Suppose you are a hedge fund. You are trying to form a portfolio out of 2 risky assetsand a risk-free asset. You can take arbitrarily large long or short positions in the risky assets at no cost.You can also take arbitrarily larger long or short positions in the risk-free asset; however, the risk-free ratedepends on whether you are lending or borrowing. You can invest positive amounts in the risk-free assetand make 2% per year. However, if you short the risk-free asset (borrow money), you must pay 9% interesteach year on what you borrow. Formally, let wrf be your portfolio weight on the risk-free asset, and rrf bethe return on the risk-free asset. We have:2% Wrf > 0Prf9% Wrf <0Asset Expected ReturnStandard DeviationA10%12%В17%22%Assume the correlation between assets A and B is 0.4. a)First, ignore the fact that r,rf depends on whether you are long or short the risk-free asset.Suppose rrf = 2%. Solve for the tangency portfolio.b)asset. Suppose rrf = 9%. Solve for the tangency portfolio.Again, ignore the fact that rrf depends on whether you are long or short the risk-freeNow, for parts c) to f) of the questions, let's take into account that rrf depends on whetherc)you are long or short the risk-free asset. Draw out the shape of the efficient frontier. (Hint: think aboutwhat (E, o) pairs you can achieve via investing positive amounts in the risk-free asset, and investingnegative amounts in the risk-free asset (borrowing). You will use your answers to parts A. and B.).The drawing does not need to be to scale, but needs to illustrate correctly the shape of the efficientfrontier.d)deviation of 10%. Solve for the optimal portfolio for the client (that is, the weights wA, WB,Wrf whichmaximize the client's expected return, conditional on the standard deviation being less than 10%).Suppose your client wants to maximize returns, but can accept a maximum standarde)deviation of 35%. Solve for the optimal portfolio for the client.Suppose your client wants to maximize returns, but can accept a maximum standardf)deviation of 18%. Solve for the optimal portfolio for the client.Suppose your client wants to maximize returns, but can accept a maximum standard

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a) First, ignore the fact that rrf depends on whether you are long or short the risk-free asset. Suppose Trf = 2%. Solve for the tangency portfolio. b) Again, ignore the fact that rrf depends on whether you are long or short the risk-free asset. Suppose Trf = 9%. Solve for the tangency portfolio. c) Now, for parts c) to f) of the questions, let's take into account that rrf depends on whether you are long or short the risk-free asset. Draw out the shape of the efficient frontier. (Hint: think about what (E, o) pairs you can achieve via investing positive amounts in the risk-free asset, and investing negative amounts in the risk-free asset (borrowing). You will use your answers to parts A. and B.). The drawing does not need to be to scale, but needs to illustrate correctly the shape of the efficient frontier.

a) First, ignore the fact that rrf depends on whether you are long or short the risk-free asset. Suppose Trf = 2%. Solve for the tangency portfolio. b) Again, ignore the fact that rrf depends on whether you are long or short the risk-free asset. Suppose Trf = 9%. Solve for the tangency portfolio. c) Now, for parts c) to f) of the questions, let's take into account that rrf depends on whether you are long or short the risk-free asset. Draw out the shape of the efficient frontier. (Hint: think about what (E, o) pairs you can achieve via investing positive amounts in the risk-free asset, and investing negative amounts in the risk-free asset (borrowing). You will use your answers to parts A. and B.). The drawing does not need to be to scale, but needs to illustrate correctly the shape of the efficient frontier.

EBK CONTEMPORARY FINANCIAL MANAGEMENT

14th Edition

ISBN:9781337514835

Author:MOYER

Publisher:MOYER

Chapter8: Analysis Of Risk And Return

Section: Chapter Questions

Problem 13QTD

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Suppose that the return on the risk-free asset is rRFrRF = 15%, the return on the market portfolio is r̂Mr̂M = 20%, the market risk is σMσM = 10%, and the portfolio risk is σpσp = 15%. Then the expected rate of return on an efficient portfolio equals . Generally, a less risky portfolio would havea lower rate of return.
The CAPM states that the expected (required) return on an asset is : E(Ri)=Rf+βi[E(RM)−Rf] where the term in square brackets is the risk-premium earned by the market portfolio. Therefore, the beta of the market portfolio (βM) must be equal to __________ . A) zero B) 0.5 C) 1.0 D) an unknown estimate
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Which 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.
assume that risk free rate, RF, is currently 8%, the market return, 1m, is 12%, and asset a beta ba, is 1.10. (a) Draw the SML on a set of "non-diversifiable risk Please sent me complete this question for further reliance.
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.
Assume CAPM holds. Consider a portfolio that consist of a risk-free asset and two risky assets A and B such that they are in equal supply in the market. This implies that the market portfolio M = 0.5A +0.5B. Given that µM = 11%, σA = 20%,σB = 40%,ρAB = 0.75 and the risk-free rate is 2%. Compute: a) The beta factor for each security. b) The values for µA and µB and verify these quantities via the SML.
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Answer whether each of the following statements is correct and explain your argument. \ (a) According to CAPM, the expected return of a risky asset is larger than the risk free rate. (b) According to CAPM, the expected return of a risky asset increases with its variance. (c) According to the separation property, the optimal risky portfolio for an investor dependson the investor’s personal preference. (d) A less risk-averse investor has a steeper indifference curve for the utility function.
Suppose that there are two assets: A and B. Asset A has expected return of 20%. B has expected return of 12% and standard deviation of σ* σ* = standard Deviation (σ) (a) “As B is strictly dominated by A in terms of total risk (standard deviation), there is no value in having B in portfolio formation.” (Without doing any calculation) (b) “If the correlation coefficient ρ between A and B = 1, it is always optimal to invest in A only.” (Show your proof) (c) “If the correlation coefficient ρ between A and B = -1, it is always optimal to invest in 50% in A and 50% in B when forming a minimum variance portfolio of the two.” (Show your proof) [ (d) “Given that σA= σB=σ*, it is always optimal to combine half of A and half of B when forming a minimum variance portfolio of the two when ρ ε (-1,1).” (Show your proof)
Now assume that your portfolio only includes a risky asset, Asset C and a risk-free asset, Asset D. If the expected return on Asset D is 18%, the expected return on your po is 12% and the percentage of your wealth allocated to Asset C is 30%, what is the risk-free rate?
d. Would this asset be considered more or less risky than the market? The asset is a. Equally as risky the market portfolio, which has a beta of a. 1 b. less risky than b. 0 c. more risky than c. -1