Capital Asset Pricing Model Applied covariance: Project Part 1.

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Presentation transcript:

Capital Asset Pricing Model Applied covariance: Project Part 1

Review variance, covariance  Variance: square the deviations and take expectation.  Covariance: multiply the deviations and take expectation.

Application  Asset B is the market portfolio  Call it asset M.  Everyone prefers to hold M, in theory  Asset A is any asset.  Think of adding a little A to the market portfolio.

Question  does adding a little of asset A to the market portfolio increase the risk?  Yes if No if

Derivation

Beta measures risk  How much risk is added depends on the relation of sigma AM and sigma squared M  Define beta

Sum of squared errors Minimize it

Divide by T-1

The estimate of   Is the ratio of sample covariance over variance of the market.  It’s beta, except for using sample statistics instead of population values.

The story of CAPM  Investors prefer higher expected return and dislike risk.  All have the same information.  Two (mutual) funds are sufficient to satisfy all such investors:

The two funds:  1) The "risk-free" asset, i.e., Treasury Bills  2) The market portfolio consisting of all risky assets held in proportion to their market value.

The market portfolio  Its expected return is 8.5% over the T- Bill rate  It bears the market risk  Its beta is unity by definition.

Capital asset pricing model T-bill rate is known. Market premium is known, approximately 8.5%. Estimate beta as in the project

Security market line  It’s straight.  Risk-return relation is a straight line.

Why is it a straight line?  Beta is the measure of risk that matters.  Given beta construct a portfolio with the same beta by a mix of T-Bills (beta = 0) and the market portfolio (beta = 1)  Expected return on the portfolio is on the SML.  So any asset with the same beta must also be on the SML.

beta Rate of return expected by the market RfRf E[R M ] Security market line 1

Review item  Return on asset A has a std dev of.05  Return on asset B has a std dev of.07  Correlation of return on asset A with return on asset B is 1.  What is the covariance of the returns?

Answer:  Covar = corr*stdevA*stdevB=.0035