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Finance
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MGFB10H3
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Sultan Ahmed
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Chapter 9

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Finance

MGFB10H3

Sultan Ahmed

Winter

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Chapter 9
9.1 The New Efficient Frontier
The Efficient Frontier with Risk-Free Borrowing and Lending
Portfolios of risky securities that lie along the efficient frontier (lies on the curve above the
minimum variance portfolio) are efficient and give the highest expected return for the level of
risk
Risk premium: the expected payoff that induces a risk-adverse person to enter into a risky
situation
o We assume most investors are risk adverse and will require a risk premium to endure
risk
Insurance premium: the payment to get out of a risky situation
The slope of the line is the height which is the expected returns on the portfolio divided by the
length, which is the std dev of the portfolio
o Steeper line= more risk-adverse investors
o Origin of the lines is the point with a zero expected rate of return and zero risk
Zero risk= risk-free asset (e.g. T-Bill)
Risk-Free Investing
Portfolio is always a weighted average of the expected returns on the individual assets so we
can estimate the expected return on this portfolio
ERp= expected return on the portfolio
Std deviation for risk free asset is zero b/c return does not vary. Correlation of return and risk of
is also zero
Tangent portfolio: the risky portfolio on the efficient frontier whose tangent line cuts the
vertical axis at the risk-free rate
New (or super) efficient frontier: portfolios composed of the risk-free rate and the tangent
portfolio that offer the highest expected rate of return for any given level of risk
Risk-Free Borrowing
Short position: a negative position in an asset; the investor achieves a short position by
borrowing part of the asset’s purchase price from the stockbroker The New Efficient Set and the Separation Theorem
Separation theorem: the theory that the investment decision (how to construct the portfolio of
risky assets) is separate from the financing decision (how much should be invested or borrowed
at the risk-free rate)
Market portfolio: a portfolio that contains all risky securities in the market
9.2 The Capital Asset Pricing Model (CAPM)
Capital asset pricing model (CAPM): a pricing model that uses one factor, beta, to relate
expected returns to risk
o all investors have identical expectations about expected returns, std deviations and
correlation coefficients
o all investors have the same one-period time horizon
o all investors can borrow or lend money at the risk-free rate of return (RF)
o there are no transaction costs
o there are no personal income taxes, so investors are indifferent whether they receive
capital gains or dividends
o There are many investors and no single investor can affect the price of a stock through
his or her buying and selling decisions. Therefore, investors are price takers
o Capital markets are in equilibrium
The Market Portfolio and the Capital Market Line (CML)
The “optimal” risky portfolio is the one that is tangent tot eh efficient frontier on a line that is
drawn from RF. It is the same for all investors
This optimal risky portfolio will be the “market portfolio” (M) which contains all risky securities.
The value of this portfolio will equal the aggregate of the market values of all the individual
assets composing it, Therefore, the weights of these assets in the market portfolio will be
represented by their proportionate weight in this total value
Capital marketing line (CML): a line depicting the highest attainable expected return for any
given risk level that includes only efficient portfolios; all rational, risk-adverse investors want to
be on this line
Market price of risk: slope of the capital market line. The incremental expected return divided
by the incremental risk; indicates the additional expected return that the market demands for
an increase in risk
Required rate of return: the rate of return investors need to tempt them to invest in a security
(kp)
CML must always slope upward b/c w/ risk-averse investors the risk premium must always be
positive and the CML predicts required returns
The observation of ex post poor returns on risky securities does not negate the validity of CML.
It merely indicates that returns actually realized differ from those that were expected
CML is based on expected rates of return so it is ex ante Risk-Adjusted Performance and Sharpe Ratios
Sharpe ratio: a measure of portfolio performance that describes

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