You have two assets to choose from for your portfolio: A and B. You choose 25% A and 75% B. The statistics of the two assets are: • E(r) = 7%, E(r₂ ) = 12% B 0² = 0.0016, 0² B = 0.0049 A Compute the expected return and variance of your portfolio under each of the following assumptions: • 1. PAB = 0.5
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- APT An analyst has modeled the stock of Crisp Trucking using a two-factor APT model. The risk-free rate is 6%, the expected return on the first factor (r1) is 12%, and the expected return on the second factor (r2) is 8%. If bi1 = 0.7 and bi2 = 0.9, what is Crisp’s required return?Two-Asset Portfolio Stock A has an expected return of 12% and a standard deviation of 40%. Stock B has an expected return of 18% and a standard deviation of 60%. The correlation coefficient between Stocks A and B is 0.2. What are the expected return and standard deviation of a portfolio invested 30% in Stock A and 70% in Stock B?Find the expected portfolio return and standard deviation if you were to invest 50% of your portfolio in Asset B, 50% in Asset C, with no allocation to Asset A. Compute your answers to the nearest tenth of a basis point. (See attached data file) We know that Asset A: B: C: expected return: 1.16 1.35 1.38 expected standard deviation: 2.88 1.58 2.19
- a. Use the following information: E[rXOM] = 15.6%, standard deviationXOM = 15.9% E[rMS]=29.7%, standard deviationMS = 35.2% Correlation of returns: ρXOM,MS = 0.139, rf=10% If the optimal amount to invest in the first asset (w) is 0.43, what is the variance of the risky portfolio when w=0.43? (write in decimal format using 5 decimal places) b. When choosing the best point of the POS (the curved line connecting two possible assets you can invest in) you need to find the point that: 1.Has the greatest difference between it’s return and the risk free rate, thus leading to the best return 2. You must solve for the optimal y allocation in order to find the best point on the POS 3. The point with the lowest standard deviation 4. The point with the greatest Sharpe ratioConsider a position consisting of a K200,000 investment in Asset A and a K300,000 investment in Asset B. Assume that the daily volatilities of the assets are 1.5% and 1.8% respectively, and that the coefficient of correlation between their returns is 0.4. What is the five day 95% Value at Risk (VaR) for the portfolio (95% confidence level represents 1.65 standard deviations on the left side of a normal distribution)?You are constructing a portfolio of two assets, Asset A and Asset B. The expected returns of the assets are 12 percent and 15 percent, respectively. The standard deviations of the assets are 29 percent and 48 percent, respectively. The correlation between the two assets is .25 and the risk-free rate is 5 percent. What is the optimal Sharpe ratio in a portfolio of the two assets? What is the smallest expected loss for this portfolio over the coming year with a probability of 2.5 percent?
- You are evaluating various investment opportunities currently available and you have calculated expected returns and standard deviations for five different well-diversified portfolios of risky assets:Portfolio Expected Return Standard DeviationQ 7.8% 10.5%R 10.0 14.0S 4.6 5.0T 11.7 18.5U 6.2 7.5a. For each portfolio, calculate the risk premium per unit of risk that you expect to receive ([E(R) − RFR]/σ). Assume that the risk-free rate is 3.0 percent.b. Using your computations in Part a, explain which of these five portfolios is most likely tobe the market portfolio. Use your calculations to draw the capital market line (CML).c. If you are only willing to make an investment with σ = 7.0%, is it possible for you toearn a return of 7.0 percent?d. What is the minimum level of risk that would be necessary for an investment to earn7.0 percent? What is the composition of the portfolio along the CML that will generatethat expected return?e. Suppose you are now willing to make an investment…Calculate the risk (standard deviation) of a 2-asset portfolio, in which asset A has a variance of return = 0.112, asset B a variance of return = 0.045, and the convariance between the return of 2 assets is = 0.102. asset A comprises 60% ans asset B comprises 40% of the total portfolio. Give your answer 0.000.Below are the returns for two assets; State of nature r1 r2 probability Weak growth 15% 15% 1/3 Strong growth 30% 12 1/3 Very strong growth 45% 9 1/3 Expected returns 30% 12 total 1.0 Calculate the two variances and Cov (r1, r2). If assets 1 and 2 are combined 50-50 into a portfolio, what is the variance of this portfolio? Show your calculations.
- You are evaluating various investment opportunities currently available and you have calculated expected returns and standard deviations for five different well-diversified portfolios of risky assets. PORTFOLIO EXPECTED RETURN STANDARD DEVIATION Q 7.8% 10.5% R 10.0% 14.0% S 4.6% 5.0% T 11.7% 18.5% U 6.2% 7.5% a) For each portfolio, calculate the risk premium per unit of risk that you expect to receive [(E(R) –RFR)/ơ]. Assume that the risk free rate is 3.0%. b) Using…An investor invests 30% of his wealth in a risky asset with an expected rate of return of 0.15 and a variance of 0.04 and 70% in a T-bill that pays 6%. His portfolio's expected return and standard deviation are __________ and __________, respectively. A. 0.087; 0.06 B. 0.295; 0.06 C. None of the options are correct. D. 0.087; 0.12 E. 0.114; 0.12Suppose Asset A has an expected return of 10% and a standard deviation of 20%.Asset B has an expected return of 16% and a standard deviation of 40%. If thecorrelation between A and B is 0.35, what are the expected return and standarddeviation for a portfolio consisting of 30% Asset A and 70% Asset B?