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FIN 521
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Eric Terry
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Chapter 7: Asset Pricing Models: CAPM and APT
The capital asset pricing model (CAPM) will allow you to determine the required return for any risky asset
Assumptions of the Capital Market Theory:
1. All investors are Markowitz-efficient in that they seek to invest in tangent points on the efficient frontier.
The exact location of this tangent point and, therefore, the specific portfolio selected will depend on the
individual investor’s risk-return utility function.
2. Investors can borrow or lend any amount of money at the risk-free return (RFR).
3. All investors have homogeneous expectations, that is, they estimate identical probability distribution for
future rates of return. Again, this assumption can be relaxed with minimal effect.
4. All investors have the same one-period time horizon, such as one month or one year.
5. All investments are infinitely divisible, which means that it is possible to buy or sell fractional shares of
any asset or portfolio
6. There are no taxes or transaction costs involved in buying or selling assets
7. There is no inflation or any change in interest rates, or inflation is fully anticipated
8. Capital markets are in equilibrium. This means we begin with all investments properly priced in line with
their risk levels.
Risk-free Asset: an asset with zero variance (such asset would have zero correlation with all other risky
assets and would provide the risk-free return (RFR)
Developing the Capital Market Line:
- Covariance with a Risk-Free Asset= recall that the covariance between two sets of returns is:
∑ [ ( ) ][ ( )]
- Correlation between any risky asset i, and the risk-free asset, RF, would be zero because it is equal to:
- Combining a risk-free asset with a risky portfolio:
o Expected Return:
( ) ( ) ( ) ( )
o Where:
= the proportion of the portfolio invested in the risk-free asset
( )= the expected rate of return on risky Portfolio M
o Standard Deviation: combines the risk-free asset with risky assets is the linear proportion of
the standard deviation of the risky asset portfolio
( )
√
- The risk-return combination: the risk-return relationship between E( ) and :
( )
( ) [ ] - The Capital Market Line: the risk-return relationship holds for every combination of the risk-free asset
with any collection of risky assets
o Investors would obviously like to maximize their expected compensation for bearing risk (i.e.
Maximize the risk premium they receive)
o Capital Market Line (CML): has the property of receiving the highest level of expected return
(in excess of the risk-free rate) per unit of risk for any available portfolio of risky assets
o Any combination on this line would dominate the portfolio possibilities that fall below it because
it would have a higher expected return for the same level of risk
- Risk-Return Possibilities with Leverage: add leverage to the portfolio by borrowing money at the
risk-free rate and investing the proceeds in the risky asset portfolio at Point M, shown as Point E (page
165)
o Both return and risk increase in a linear fashion along the CML
o Because the CML is a straight line, it implies that all the portfolios on the CML are perfectly
positively correlated
o The positive correlation occurs because all portfolios on the CML combine the risky asset
Portfolio M and the risk-free asset
o You either invest part of your money in the risk-free asset and the rest in the risky asset
Portfolio M, or you borrow at the risk-free rate and invest these funds in the risky asset portfolio
Risk, Diversification, and the Market Portfolio:
- Investors should only invest in two types of assets with the weights of these two holdings determined
by the investors’ tolerance for risk
1. The risk-free security
2. Risky asset Portfolio M
- Because of the special place that the market Portfolio M holds to all investors, it must contain all risky
assets for which there is any value in the marketplace
o This includes not just Canadian common stocks, but also foreign stocks, foreign bonds, real
estate, private equity, options and futures contracts, art, antiques, and so on
o These assets should be represented in Portfolio M in proportion to their relative market values
- Because the market portfolio contains all risky assets, it is a completely diversified portfolio, which
means that all risk unique to individual assets in the portfolio is diversified away
- The unique risk, or unsystematic risk, of any single asset is offset by the unique variability of all of the
other holdings in the portfolio
- Systematic risk: defined as the variability in all risky assets caused by macroeconomic variables,
remains in Portfolio M
o Can be measured by the standard deviation of returns to the market portfolio and it changes
over time whenever there are changes in the underlying economic forces that affect the
valuation of all risky assets
o Such economic forces would be variability of money supply growth, interest rate volatility and
variability in industrial production or corporate earnings
- How to Measure Diversification:
o A complete diversified portfolio would have a correlation with the market portfolio of +1.00
o Complete diversification means the elimination of all the unsystematic or unique risk
o Once you have eliminated all unsystematic risk, only systematic risk is left, which cannot be
diversified away
o Therefore, completely diversified portfolios would correlate perfectly with the market portfolio,
which has only systematic risk
- Diversification and the Elimination of Unsystematic Risk:
o As you add securities, the average covariance for the portfolio declines
o The typical correlation between Canadian securities ranges from 0.2- 0.60 o You can reduce the overall standard deviation of the portfolio, which will eventually reach the
level of the market portfolio, by adding stocks that are not perfectly correlated with the other
stocks in the portfolio
o At that point, you have diversified away all unsystematic risk, but you still have market or
systematic risk
o You cannot eliminate the variability and uncertainty of macroeconomic factors that affect all risky
assets
o You can attain a lower level of systematic risk by diversifying globally versus only diversifying
within Canada because some of the systematic risk factors in the Canadian market (such as
Canadian monetary policy) are not perfectly correlated with systematic risk variables in other
counties such as Germany, and Japan
o If you diversify globally, you eventually ge

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