INVESTMENTS(LL)W/CONNECT
11th Edition
ISBN: 9781260433920
Author: Bodie
Publisher: McGraw-Hill Publishing Co.
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Chapter 10, Problem 2CP
Summary Introduction
To select: Compare the portfolio X and portfolio Y.
Introduction : When there are many portfolios then comparison of their expected return value decide whether there is an arbitrage opportunity of equilibrium opportunity. Equal values of returns offer the equilibrium condition otherwise arbitrage opportunity.
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A zero-investment portfolio with a positive alpha could arise if:a. The expected return of the portfolio equals zero.b. The capital market line is tangent to the opportunity set.c. The Law of One Price remains unviolated.d. A risk-free arbitrage opportunity exists.
We believe that the single factor model can predict any individual asset’s realized rate of return well. Both Portfolio A and Portfolio B are well-diversified: ri = E(ri) + βiF + Ei, where E(ei) = 0 and Cov(F, i) = 0
A
B
β
1.2
0.8
E(r)
0.1
0.08
(1) What is the rate of return of the risk-free asset?
(2) What is the expected rate of return of the well-diversified portfolio C with βC = 1.6, which also exists in the market?
(3) A fund constructs a well-diversified portfolio D. Studies show that βD = 0.6. The expected rate of return of D is 0.06. Is there an arbitrage opportunity? If so, construct a trading strategy to earn profits with no risk. If not, why?
1. The diversifiable risk of a portfolio:
a. Is correlated with systematic risk.
b. Can be made sufficiently small.
c. Is zero in the real world.
d. Is the risk that investors lose because of transaction costs.
Which one of the following conditions determines the investor’s overall optimal portfolio?
a. The marginal ratio of substitution of the investor’s utility function must be equal to the Sharpe ratio of the optimal risky portfolio.
b. The standard-deviation of the overall portfolio in minimised.
c. The expected return of the overall portfolio is maximised.
d. The slope of the Sharpe-ratio is equal to zero.
4. Markets can never be strong-form efficient because:
a. There are too many traders in them.
b. Investors are rational.
c. Information is costly to acquire.
d. All information is public.
5. Which one of the following is not a property of a pure arbitrage portfolio? a. Zero investment.
b. Zero systematic risk.
c. Positive net return.
d. All of the above.
Chapter 10 Solutions
INVESTMENTS(LL)W/CONNECT
Ch. 10 - Prob. 1PSCh. 10 - Prob. 2PSCh. 10 - Prob. 3PSCh. 10 - Prob. 4PSCh. 10 - Prob. 5PSCh. 10 - Prob. 6PSCh. 10 - Prob. 7PSCh. 10 - Prob. 8PSCh. 10 - Prob. 9PSCh. 10 - Prob. 10PS
Ch. 10 - Prob. 11PSCh. 10 - Prob. 12PSCh. 10 - Prob. 13PSCh. 10 - Prob. 14PSCh. 10 - Prob. 15PSCh. 10 - Prob. 16PSCh. 10 - Prob. 17PSCh. 10 - Prob. 18PSCh. 10 - Prob. 19PSCh. 10 - Prob. 1CPCh. 10 - Prob. 2CPCh. 10 - Prob. 3CPCh. 10 - Prob. 4CPCh. 10 - Prob. 5CPCh. 10 - Prob. 6CPCh. 10 - Prob. 7CPCh. 10 - Prob. 8CP
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- Return on a portfolio of two risky assets which are perfectly negatively correlated is equivalent to a. Risk-free rate b. Return on market portfolio c. Zero return d. -1%arrow_forwardA portfolio that is positively correlated with the market portfolio but not particularly sensitive to market risk factors would have a beta that is A. Equal to zero. B. Equal to one. C. Less than zero. D. Between 0 and 1. E. Greater than 1.arrow_forwardThe following figures show the optimal portfolio choice for two investors with different levels of risk-aversion graphically. Which statement is correct? E[R] 0.3 0.25 0.2 0.15 0.1 0.05 0 0 0.05 0.1 0.15 Figure 1 0.2 0.25 0.3 0.35 o(R) 0.4 0.45 [H]Z 0.3 0.25 0.2 0.15 0.1 0.05 0 0 0.05 0.1 Figure (2) shows an investor that borrows in risk-free rate and invests in the risky asset. Figure (1) shows an investor with a conservative investment behavior. In the optimal point of both figures, the highest indifference curve is tangent to the efficient frontier. In Figure (1), more aggressive investment decision led to a higher Sharpe ratio. 0.15 Figure 2 0.2 0.25 o (R) 0.3 0.35 0.4 0.45arrow_forward
- Find the weights of the two pure factor portfolios constructed from the following three securities: r1 = .06 + 2F¡ + 2F, r2 = .05 + 3F, + IF, r3 = .04 + 3F, + OF, Then write out the factor equations for the two pure factor portfolios, and determine their risk premiums. Assume a risk-free rate that is implied by the factor equations and no arbitrage.arrow_forwardThe market portfolio (M) has the expected rate of return E(rM) = 0.12. Security A is traded in the market. We know that E(rA) = 0.17 and βA = 1.5. (1) What is the rate of return of the risk-free asset (rf)? (2) Security B is also traded in the market. βB = 0.8. Then what is “fair” expected rate of return of security B according to the CAPM? (3) Security C is a third security traded in the market. βC = 0.6, and from the market price, investors calculate E(rC) = 0.1. Is C overpriced or underpriced? What is αC?arrow_forwardWhich of the following statements regarding the graph of the SML is most accurate? Select one O A. O B. B-1.0 The beta of Portfolios A, B, and C are identical as they fall directly on the line. The expected return of Portfolio C is the difference between the market's expected return and the risk-free rate. O C. Portfolio A has lower systematic risk than Portfolio B. OD. The slope of the line is the market risk premium.arrow_forward
- Consider the following financial market with two risky assets x and y as well as a risk-free asset f: E[r]. x (10%, 8%) •z (6.6%, 6.3%) y (8%, 5%) (0%, 3%) f Is it possible to construct portfolio z with existing assets? Explain.arrow_forwardConsider the following portfolio choice problem. The investor has initial wealth w and utility u(x) = −e. There is a safe asset (such as a US government bond) that has net real return of zero. There is also a risky asset with a random net return that has only two possible returns, R₁ with probability 1 − q and Ro with probability q. We assume R₁ ≤ 0, Ro > 0. Let a be the share of wealth w invested in the risky asset, so that 1 – a share of wealth is invested in the safe asset. (a) Find a as a function of w. How does a change with wealth? Explain the intuition.arrow_forwardThe following figures show the optimal portfolio choice for two investors with different levels of risk-aversion graphically. Which statement is correct? E[R] 0.3 0.25 0.2 0.15 0.1 0.05 0 0 0.05 0.1 0.15 Figure 1 0.2 0.25 0.3 0.35 0.4 0.45 o (R) E[R] Figure (1) shows an investor with a conservative investment behavior. 0.3 0.25 0.2 0.15 0.1 0.05 0 0 Figure (2) shows an investor that borrows in risk-free rate and invests in the risky asset. 0.05 0.1 0.15 In the optimal point of both figures, the highest indifference curve is tangent to the efficient frontier. O In Figure (1), more aggressive investment decision led to a higher Sharpe ratio. Figure 2 0.2 0.25 o(R) 0.3 0.35 0.4 0.45arrow_forward
- An efficient portfolio is one that: Select one: a. maximises return for a given level of risk. b. maximises risk for a given level of return. c. minimises risk for a given rate of return. d. Both A and C. are efficient portfolios.arrow_forwardWhich of the following statements regarding non-systematic risk, systematic risk and total risk is/are true? Select one or more:a. As the number of assets within a portfolio increases, the total risk of a portfolio will go to zero.b. A riskfree asset must have zero non-systematic risk.c. A well diversified portfolio must have zero systematic riskd. Under the Capital Asset Pricing Model (CAPM).an asset with zero systematic risk must have expected return equal to the riskfree rate.arrow_forwardWhich of the following statements are true? Explain.a. A lower allocation to the risky portfolio reduces the Sharpe (reward-to-volatility) ratio.b. The higher the borrowing rate, the lower the Sharpe ratios of levered portfolios.c. With a fixed risk-free rate, doubling the expected return and standard deviation of the risky portfolio will double the Sharpe ratio.d. Holding constant the risk premium of the risky portfolio, a higher risk-free rate will increase the Sharpe ratio of investments with a positive allocation to the risky asset.arrow_forward
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