12 + 0.09) / 4 = 0.055 = 5.5% Step 2: Difference between expected return and actual return Supertech Depression: 0.2 0.175 = 0.375 Recession: 0.1 0.175 = 0.075 Normal: 0.3 0.175 = 0.125 Boom: 0.5 0.175 = 0.325 Slowpoke Depression: 0.05 0.055 = 0.005 Recession: 0.20 0.055 = 0.145 Normal: 0.12 0.055 = 0.175 Boom: 0.09 0.055 = 0.035 Step 3: Take the square of...
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This note was uploaded on 12/05/2011 for the course ECON 134a taught by Professor Lim during the Fall '08 term at UCSB.

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Lecture12_student - More on CAPM The math behind...

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