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a) Explain the practical relevance of the mean-variance model of portfolio selection
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- Portfolios A, B, and C all lie on the efficient frontier that allows for risk-free borrowing and lending. Portfolio A and B have the following expected returns and return variances: A: μ_A=0.0925 , σ_A^2=0.0225 ; B: μ_B=0.11 , σ_B^2=0.04. Portfolio C’s return has variance σ_C^2=0.1225. What is the expected return and Sharpe ratio of Portfolio C? What is the risk-free interest rate? Explain your calculationsFrom the following equation for expected returns, explain what may cause stock prices to decrease in economic recessions: E(r) – risk-free rate = A*Var(r) A is the risk aversion for the average investor, and Var(r) is the variance of the market portfolio. Assume that investor risk aversion is constant.How to replicate the payoff of a bond (riskless portfolio) using shares and call options? Based on this conclusion, how does a single-step binomial tree option pricing model work?
- Consider two investors A and B.If the Certainty-Equivalent end-of-period wealth of A is less than the Certainty-Equivalent end-of-period wealth of B for the same portfolio choice,then A. Risk aversion of A > Risk aversion of B B. Risk aversion of A = Risk aversion of B C. Risk aversion of A< Risk aversion of B D. Not enough Information Justify your choice in a sentence or two:Using the Utility Function in Portfolio Management, where the utility function is the constant relative risk aversion utility of wealth function U(W) = W^(gamma)/gamma, set gamma to 0.5 and consider a 50-50 bet on winning 50,000 or getting nothing. What is the certainty equivalent wealth for this bet under these assumptions? Group of answer choices 30,000 10,000 25,000 12,500Suppose the expected return on the tangent portfolio is 12% and its volatility is 30%.The risk-free rate is 3%.(a) What is the equation of the Capital Market Line (CML)?(b) What is the standard deviation of an efficient portfolio whose expected return of16.5%? How would you allocate $3,000 to achieve this position
- which one is correct? QUESTION 12 Exhibit 6B.1 USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) The general equation for the weight of the first security to achieve the minimum variance (in a two-stock portfolio) is given by: W1 = [E(σ1)2 − r1.2 E(σ1) E(σ2)] &χεδιλ; [E(σ1)2 + E(σ2)2 − 2 r1.2 E(σ1) E(σ2)] Refer to Exhibit 6B.1. Show the minimum portfolio variance for a portfolio of two risky assets when r1.2 = − 1. a. E(σ1) &χεδιλ; [E(σ1) − E(σ2)] b. E(σ2) &χεδιλ; [E(σ1) − E(σ2)] c. None of these are correct. d. E(σ1) &χεδιλ; [E(σ1) + E(σ2)] e. E(σ2) &χεδιλ; [E(σ1) + E(σ2)]compare and contrast the three portfolio management theories: a) Modern Portfolio Theory by Markowitz b) Active Portfolio Management by Grinold & Kahn c) Equilibrium Approach by Black-LittermanWhich statement about portfolio diversification is CORRECT? i) Typically, as more securities are added to a portfolio, total risk would be expected to decrease at an increasing rate.ii) Proper diversification can reduce or eliminate total risk.iii) The risk-reducing benefits of diversification do not occur meaningfully until at least 50-60 individual securities have been purchased.iv) Because diversification reduces a portfolio's total risk, it necessarily reduces the portfolio's expected return.
- Consider the following portfolio choice problem. The investor has initial wealth w and utility u(x) = X^n/n . There is a safe asset (such as a US government bond) that has a 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 R0 with probability q. We assume R1 < 0, R0 > 0. Let A be the amount invested in the risky asset, so that w−A is invested in the safe asset. Now find the share of wealth, α, invested in the risky asset. How does α change with wealth?From the information generated in the previous two questions;a) Identify two investment alternatives that can be combined in a portfolio. Assume a 50-50 investment allocation in each investment alternative b) Compute the expected return of the portfolio thus formed c) Compute the portfolio’s beta. Is the portfolio aggressive or defensive?Consider the following portfolio choice problem. The investor has initial wealth w and utility u(x) = x^n/n . 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 R0 with probability q. We assume R1 < 0, R0 > 0. Let A be the amount invested in the risky asset, so that w − A is invested in the safe asset. 1. What are risk preferences of this investor, are they risk-averse, riskneutral or risk-loving? 2. Find A as a function of w. 3. Does the investor put more or less of his portfolio into the risky asset as his wealth increases? 4. Now find the share of wealth, α, invested in the risky asset. How does α change with wealth? 5. Calculate relative risk aversion for this investor. How does relative risk aversion depend on wealth?