15/03
MN10500 Lecture 6: The Cost of Capital
Lecture Summary
● Market risk is the only relevant risk in a diversified portfolio.
● Capital Asset Pricing Model (CAPM)
○ Calculations
○ Critiques: Its assumptions & arguments/evidence against them.
● Cost of Capital (WACC)
○ Always after-tax, unless otherwise indicated.
The Perfect Investment in a Perfect World
● A 'perfect' world looks like this:
○ People trade actively in the market (the marginal investors)
○ Investors are risk-averse and well-diversified.
○ Diversification has no cost
○ Investors have homogenous expectations
● Everyone's goal is to make investment with the best risk-return trade-off (the farthest
upper-left corner of efficient frontier)
● Implications of these 'perfect world' assumptions:
○ Free diversification and diversified investors: only systematic risk matters.
○ Marginal investors are price takers rather than price makers.
○ An argument for the marginally diversified investor: Assume that a
diversified investor and a non-diversified investor are both looking at Disney.
The latter looks at the stock and sees all risk. The former looks at it and sees
only the non-diversifiable risk. If they agree on the expected earnings and
cash flows, the former will be willing to pay a higher price. Thus, the latter will
get driven out of the market.
○ Homogenous Expectations: Everyone has the same view/assessment of
the risk and return for an asset so has the same efficient frontier of risky
assets.
Introducing Risk-Free Asset
● There exists a 'certain' risky asset, when combined with a risk-free asset, offers the
HIGHEST return for any level of risk.
● Since investors are homogenous, everyone will choose the same 'certain' risky
asset, i.e., Market Portfolio.
, 15/03
● By introducing a risk-free asset, a new efficient frontier is created. (The risk-free
asset is located on the y-axis). This line will give a higher return for every level of risk
except at the tangential point. A market portfolio is a tangential portfolio. The market
portfolio is an efficient portfolio and is also a risky portfolio.
Individual Security Risk in Terms of Market Portfolio Risk
● The risk of a well-diversified portfolio depends on the market risk of the securities
included in the portfolio.
● The risk of any asset/security is the risk that it adds to the market portfolio.
○ Correlation between the asset and market portfolio.
● The equilibrium security return depends on the asset's systematic return, not its
total risk (standard deviation).
● An investor should not expect to receive additional return for bearing unsystematic
risk.
● Of course we have to assume that diversification is free.
● Implication: The riskiest stock with the highest standard deviation (total risk) does
not necessarily have the highest expected return.
Introducing Beta (β)
● Sensitivity of stock's return to return on market portfolio.
● Standardised measure of correlation between the asset and the market portfolio.
● Defining Beta (β): A measure of the non-diversifiable risk for any asset, as the
covariance of its returns with returns on market portfolio divided by the variance of
the returns on the market.
○ Beta is a relative measure of risk. It is a measure of market risk.
○ Beta of the market portfolio is one.
○ Beta represents the sensitivity of a stock's return to the return on the market
portfolio.
Calculating & Interpreting Beta (β)
● In practice, beta is the estimated slope coefficient of the line that fits returns on the
asset and those of a market index.
○ By 'regression'.
○ Theoretically, the market portfolio/index has a beta = 1.
○ A risk-free asset has a beta = 0
● Interpreting beta:
○ b > 1: Security risk is higher than market risk. The returns on the asset are
more variable in response to systematic risk factors than is the overall
market.
○ β = 1: Security risk equal to market risk.
○ β < 1: Security risk lower than market risk. The returns on the asset are less
variable in response to systematic risk factors than is the overall market.
Capital Asset Pricing Model (CAPM)
● Let ri = expected (required) return on asset i, and rm = return of market.
● Risk Premium on Asset i = b x Market Risk Premium
MN10500 Lecture 6: The Cost of Capital
Lecture Summary
● Market risk is the only relevant risk in a diversified portfolio.
● Capital Asset Pricing Model (CAPM)
○ Calculations
○ Critiques: Its assumptions & arguments/evidence against them.
● Cost of Capital (WACC)
○ Always after-tax, unless otherwise indicated.
The Perfect Investment in a Perfect World
● A 'perfect' world looks like this:
○ People trade actively in the market (the marginal investors)
○ Investors are risk-averse and well-diversified.
○ Diversification has no cost
○ Investors have homogenous expectations
● Everyone's goal is to make investment with the best risk-return trade-off (the farthest
upper-left corner of efficient frontier)
● Implications of these 'perfect world' assumptions:
○ Free diversification and diversified investors: only systematic risk matters.
○ Marginal investors are price takers rather than price makers.
○ An argument for the marginally diversified investor: Assume that a
diversified investor and a non-diversified investor are both looking at Disney.
The latter looks at the stock and sees all risk. The former looks at it and sees
only the non-diversifiable risk. If they agree on the expected earnings and
cash flows, the former will be willing to pay a higher price. Thus, the latter will
get driven out of the market.
○ Homogenous Expectations: Everyone has the same view/assessment of
the risk and return for an asset so has the same efficient frontier of risky
assets.
Introducing Risk-Free Asset
● There exists a 'certain' risky asset, when combined with a risk-free asset, offers the
HIGHEST return for any level of risk.
● Since investors are homogenous, everyone will choose the same 'certain' risky
asset, i.e., Market Portfolio.
, 15/03
● By introducing a risk-free asset, a new efficient frontier is created. (The risk-free
asset is located on the y-axis). This line will give a higher return for every level of risk
except at the tangential point. A market portfolio is a tangential portfolio. The market
portfolio is an efficient portfolio and is also a risky portfolio.
Individual Security Risk in Terms of Market Portfolio Risk
● The risk of a well-diversified portfolio depends on the market risk of the securities
included in the portfolio.
● The risk of any asset/security is the risk that it adds to the market portfolio.
○ Correlation between the asset and market portfolio.
● The equilibrium security return depends on the asset's systematic return, not its
total risk (standard deviation).
● An investor should not expect to receive additional return for bearing unsystematic
risk.
● Of course we have to assume that diversification is free.
● Implication: The riskiest stock with the highest standard deviation (total risk) does
not necessarily have the highest expected return.
Introducing Beta (β)
● Sensitivity of stock's return to return on market portfolio.
● Standardised measure of correlation between the asset and the market portfolio.
● Defining Beta (β): A measure of the non-diversifiable risk for any asset, as the
covariance of its returns with returns on market portfolio divided by the variance of
the returns on the market.
○ Beta is a relative measure of risk. It is a measure of market risk.
○ Beta of the market portfolio is one.
○ Beta represents the sensitivity of a stock's return to the return on the market
portfolio.
Calculating & Interpreting Beta (β)
● In practice, beta is the estimated slope coefficient of the line that fits returns on the
asset and those of a market index.
○ By 'regression'.
○ Theoretically, the market portfolio/index has a beta = 1.
○ A risk-free asset has a beta = 0
● Interpreting beta:
○ b > 1: Security risk is higher than market risk. The returns on the asset are
more variable in response to systematic risk factors than is the overall
market.
○ β = 1: Security risk equal to market risk.
○ β < 1: Security risk lower than market risk. The returns on the asset are less
variable in response to systematic risk factors than is the overall market.
Capital Asset Pricing Model (CAPM)
● Let ri = expected (required) return on asset i, and rm = return of market.
● Risk Premium on Asset i = b x Market Risk Premium
