FINANCE IN A FINANCE IN A CANADIAN SETTINGCANADIAN SETTING

Sixth Canadian EditionSixth Canadian EditionLusztig, Cleary, Lusztig, Cleary,

SchwabSchwab

CHAPTER EIGHTCHAPTER EIGHT

CAPITAL MARKET THEORYCAPITAL MARKET THEORY

Learning ObjectivesLearning Objectives

1.1. Explain the role of risk-free assets in Explain the role of risk-free assets in an efficient portfolio.an efficient portfolio.

2.2. Define the capital market line (CML), Define the capital market line (CML), and explain what its slope indicates.and explain what its slope indicates.

3.3. Compare and contrast systematic and Compare and contrast systematic and non-systematic risk, and discuss the non-systematic risk, and discuss the role of each in establishing the role of each in establishing the security market line (SML).security market line (SML).

Learning ObjectivesLearning Objectives

4.4. Define beta measure, and explain why Define beta measure, and explain why it is more stable for large portfolios it is more stable for large portfolios than for small ones than for individual than for small ones than for individual stocks.stocks.

5.5. Identify some of the weaknesses in the Identify some of the weaknesses in the capital asset pricing model (CAPM), capital asset pricing model (CAPM), and discuss alternative theories.and discuss alternative theories.

Building Efficient Building Efficient PortfoliosPortfolios

Use approach based on portfolio theory Use approach based on portfolio theory developed by Harry Markowitzdeveloped by Harry Markowitz

Portfolio theory is a normative meaning that Portfolio theory is a normative meaning that tells investors how they should act to diversify tells investors how they should act to diversify optimally, which is based on the following optimally, which is based on the following assumptions:assumptions:

1.1. A single investment periodA single investment period2.2. Liquidity of positionsLiquidity of positions3.3. Investors preference based only onInvestors preference based only on

a portfolio’s expected return and riska portfolio’s expected return and risk4.4. Homogenous expectations among investors Homogenous expectations among investors

regarding expected return and riskregarding expected return and risk

The Efficient Set of The Efficient Set of PortfoliosPortfolios

• According to Markowitz’s approach, According to Markowitz’s approach, investors should evaluate portfolios investors should evaluate portfolios based on their return and risk as based on their return and risk as measured by the standard deviationmeasured by the standard deviation

Efficient portfolioEfficient portfolio – a portfolio that has – a portfolio that has the smallest portfolio risk for a given the smallest portfolio risk for a given level of expected return or the largest level of expected return or the largest expected return for a given level of riskexpected return for a given level of risk

The Efficient Set of The Efficient Set of PortfoliosPortfolios

The construction of efficient portfolios of The construction of efficient portfolios of financial assets requires identification of financial assets requires identification of optimal risk-expected return optimal risk-expected return combinations attainable from the set of combinations attainable from the set of risky assets availablerisky assets available

Efficient portfolios can be identified by Efficient portfolios can be identified by specifying an expected portfolio return specifying an expected portfolio return and minimizing the portfolio risk at this and minimizing the portfolio risk at this level of returnlevel of return

The Efficient Set of The Efficient Set of PortfoliosPortfolios

The Attainable Set and the Efficient Set of The Attainable Set and the Efficient Set of PortfoliosPortfolios

The Efficient Set of The Efficient Set of PortfoliosPortfolios

Risk averse investors should only be Risk averse investors should only be interested in portfolios with the lowest interested in portfolios with the lowest possible risk for any given level of returnpossible risk for any given level of return

Efficient set (frontier)Efficient set (frontier) – is the segment of the – is the segment of the minimum variance frontier above the global minimum variance frontier above the global minimum variance portfolio that offers the minimum variance portfolio that offers the best risk-expected return combinations best risk-expected return combinations available to investorsavailable to investors

Portfolios along the efficient frontier are Portfolios along the efficient frontier are equally “good”equally “good”

Borrowing and Lending Borrowing and Lending PossibilitiesPossibilities

Investors have the option of buying Investors have the option of buying risk-free assetsrisk-free assets

Investors can invest part of their Investors can invest part of their wealth in risk-free asset and the wealth in risk-free asset and the rest in risky assets resulting in a rest in risky assets resulting in a new efficient frontiernew efficient frontier

Borrowing and Lending Borrowing and Lending PossibilitiesPossibilities

The Markowitz Efficient Frontier and the The Markowitz Efficient Frontier and the Possibilities Resulting from Introducing a Risk-Possibilities Resulting from Introducing a Risk-

Free AssetFree Asset

Risk-Free LendingRisk-Free Lending The expected return on a combined The expected return on a combined

portfolio of risk-free and risky assets portfolio of risk-free and risky assets would be:would be:

Since theSince the of risk-free assets is equal of risk-free assets is equal to 0 than the to 0 than the of the portfolio would be: of the portfolio would be:

)()1()( xrfrfp REwwRE

xRFp w )1(

Risk-Free LendingRisk-Free Lending

Through a combination of risk-free Through a combination of risk-free investing and investing in a investing and investing in a portfolio of risky assets, investors portfolio of risky assets, investors can improve the opportunity set can improve the opportunity set available from the efficient frontieravailable from the efficient frontier

Borrowing PossibilitiesBorrowing Possibilities Investors are no longer restricted to their Investors are no longer restricted to their

initial wealth when investing in risky initial wealth when investing in risky assets.assets.

Investors can:Investors can: Buy stock on marginBuy stock on margin Borrow at the risk-free rateBorrow at the risk-free rate

Borrowing additional funds for investment Borrowing additional funds for investment purposes allows investors to seek higher purposes allows investors to seek higher expected returns while assuming more riskexpected returns while assuming more risk

Borrowing PossibilitiesBorrowing PossibilitiesThe Efficient Frontier when Lending and The Efficient Frontier when Lending and

Borrowing Possibilities Are AllowedBorrowing Possibilities Are Allowed

Borrowing PossibilitiesBorrowing Possibilities

The proportion to be invested in The proportion to be invested in the alternatives are stated as a the alternatives are stated as a percentage of an investor’s total percentage of an investor’s total investable funds with the different investable funds with the different combinations adding up to 1.0combinations adding up to 1.0

%1000.1)1( RFRF ww

The Capital Asset Pricing The Capital Asset Pricing Model (CAPM)Model (CAPM)

Capital market theory is concerned with Capital market theory is concerned with equilibrium security prices and returns equilibrium security prices and returns and how they are related to the risk-and how they are related to the risk-expected return trade-off that investors expected return trade-off that investors faceface

It measures the relative risk of an It measures the relative risk of an individual security and the relationship individual security and the relationship between risk and the returns expected between risk and the returns expected from investingfrom investing

Capital Market Line Capital Market Line (CML)(CML)

Depicts the equilibrium conditions Depicts the equilibrium conditions that prevail in the market for efficient that prevail in the market for efficient portfolios consisting of the optimal portfolios consisting of the optimal portfolio of risk-free and risky assetsportfolio of risk-free and risky assets

All combinations of assets are bound All combinations of assets are bound by the CML and at equilibrium all by the CML and at equilibrium all investors end up with efficient investors end up with efficient portfoliosportfolios

Capital Market Line Capital Market Line (CML)(CML)

Slope of the CML is the market price of Slope of the CML is the market price of risk for efficient portfoliosrisk for efficient portfolios

Slope of the CML =Slope of the CML =

The CML is always upward sloping The CML is always upward sloping because the price of risk is always positivebecause the price of risk is always positive

M

M RFRE

)(

Capital Market Line Capital Market Line (CML)(CML)

The CML and the Components of Its SlopeThe CML and the Components of Its Slope

The Security Market Line The Security Market Line (SML)(SML)

The SML is the key contribution of the The SML is the key contribution of the CAPM to asset pricing theoryCAPM to asset pricing theory

The SML equation is:The SML equation is:

The SML represents the trade-off between The SML represents the trade-off between systematic (as measured by beta) and systematic (as measured by beta) and expected returns for all assetsexpected returns for all assets

iMi RFRERFRE )()(

The Security Market Line The Security Market Line (SML)(SML)

It is depicted as the line from RF-Z It is depicted as the line from RF-Z in Figure 8.6in Figure 8.6

BetaBeta BetaBeta – the measure of the systematic – the measure of the systematic

risk of a security that cannot be avoided risk of a security that cannot be avoided through diversificationthrough diversification

Beta measures a security’s volatility in Beta measures a security’s volatility in price relative to a benchmarkprice relative to a benchmark

• Beta – risk-free asset = 0Beta – risk-free asset = 0 – – market portfolio = 1.0market portfolio = 1.0

• Stocks - Stocks - betas are higher risk securities betas are higher risk securities betas are lower risk securitiesbetas are lower risk securities

Portfolio BetasPortfolio Betas

Are weighted averages of the Are weighted averages of the betas for individual securities in betas for individual securities in the portfoliothe portfolio

The equation is:The equation is:nnp www ...2211

Over- and Undervalued Over- and Undervalued SecuritiesSecurities

• Securities plotted above the SML Securities plotted above the SML are undervalued because they are undervalued because they offer more expected return given offer more expected return given its betaits beta

• Securities plotted below the SML Securities plotted below the SML are overvalued because they offer are overvalued because they offer less expected return given its betaless expected return given its beta

SummarySummary

1.1. An efficient portfolio has the highest An efficient portfolio has the highest expected return for a given level of risk or expected return for a given level of risk or the lowest level of risk for a given level of the lowest level of risk for a given level of expected return.expected return.

2.2. Capital market theory, based on the Capital market theory, based on the concept of efficient diversification, concept of efficient diversification, describes the pricing of capital assets in describes the pricing of capital assets in the market place. The new efficient the market place. The new efficient frontier is called the capital market line frontier is called the capital market line (CML), and its slope indicates the (CML), and its slope indicates the equilibrium price of risk in the market.equilibrium price of risk in the market.

SummarySummary

33.. Based on the separation of risk into its Based on the separation of risk into its systematic and non-systematic systematic and non-systematic components, the security market line components, the security market line (SML) can be constructed for individual (SML) can be constructed for individual securities (and portfolios).securities (and portfolios).

4.4. Beta is a relative measure of risk, which Beta is a relative measure of risk, which indicates the volatility of a stock relative indicates the volatility of a stock relative to a market index. While all betas change to a market index. While all betas change through time, betas for large portfolios through time, betas for large portfolios are much more stable than those for are much more stable than those for individuals stocksindividuals stocks