1. Suppose S₁ = 4, S₁(H) = 8, S₁(T) = 2 and the risk-free interest rateSois r = 0. Someone is willing to buy or sell European Call options withstrike price k = 10 for the price Vo = 2. Explain why there exists anarbitrage opportunity; ie construct a portfolio which starts with nothing,has a positive chance of earning money and zero probability of losing money.SOLUTION

This constitutes an arbitrage opportunity since it is costless to construct the portfolio but still…

Answered: 1. Suppose S₁ = 4, S₁(H) = 8, S₁(T) = 2…

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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Suppose you observe the following situation:Security Beta Expected ReturnDiamond Co 1.3 0.2Spade Co 0.8 0.14 (a) According to the above information, could we figure out the market return and risk-free rate? Explain your answer. (b) Discuss the possibility of including zero beta or negative beta assets in your portfolio. Explain the pros and cons of including these types of assets.
Consider the following portfolio choice problem. The investor has initial wealth w andutility u(x) = (x^n) /n. There is a safe asset (such as a US government bond) that has netreal return of zero. There is also a risky asset with a random net return that has onlytwo possible returns, R1 with probability 1 − q and R0 with probability q. We assumeR1 < 0, R0 > 0. Let A be the amount invested in the risky asset, so that w − A isinvested in the safe asset.i) What are risk preferences of this investor, are they risk-averse, riskneutral or risk-loving?ii) Find A as a function of w.
Consider a world with only two risky assets, A and B, and a risk-free asset. The two riskyassets are in equal supply in the market, i.e., the market portfolio M = 0.5A + 0.5B. Itis known that R¯M = 11%, σA = 20%, σB = 40% and ρAB = 0.75. The risk-free rate is2%. Assume CAPM holds.(a) What is the beta for each stock?(b) What are the values for R¯A and R¯B?
ANSWER C AND D PLEASE ONLY Consider the following portfolio choice problem. The investor has initial wealth w andutility u(x) = (x^n) / n. There is a safe asset (such as a US government bond) that has netreal return of zero. There is also a risky asset with a random net return that has onlytwo possible returns, R1 with probability 1 − q and R0 with probability q. We assumeR1 < 0, R0 > 0. Let A be the amount invested in the risky asset, so that w − A isinvested in the safe asset.a) What are risk preferences of this investor, are they risk-averse, riskneutral or risk-loving?b) Find A as a function of w. c) Does the investor put more or less of his portfolio into the risky assetas his wealth increases? d) Now find the share of wealth, α, invested in the risky asset. How doesα change with wealth?
The 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?
Consider an economy with a (net) risk-free return r1 = 0:1 and a market portfolio with normally distributed return, with ErM = 0:2 and 2M = 0:02. Suppose investor A has CARA preferences, with risk aversion coe¢ cient equal to 1 and an endowment of 10. a) Write down the maximization problem for the investor. b) Determine the amount invested in the risky portfolio and in the risk-free asset. c) Suppose another investor (B) has a coe¢ cient of absolute risk aversion equal to 2 (and the same endowment 10). Compute his optimal portfolio and compare it to that of investor A. Explain the di§erent results for investors A and B. d) Finally, consider Investor C with mean-variance preferences Ec V ar(c) (and endowment 10). Compute his optimal portfolio and compare it to that of investors A and B (as obtained in questions b and c). Compare your result with those obtained for investors A and B.
Consider the following portfolio choice problem. The investor has initial wealth w and utility u(x)=. 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. Let A be the amount invested in the risky asset, so that w - A is invested in the safe asset. 1) Does the investor put more or less of his portfolio into the risky asset as his wealth increases?
Suppose that C is the price of a European call option to purchase a security whose present price is S.Show that if C > S then there is an opportunity for arbitrage (i.e. riskless profit). You may assume theinterest rate is r = 0 so that present value calculations are unnecessary.
Suppose that C is the price of a European call option to purchase a security whose present price is S. Show that if C>S then there is an opportunity for arbitrage (i.e. risk-less profit). You may assume the interest rate is r=0 so that the present value calculations are unnecessary.
Suppose the Capital Asset Pricing Model (CAPM) is valid in a market. Use CAPM to ex- plain and answer following questions. Note: There is no relationship between each situation. (a) Can security A exist in the market? (Hint: Security market line) If yes, compute risk premium on security A. If not, is this security underpriced or overpriced? Expected return 5% Asset Beta Risk-free Market 12% 1 A 15% 1.3 (b) Can security B exist in the market? (Hint: Security market line) If yes, compute risk premium on security B. If not, is this security underpriced or overpriced? Expected return 6% Asset Beta Risk-free Market 13% 16.5% 1 1.5 Suppose the expected cash flow can be collected from investment in security B is $1000 at time 1. And an investor thinks the beta of security B is 1.8. But the actual beta is given in the above table. Then how much more/less (you also need to select "more" or "less") will he offer for the firm than it is truly worth at time 0? Hint: the present value of the cash…
a) Suppose the risk-free rate is `X'% and the expected rate of return on the market portfolio is 10%. In your view, the expected rate of return of a security is 12.2%. Given that this security has a beta of 1.4, do you consider it to be overpriced, under-priced or fairly priced according to the Capital Asset Pricing Model? Please provide the details of your calculations and discuss your results. b) Using a graph, explain when a security is overpriced, under-priced or fairly priced according to the Capital Asset Pricing Model. Plot your answer from (a) onto this graph.
a) Suppose the risk-free rate is 7% and the expected rate of return on the market portfolio is 10%. In your view, the expected rate of return of a security is 12.2%. Given that this security has a beta of 1.4, do you consider it to be overpriced, under-priced or fairly priced according to the Capital Asset Pricing Model? Please provide the details of your calculations b) explain when a security is overpriced, under-priced or fairly priced according to the Capital Asset Pricing Model.

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