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Lecture 9

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

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David Cimon

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BU-473 Lecture 9
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
 
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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