APPLIED FINANCIAL
MANAGEMENT
Theoretical Foundation of the Capital Asset Pricing Model
(CAPM).
LONDON’S EVENING UNIVERSITY
BBK.AC.UK
INVESTORS’ CHOICES
• Investors want to maximise returns and minimise risk.
• Would seek to invest in those investments with high
return and low risk.
• Which investment would you choose?
• A – Return = 5%, Standard Deviation = 5%
• B – Return = 10%, Standard Deviation = 10%
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INVESTORS’ CHOICES
• However, when two investments with different
investment payoffs (return and risk compositions) and
correlation, we can always construct a portfolio which
offers either higher risk and higher return or lower risk
and lower return (provided that they are not perfectly
and positively correlated).
• Investors will choose the best portfolio that reflects their
risk tolerance.
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TWO FUND SEPARATION THEOREM
• In a perfect and complete world:
• no tax,
• no transactions cost, and
• lending rate = borrowing rate),
• rational investors will combine all marketable assets in their
portfolios (the most efficient portfolio as all diversifiable risks
are gone).
• If the risk-free asset is available, then everyone will split their
capital into two funds: one in the risk-free and the other in
the risky market portfolio; regardless of their risk preference.
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EFFICIENT FRONTIER
• Lending or Borrowing at the risk-free rate (rf) allows us
to exist outside the efficient frontier.
• Two-fund Separation Theorem
T
Expected Return (%)
rf
S
Standard Deviation
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CAPITAL MARKET LINE
Return
Market Return = rm
Efficient Portfolio
Risk Free
Return
.
= rf
Risk
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CAPITAL MARKET LINE (CML)
• Given the Two-Fund Separation Theorem and the
implications from the portfolio theory, any efficient
portfolio will lie on the CML, which has the following
form:
E  R p   R f   p
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EXAMPLE 1
• Suppose an investor wants to create a portfolio with a
risk (measured in terms of the portfolio’s standard
deviation) of 10%.
• The market is offering a return of 12% (with a standard
deviation of 7%) and a risk-free rate is at 5%.
• What is the expected return on the portfolio?
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EXAMPLE 1
• Risk-free rate = 5%
• The slope of the CML
• = (Return on the market – risk-free rate)/market’s sd
• = (12% - 5%)/7% = 1
• The risk required by the investor = 10%
• Using the CML =>
• E(Rp) = 5% + 1 x 10% = 15%
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THINK:
• What if the risk-free lending rate and the borrowing rate
are not identical?
• What if investors are not allowed to short-sell their
investments?
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CAPITAL ASSET PRICING MODEL (CAPM)
• Assumptions
• Investors operate within the mean-variance framework
• Capital markets are frictionless (no taxes, no transaction costs,
or restrictions on short-selling)
• All assets are marketable
• Investors can lend and borrow at the same risk-free rate
• Investors share the same belief for the return distribution of
any given asset
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IMPLICATIONS
• Investors will hold the most diversified portfolio (i.e. the
market portfolio).
• Extra risk which can be diversified would not be priced in
securities.
• The only risk that would be priced would be the risk
relative to the market.
• CAPM defines the market risk of a company, beta, as the
covariance between the returns of the company and the
market divided by the variance of the return on the
market.
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SECURITY MARKET LINE
Return
Market Return = Rm
.
Efficient Portfolio
Risk Free
Return
=
Rf
1.0
BETA
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