If an equal amount of risk is added to a portfolio moving along the Markowitz Efficient Frontier to the northeast, the return will: Decrease at an increasing rate Decrease at a decreasing rate Increase at an increasing rate Increase at a decreasing rate Remain constant None of the above answers is correct
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- The Sharpe ratio Select one: O is computed using idiosyncratic risk only is computed using systematic risk only Ois maximized for the risk-free asset is the highest for a minimum variance portfolio is the same along the capital market lineThere are two assets 1 and 2, with returns X and Y correspondingly. Return X is a random variable with mean 1 and variance 1; return Y is a random variable with mean 1 and variance 3. We know that the expectation of X*Y is equal to 0. Find the share of asset 1 in the risk-minimizing portfolio.Mean-variance expected utility is given by Eu = e-, where e is expected return, v is the variance of the portfolio and tis risk tolerance. Suppose an investor has risk-loving preferences. What can we say about the value of t? Select one: Ot1 O. t>0 O t=0
- Supposing the return from an investment has the following probability distribution Return Probability R (%) 8 0.2 10 0.2 12 0.5 14 0.1 Required: What is the expected return of the investment? What is the risk as measured by the standard deviation of expected returns?Consider the following linear regression model: (R₁-r)= a; + b(RMkt - rf) + e; The b; in the regression: O measures the deviation from the best fitting line and is zero on aver- measures the sensitivity of the security to market risk. measures the diversifiable risk in returns.In a two-asset portfolio, a ________ covariance of returns between the two securities will lead to the greatest reduction in the variance of the portfolio. O negative O positive O relative systematic
- 2. Suppose that you have a riskfree asset and N risky assets for investment. The rate of return on the riskfree asset is r,, while the (Nx1) vector of the rate of return on the N risky assets is r, which is multivariate normal, i.e., r N(u, E). Your utility function for a portfolio that consists of the riskfree asset and the N risky asset is u(r,)=r,-=o, 2 Suppose that the sum of investment proportions on the riskfree and risky assets is one. Answer the following question. A. What is your optimal investment proportion in the risky assets? How is your investment on the riskfree asset affected by different values of 2? B. Suppose that there is only one risky asset i. Show the effects of the Sharpe ratio (4,/0, ) on the investment proportion in the risky asset.A plot/graph of the positive relation between systematic risk and expected return is called: O security market line standard deviation and width of the normal distribution O covariance graph O capital asset pricing modelThe expected rate of return of an investment ________. a. equals one of the possible rates of return for that investment b. equals the required rate of return for the investment c. is the mean value of the probability distribution of possible returns d. is the median value of the probability distribution of possible returns e. is the mode value of the probability distribution of possible returns
- Risk and Return Suppose you hold an asset that delivers a return R. You wish to hedge against a decline in the price of this asset using a risk-free asset with return r; and a market index with return RM. Using the CAPM, explain how you would allocate money between the risk-free asset and the market index so as to minimize your portfolio variance.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?Which one of the following statements is correct? Multiple Choice The risk-free rate of return has a risk premium of 1.0. The reward for bearing risk is called the standard deviation. Risks and expected return are inversely related. The higher the expected rate of return, the wider the distribution of returns. Risk premiums are inversely related to the standard deviation of returns.