# BU473 Lecture Notes - Lecture 9: Capital Asset Pricing Model, Sharpe Ratio, Economic Equilibrium

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CAPM

• CAPM assumes that all investors follow identical portfolio strategies, and all select an identical

tangency portfolio

o The Market Portfolio

CAPM – Individual Behavior

1. Investors are rational mean-variance optimizers

2. Investors plan for a single time period in the future

3. All investors have homogenous expectations:

a. That is to say that all investors have the same beliefs about asset returns, asset

variances, and asset covariances, based on identical public info

CAPM – Markets

• All assets are publicly held and trade on public exchanges

• Investors can lend and borrow at a common risk-free rate

• Investors can take short positions on traded securities

• There are no taxes

• There are no transaction costs

Individual Securities and their Contribution to Market Risk

• In CAPM, we assume that there are sufficient securities in the market portfolio that firm-specific

risk has been diversified away. Instead, each security contributes risk to the covariance of the

market portfolio

• Imagine that a stock has a weight in the market portfolio with total securities

• Contribution of Stock to the market return is:

• Contribution of stock to the market variance is given by the sum of its covariances to the other

assets:

• We can show that, because rM=w1r1+ … + wNrN and because covariance is additive, the total

contribution to the market variance is:

Market Price of Risk

• In CAPM, we find the market portfolio using the Sharpe ratio

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