Which of the following is a possible investment strategy for an investor who wishes to hold a portfolio with a standard deviation of 6%? 30% invested in the risk-free and 70% in security j 60% invested in the risk-free and 40% in security i 50% invested in the risk-free and 50% in security i
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- Assume that the following two assets are priced according to the zero-beta security market line: asset 1 has expected return of 6% and beta 0.5; asset 2 has expected return 14% and beta 2. (i) A third asset is mispriced by the market: it has beta 1.5 and expected return of 8%. Explain how you can set up a portfolio to exploit the arbitrage opportunity. What is the expected return of such portfolio? [33%] (ii) A fourth asset is mispriced by the market: it has beta 1.2 and expected return of 18%. Explain how you can set up a portfolio to exploit the arbitrage opportunity. What is the expected return of such portfolio? [33%] (iii) What should be the expected return for an asset with beta 0.8?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?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?
- Consider two perfectly negatively correlated risky securities A and B. A has an expected rate of return of 10% and a standard deviation of 16%. B has an expected rate of return of 8% and a standard deviation of 12%. An investor who wishes to form a portfolio that lies to the right of the optimal risky portfolio on the Capital Allocation Line must: A. lend some of her money at the risk-free rate. B. borrow some money at the risk-free rate and invest in the optimal risky portfolio C. invest only in risky securities D. such a portfolio cannot be formed E. both borrow some money at the risk-free rate and invest in the optimal risky portfolio and invest only in risky securitiesAssume an economy in which there are three securities: Stock A with rA = 10% and σA = 10%; Stock B with rB = 15% and σB = 20%; and a riskless asset with rRF = 7%. Stocks A and B are uncorrelated (rAB = 0). Which of the following statements is most CORRECT? 1. b. The expected return on the investor’s portfolio will probably have an expected return that is somewhat below 10% and a standard deviation (SD) of approximately 10%. 2. d. The investor’s risk/return indifference curve will be tangent to the CML at a point where the expected return is in the range of 7% to 10%. 3. e. Since the two stocks have a zero correlation coefficient, the investor can form a riskless portfolio whose expected return is in the range of 10% to 15%. 4. a. The expected return on the investor’s portfolio will probably have an expected return that is somewhat above 15% and a standard deviation (SD) of approximately 20%. 5.…Consider 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.
- 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.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.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.
- 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.2C) Assume that the CAPM holds in the economy. The following data is available about the market portfolio, the riskless rate, and two risky assets, W and X: The market portfolio has a standard deviation equals to 10%, stock W has an expected return equals to 16%, standard deviation equals to 12%, and beta equals to one, stock X has a standard deviation equals to 6% and beta equals to 0.7. The risk-free rate is 3%. What is the expected return and the beta of the market portfolio? What is the expected return on asset X? Does asset W lie on the Capital Market Line? Explain why or why not. Suppose you invested $100,000 in these two stocks. The beta of your portfolio is 1.25. How much did you invest in each stock? What is the expected return of this portfolio?Suppose that many stocks are traded in the market and that it is possible to borrow at the risk-free rate, rƒ. The characteristics of two of the stocks are as follows: Stock Expected Return Standard Deviation A 12% 40% B 21% 60% Correlation = −1 Required: a. Calculate the expected rate of return on this risk-free portfolio? (Hint: Can a particular stock portfolio be formed to create a “synthetic” risk-free asset?) (Round your answer to 2 decimal places.) b. Could the equilibrium rƒ be greater than rate of return? multiple choice Yes No