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What is the minimum variance portfolio of 2 risky assets?
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- Define the term Risk Analysis?What is the risk premium(s)?1. Sally is evaluating two portfolios which consist of four assets but with different proportions. She is interested in using beta to compare the risk of the portfolio. Given below is the information on each of the portfolios: Portfolio Weights (%) Portfolio Weights (%) Asset Asset Beta Portfolio X Portfolio Y 1 1.20 15 25 2 0.95 20 20 3 0.70 40 25 4 1.30 25 30 Total 100 100 (a) Calculate the betas for portfolios X and Y. (6) (b) Compare the risk of each portfolio to the market portfolio as well as to each other. Assume the market beta is 1.0. (4) (c) Determine which portfolio is riskier. Explain. (4) (d) Calculate the required return for each portfolio based on the capital asset pricing model (CAPM), assuming the risk-free rate is 2% and the market return is 9%. (6) (Total / Jumlah: 20)
- 3. The risk free rate is 3%. The optimal risky portfolio has an expected return of 9% and standard deviation of 20%. Answer the following questions. (a) Assume the utility function of an investor is U = E(r) − 0.5Aσ2. What is condition of A to make the investors prefer the optimal risky portfolio than the risk free asset? (b) Assume the utility function of an investor is U = E(r) − 2.5σ2. What is the expected return and standard deviation of the investor’s optimal complete portfolio?Problem 2 Suppose a firm needs $100 to invest in a project. The firm can choose between two projects: S (safe) or R (risky). The bank cannot directly control the choice of project. If it is S, then it will yield a cash flow of $300 with probability 0.8 and zero with probability 0.2. If it is R., the project will yield a cash flow of $423 with probability 0.5 and zero with probability 0.5. Everybody is risk neutral. The riskless interest rate is 20%. The bank would like to induce the choice of project S. Assume that collateral worth $1 to the firm is worth $0.9 to the bank. The banking sector is perfectly competitive. a. Demonstrate that when the bank offers an unsecured loan, project S will never be chosen. b. Calculate the interest rate when the bank offers an unsecured loan. c. What kind of secured contract would the bank offer to induce the choice of project S? d. Calculate the collateral and interest rate associated with this secured contract.Which type of risk can be affected by outside factors such as natural disasters or power outages? financial risk strategic risk operational risk compliance risk
- A risk-averse investor will: a. Always accept a greater risk with a greater expected return b. Only invest in assets providing certain returns c. Sometimes accept a lower expected return if it means less ri d. Never accept lower risk if it means accepting a lower expected return"Your company is comparing three projects that have risks associated with them. Based on the data in the foliowing data in the table, which should be chosen? Project A Project B Project C Probability 0.3 EUAW Probability 0.3 0.2 EUAW EUAW -$2,400 $2,000 $3,500 $3,000 -$2,300 $3,800 Probability 0.1 0.4 -$5,500 $7,200 $1,900 0.45 0.25 0.5 0.51. Which of the following is INCORRECT? a All of a stock's risk could be unsystematic. b. A negative beta stock has an expected return less than the risk-free rate. c. Anticipated returns on any given stock are always greater than 0. d. Two assets with a correlation of -1 could be combined to create a portfolio with a standard deviation of zero (no risk). 2. Which of the following measures the total risk of a portfolio? a. Beta b. Standard Deviation c. Correlation Coefficient d. Alpha 3. Which of the following stocks have the highest systematic risk? a A stock with high correlation to the market and high returm volatility. b. A stock with low correlation to the market and a high return volatility. c A stock with high correlation to the market and a low return volatility. d. A stock with low correlation to the market and a low return volatility. 4. Which of the following companics have the lowest systematic risk? a A company that sells soups (Campbells), beta=0.60 b. A coffee company…
- Optimal Portfolio: Mean-Variance OptimizationIf you are a portfolio manager who predicted that the tension in Ukraine might spiral into a global economic problem back in December 2021. She decided to construct a portfolio that, she think, would outperform in a war scenario, or in a heightened war risk scenario. Please use the following ETFs:IAU: iShares Gold Trust ETFVDE: Vanguard Energy ETFXLB: Materials Sector SPDR ETFDBC: Invesco DB Commodity Index Tracking FundCQQQ: China Technology Index ETFConstraints:i. Use all ETF products. (Weight of each ETF>= 2% )ii. No ETF is to have more than 40% weight in portfolioObjective: Maximize Expected Return, Minimize volatility, ie. MaximizeSharpe RatioStep 1: Collect historical price/return data for the ETFs over Jan-2018 to Dec-21 period.Step 2: Assume the Average Historical Return is the Expected Return for each asset (strong assumption) and Historical Volatility is the Expected Volatility (strong assumption).Step 3: Present the var-cov…Question 11 The beta of an active portfolio is 1.45. The standard deviation of the returns on the market index is 22%. The nonsystematic variance of the active portfolio is 3%. The standard deviation of the returns on the active portfolio is a) 36.30%. b) 5.84%. c) 19.60%. d) 24.17%. e) 26.0%.Suppose you visit with a financial adviser, and you are considering investing some of your wealth in one of three investment portfolios stocks, bonds, or commodities. Your financial adviser provides you with the following table, which gives the probabilities of possible returns from each investment To maximize your expected return, you should choose: Stocks Bonds Probability Return Probability Return 0.15 20% 0.15 16.7% 06 10% T 04 7.5% 0.25 8% 0.45 3.3% OA bonds OB stocks OC. commodities OD. All of the portfolios have the same expected return. If you are risk-averse and had to choose between the stock or the bond investments, you would choose OA the stock portfolio because there is less uncertainty over the outcome OB. the bond portfolio because there is less uncertainty over the outcome. OC. the stock portfolio because of greater expected return. OD. the bond portfolio because of greater expected return. Commodities Probability Return 02 20% 0.2 15% 0.2 8% 02 02 5% 0%