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a) Explain the practical relevance of the mean-variance model of portfolio selection
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- Suppose one uses the single-index model to estimate characteristics of securities.Which of the following statements is correct? (a)The covariances between securities are the same as in the data. (b)The variance of a portfolio is the same as in the data. (c)The expected return and the variance of a security are the same as in the data. (d)The expected return,variance and covariances of a security are the same as in the daThe variance of six-monthly changes in the price of a commodity is 90.25, the variance of six-monthly changes in the futures price of the commodity is 110.25 and the coefficient of correlation between the two changes is 0.85. A company plans to buy 10,000 units of the commodity in 6 months, the size of the futures contract is on 1,000 units of the commodity and the delivery date of the contract is in 9 months. Consider the following statements. I. The optimal hedge ratio if the futures contract that is used to hedge is 0.6958. II. The hedging effectiveness of the futures contract is 0.85. II. The company should hedge by buying 7.69 futures contracts. IV. If the company hedges optimally, the difference between the variance of the unhedged position and the variance of the optimally hedged position would be 65.21. Which of the following is correct? a. Statement I, |l and IIl are incorrect, Statement IV is correct. O b. Statement I and Il are incorrect, Statement IIlI and IV are correct.…In a binomial interest rate tree model, assume that the six-month rate process starts on date 0 ((=0) at 5% and then increases or decreases by 100 basis points every six months. On date 0. the prices of a six-month zero (A) and a 1-year zero (B) are 97.5610 and 95.0908 respectively. a) Find the risk-neutral probability of an up move on date 0 for the six-month rate process over the next 6-month. b) Find the price of the 1-year zero (B) in the down state of the binomial tree on date 1 (t-1).
- Explain why the variance of an investment is a useful measure of the risk associated with itWhat is the Risk-Adjusted Discount Rate Approach?Which of the following describes the attribute of a risk neutral investor? Select one: a. An investor that makes decisions based on the advice of financial planners. b. An investor that makes decisions based on the expected return of assets. C. An investor that makes decisions based on the credit rating of assets.
- What is the mostly commonly used utility functions for the following and why: Risk Aversion Risk Seeking Risk Neutral1) Explain the importance of continuous variables. 2) How do we define the probability P(X) of a continuous random variable? Provide two examples of continuous random variables. 3) Explain what is meant by a discrete random variable (X), its expected value and standard deviation. 4) What is the usefulness of the Central Limit Theorem?The value of Jon’s stock portfolio is given by the function v(t) = 50 + 77t + 3t2, where v is the value of the portfolio in hundreds of dollars and t is the time in months. How much money did Jon start with? (y-intercept) What is the minimum value of Jon’s portfolio? (vertex)
- 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 calculations8. Risk and return Suppose Frances is choosing how to allocate her portfolio between two asset classes: risk-free government bonds and a risky group of diversified stocks. The following table shows the risk and return associated with different combinations of stocks and bonds. Combination A B с D E Fraction of Portfolio in Diversified Stocks (Percent) 0 25 50 75 100 Average Annual Return (Percent) 2.00 4.50 7.00 9.50 12.00 As the risk of Frances's portfolio increases, the average annual return on her portfolio Standard Deviation of Portfolio Return (Risk) (Percent) 0 Accept more risk Sell some of her bonds and use the proceeds to purchase stocks Sell some of her stocks and place the proceeds in a savings account Sell some of her stocks and use the proceeds to purchase bonds 5 10 15 20 Suppose Frances currently allocates 25% of her portfolio to a diversified group of stocks and 75% of her portfolio to risk-free bonds; that is, she chooses combination B. She wants to increase the average…Why does the limitation of Portfolio analysis is Naively following the prescriptions of a portfolio model may actually reduce corporateprofits if they are used inappropriately?