Chapter 9 Lecture Notes

# Chapter 9 Lecture Notes - The Capital Asset Pricing Model...

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The Capital Asset Pricing Model BKM Chapter 9 Assumptions of the CAPM Proof of the CAPM Intuition behind the CAPM The Security Market Line

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Introduction - Markowitz portfolio theory provides us with tools to select optimal portfolios given expected returns, variances and covariances. Where do we get these inputs? We need Asset Pricing Models to tell us how these inputs are determined. - Asset Pricing Models could be theoretical (derived rigorously from fundamental principles), or empirical (based on observed relationships in historical data on asset returns). - We shall study one such Asset Pricing Model, the Capital Asset Pricing Model (hereafter, the CAPM). The CAPM is: a) a theoretical APM. b) The earliest APM of modern finance c) An equilibrium model, which specifies the relationship between expected return and systematic risk . - What is equilibrium? In economics, equilibrium characterizes a situation where no investor wants to do anything differently. - A bit of bad news in advance: The CAPM does not seem to hold up in the data i.e. asset prices do not seem to follow the relationship posited by the CAPM. Then, you may ask, why do we study it? Because, it gives us some nice intuition in order to understand more advanced and complicated APMs. Assumptions underlying the CAPM 1. Investors are in perfect competition with each other. In our context, this means that no one investor has the ability to influence prices with her/his trade. 2. All investors have the same one-period horizon. The theory does not say whether this period is one year, one month or one week. 2
3. All investors are Markowitz efficient investors, who care only about the mean and variance (standard deviation) of their portfolios. 4. All investors have homogeneous expectations i.e. have identical probability distributions regarding rate of return. This means all investors calculate the same ( ) E r % and ( ) r σ % for different securities, and identical covariances between pairs of securities. 5. Markets are frictionless. This is a collection of assumptions that includes: - Investors can borrow or lend any amount at the risk-free rate - All investments are infinitely divisible, which means one can buy or sell any fraction of any asset. - No taxes or transactions costs - There is no inflation or change in interest rates, or inflation is fully anticipated. 6. Capital Markets are in equilibrium. That means all securities are properly priced taking into account their risk. These assumptions are clearly very stringent and nobody is naïve enough to believe that these assumptions are actually true . However, the nature of these assumptions is the price we pay for the simple, yet powerful, results of this theory. Many of these assumptions can be, and have been, relaxed. In most cases the basic intuition is still the same (even though the algebra and calculations get a lot messier).

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