Investment risks - Lecture 8: Capital asset pricing model
Capital Asset Pricing Model
Equilibrium model that underlies all modern financial theory: What should be the
“appropriate” level of return commensurate with a given amount of “risk” for an
individual security
Derived using principles of diversification, with other simplifying assumptions
This was Nobel Prize winning work first proposed by William Sharpe.
This model captures all of the risk/return tradeoff we have been discussing up until now.
Derived with very strong limiting assumptions (discuss on next slides)
Simplifying Assumptions
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Individual investors are price takers
Single-period investment horizon
Investments are limited to traded financial assets
No taxes and no transaction costs
Think of a world where individuals are all very similar except their initial wealth and their
level of risk aversion. ( I was born poor and chicken)
“Price Takers” means that individuals do not effect prices. (Big assumption! An
individual’s behavior does not effect price.)
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Information is costless and available to all investors
Investors are rational mean-variance optimizers
Homogeneous expectations
Rational mean-variance optimizers means that all investors attempt to construct
efficient frontier portfolios like we discussed in chapter 7.
Homogeneous expectations means that if two investors examine the same investment
opportunity they will have identical beliefs about the expected returns, variance of
returns and correlations with other investments. Isn’t that a heroic assumption!
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Investment risks - Lecture 8: Capital asset pricing model
Resulting Equilibrium Conditions
All investors will hold the same portfolio for risky assets; the “market portfolio” and CML
Market portfolio contains all securities and the proportion of each security is its market
value as a percentage of total market value
Equilibrium security prices or “risk-appropriate” level of return is determined according
to CAPM
The result will be that all investors will find that the Market portfolio is on the efficient
frontier. In fact, it will be the Tangent portfolio. So all investors will choose to hold a
portion of their wealth in the risk free and a portion in the risky Market portfolio.
Capital Market Line
M = The value weighted “Market” Portfolio of all risky assets.
All investors will hold the same portfolio for risky securities
The Capital Market Line should look very familiar. It is basically the Capital allocation
line with the Market portfolio, M, as the tangent portfolio.
All investors should now choose to invest somewhere along the Capital Market Line.
Remember, any other portfolio on the efficient frontier will be dominated by the tangent
portfolio or any other point on the Capital market line.
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Investment risks - Lecture 8: Capital asset pricing model
Slope and Market Risk Premium
For one standard deviation of the Market we expect to get the reward of the risk
premium.
Stress that this ratio should be highest for market.
Expected Return and Risk on Individual Securities
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The risk premium on individual securities is a function of the individual security’s
contribution to the risk of THE market portfolio
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What type of individual security risk will matter, systematic or unsystematic risk?
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An individual security’s total risk (2i) can be partitioned into systematic and unsystematic
risk: s2i = bi2 sM2 + s2(ei)
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M = market portfolio of all risky securities
The equilibrium conditions we just described suggest that all investors will hold the same portfolio
of risky investments.
Pricing of individual securities is therefore related to the risk that individual securities have when
they are included in the market portfolio.
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Individual security’s contribution to the risk of the market portfolio is a function of the
covariance of the stock’s returns with the market portfolio’s returns and is measured by BETA
With respect to an individual security, systematic
risk can be measured by bi = [COV(ri,rM)] / s2M
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Investment risks - Lecture 8: Capital asset pricing model
Individual Stocks: Security Market Line
The security market line now changes the x axis to represent the risk associated with a given individual
investment. Beta is the relevant measure of risk of a particular asset with respect to the market
portfolio.
Here as Beta, the measure of risk of an asset increases, the expected return increases.
Note that Beta M = 1.
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Investment risks - Lecture 8: Capital asset pricing model
Any Beta above one should result in a return above the market return.
What is the return of a stock with a beta of 1?
Here we can look at the returns with respect to the asset betas in a graphical format.
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Investment risks - Lecture 8: Capital asset pricing model
Measuring Beta
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Concept:
We need to estimate the relationship between the
security and the “Market” portfolio.
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Method
Can calculate the Security Characteristic Line or SCL
using historical time series excess returns of the
security, and a proxy for the Market portfolio (DJI, S&P, etc).
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Investment risks - Lecture 8: Capital asset pricing model
The security characteristic line is basically the historical values of the excess returns of an individual
asset versus those of the market portfolio. The CAPM model suggests that alpha should equal zero since
all returns are based on the constant rf, the stock beta and the market risk.
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