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P1.T1.62. Nonstandard capital asset pricing model (nonstandard CAPM)

David Harper CFA FRM

David Harper CFA FRM
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AIMs: Describe the impact on the CAPM of the following: Short sales disallowed; Riskless lending and borrowing; Personal taxes; Nonmarketable assets; Heterogeneous expectations; Non-price-taking behavior. Describe the following multi-period versions of CAPM: Consumption-oriented CAPM; CAPM including inflation; Multi-beta CAPM (Edwin J. Elton, Martin J. Gruber, Stephen J. Brown, William N. Goetzmann, Modern Portfolio Theory and Investment Analysis (John Wiley & Sons, Nov 16, 2009))
Questions:

62.1. The standard CAPM makes several unrealistic assumptions (ten, according to Elton!) in order to prove a general equilibrium relationship. The financial literature includes many analyses of an equilibrium relationship in the event that some of these restrictive assumptions are relaxed or violated, including: disallowing short sales; inability to borrow at the riskless rate; the introduction of capital gains and income (divided) tax rates; the presence of nonmarketable assets; and heterogeneous expectations. Which of the following statements most nearly summarizes the viability of relaxing the assumptions of the standard CAPM?

a. The CAPM is "simply not robust" to any relaxation of assumption; even weakly, equilibrium requires all assumptions
b. The CAPM is "restrictively robust" to the introduction of personal taxes, but equilibrium "generally fails" if either short sales are disallowed or investors cannot borrow at the riskfree rate
c. The CAPM is "remarkably robust" (an general equilibrium relationship exists) to the relaxation (or violation) of any ONE of these assumptions
b. The CAPM is "remarkably robust" (an general equilibrium relationship exists) to the simultaneous relaxation (and violation) of ALL assumptions


62.2. One assumption of the standard CAPM is unlimited lending and borrowing at the riskless rate: "The investor can lend or borrow any amount of funds desired at a rate of interest equal to the rate for riskless securities."(Edwin J. Elton, Martin J. Gruber, Stephen J. Brown, William N. Goetzmann, Modern Portfolio Theory and Investment Analysis (John Wiley & Sons, Nov 16, 2009))

If this assumption is eliminated, such that investor can neither lend nor borrow at the riskfree rate, Elton shows that the zero-beta CAPM follows. Each of the following is TRUE about the zero-beta CAPM EXCEPT:

a. Zero-beta CAPM still implies a security market line (SML), although the slope and intercept are different
b. Zero-beta CAPM still has all investors holding the same portfolio in equilibrium
c. In the Zero-beta CAPM the market portfolio is still efficient
d. Although there is no riskless asset in the zero-beta CAPM, theoretically a riskless portfolio (zero standard deviation) is possible


62.3. The consumption-oriented CAPM is directly analogous to the simple form of the CAPM. But which of the following most nearly summarizes the key difference?

a. The consumption-oriented CAPM replaces the single common factor, switching the CAPM's excess return on the market portfolio with the growth rate in per capita consumption
b. The consumption-oriented CAPM adds an additional factor such that its two common factors include both the market risk premium (market's price of risk) and per capita consumption growth
c. The consumption-oriented CAPM exhibits a non-linear relationship between expected return and per capita consumption growth
d. It is false that the consumption-oriented CAPM is analogous to CAPM

Answers:
 
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