Chapter 9 The Capital Asset Pricing Model (CAPM) Notes

9.1 The New Efficient Frontier

The Efficient Frontier with Risk-Free Borrowing and Lending

•risk premium the expected payoff that induces a risk-averse person to enter into a risky situation

•generally, investor behaviour is consistent with risk aversion and existence of risk premiums to induce individuals to bear risk

•insurance premium the payment to get out of a risky situation

•the existence of insurance markets indicates how risk aversion creates a demand to remove risk, whereas the existence of capital

markets indicates how risk aversion generates the risk premiums required to induce people to bear risk

Risk-Free Investing

•ER

p

= RF + w (ER

A

– RF) where ER

p

is the expected return on the portfolio that starts out with w = 0

•as w increases, more is placed in the risky portfolio, so the investor picks up ER

p

at the cost of taking money out of T-bill

•p

= √ [(w)

2

(A

)

2

+ (1 – w)

2

(RF

)

2

+ 2 (1 – w) (w) (A, RF

) (A

) (RF

)] = √ [(w)

2

(A

)

2

] = w A

•ER

p

= RF + [(ER

A

– RF) / A

] p

•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 negative position in asset; investor achieves it by borrowing part of asset’s purchase price from stockbroker

•of course, investors must pay interest on the borrowed money, which can be assumed to be at the risk-free rate

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

•in theory, market portfolio should contain all risky assets, including stocks, bonds, options, futures, gold, real estate, and so on,

in proper proportions; however, in practice, market portfolio is unobservable, so proxies are used to measure its behaviour

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

•the initial development of the CAPM was based on a number of assumptions:

1) All investors have equal expectations about expected returns, standard deviations, and correlation coefficients for securities.

2) All investors have the same one-period time horizon.

3) All investors can borrow or lend money at the risk-free rate of return (RF).

4) There are no transaction costs.

5) There are no personal income taxes, so investors are indifferent whether they receive capital gains or dividends.

6) 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.

7) Capital markets are in equilibrium.

The Market Portfolio and the Capital Market Line (CML)

•capital market line (CML) a line depicting the highest attainable expected return for any given risk level that includes only

efficient portfolios; all rational, risk-averse investors want to be on this line

•slope of the CML = (ER

M

– RF) / M

•market price of risk incremental expected return divided by incremental risk; return that market demands for increase in risk

•ER

P

= RF + [(ER

M

– RF) / M

] P

where ER

M

= the expected return on the market portfolio M, M

= the standard

deviation of returns on the market portfolio, P

= the standard deviation of returns on the efficient portfolio being considered

•required rate of return the rate of return investors need to tempt them to invest in a security

Risk-Adjusted Performance and Sharpe Ratios

•Sharpe ratio measure of portfolio performance that describes how well an asset’s return compensates investors for risk taken

•Sharpe ratio = (ER

P

– RF) / P

•when the portfolio is the market portfolio, the Sharpe ratio is the slope of CML

9.3 The CAPM and Market Risk

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## Document Summary

Chapter 9 the capital asset pricing model (capm) notes. p = [(w)2 (a)2 + (1 w)2 (rf)2 + 2 (1 w) (w) (a, rf) (a) (rf)] = [(w)2 (a)2] = w a. Therefore, investors are price-takers: capital markets are in equilibrium. Sharpe ratio measure of portfolio performance that describes how well an asset"s return compensates investors for risk taken. p = w1 1 + w2 2 + + wn n. i = (ri rf) [i (rm rf)] Summary of learning objectives: describe how the efficient frontier is affected once the possibility of risk-free borrowing and investing is introduced. Once the possibility of risk-free borrowing and investing is introduced, the efficient frontier becomes a straight line. The optimal risky portfolio is the one that is tangent to the efficient frontier on a line that is drawn from rf. This portfolio will be the same for all investors.