the following return schedules for 3 investments: return -2% 6% 10% Prob 0.4 0.3 0.3 8.72% 2 return Prob -5% 12% 0.5 0.5 return 2% 3 Prob 1 std dev (a) 12.02% 0.00% Can you say for certain which investment would be preferred by a risk averse investor? Can you say for certain which investment would NOT be chosen by a risk averse investor? Explain your answer. [HINT: start by calculating the expected values!]
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- Compute the expected rate of return on investment i given the followinginformation: Rf = 8%; E(RM) = 14%; βi = 1.0.b. Recalculate the required rate of return assuming βi is 1.8.25. a. Compute the expected rate of return on investment i given the followinginformation: the market risk premium is 5%; Rf = 6%; βi = 1.2.b. Compute E(RM)Suppose there are two investments A and B. Either investment A or B has a 4.5% chance of a loss of $15 million, a 2% chance of a loss of $2 million, and a 93.5% change of a profit of $2 million. The outcomes of these two investments are independent of each other. (a) What is the 95% VaR of investment A? How about investment B? (b) What is the 95% for a portfolio consisting of both investments A and B?(Hint: write out the probabilities of all possible portfolio outcomes.) (c) Is the summation of the 95% VaRs of the individual investments greater or smaller than the 95% VaR of the portfolio? If we measure the risk of an investment or portfolio using VaR, does this suggest that diversificationmust decrease risk? (Intuitively, putting A and B in a portfolio is a form of diversification.)You manage a risky portfolio with an expected rate of return of 18% and a standard deviation of 30%. The T-bill rate is 6%. Your client’s degree of risk aversion is A = 3.4, assuming a utility function U = E(r) - ½Aσ². a. What proportion, y, of the total investment should be invested in your fund? (Do not round intermediate calculations. Round your answer to 2 decimal places.) b. What is the expected value and standard deviation of the rate of return on your client’s optimized portfolio? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
- Assume that an investment is forecasted to produce the following returns: a 20% probability of a 12% return; a 50% probability of a 16% return; and a 30% probability of a 19% return What is the standard deviation of return for this investment? A) 5.89% B) 16.1% C) 2.43% D) 15.7%For investment A, the probability of the return being 20.0% is 0.5, 10.0% is 0.4, and -10.0% is 0.1 Compute the standard deviation for the investment with the given information. (Round your answer to one decimal place.) a. 85.00% b. 15.00% c. 34.00% d. 17.00% e. 9.00%Please help me answer this question in Excel Form 2. The risk-free rate is 4%, and the required return on the market is 12%. b. A portfolio invests 40% in the asset in (a) and the rest in a market portfolio. What is the required return on this portfolio? Thanks :)
- As per Capital Asset Pricing Model (CAPM) : Re=Rf+(Rm-Rf)βwhere, Re= Required rate of returnRf= Risk free rate of return = 0%Rm = Market return or Expected return on market = 3.3%β = Beta of the stock = 1.24Now, Re= Rf + Rm - Rf βRe= 0 + 3.3 - 0 ×1.24Re= 4.092% To calculate the abnormal return we will use the formula: = E(R) - Re= 3% - 4.092% = -1.092% or - 0.01092 How did you get the 4.092%?2) A risky portfolio is provided with an expected rate of return of 19.5%, standard deviation of 30% and risk free rate of 8.5%. If the client chooses to invest three different risky assets a proportion of equal investments and also in T bills. a) Determine weights of all the distributed assets. b) Determine the Sharpe ratio of the portfolio c) If the investment is done such a way that the expected return is maximized with standard deviation not exceeding 25%. Determine the investment proportion and expected return of the portfolio.Consider 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)?
- The risk-free rate is currently 3.3%, and the market return is 14.8%. Assume you are considering the following investments: Investment Beta A 1.54 B 1.16 C 0.51 D 0.11 E 2.14 . a. Which investment is most risky? Least risky? b. Use the capital asset pricing model (CAPM) to find the required return on each of the investments. c. Find the security market line (SML), using your findings in part b. d. On the basis of your findings in part c, what relationship exists between risk and return? Explain.QH. The data for the two companies X and Y are as follows: X Y Return 20% 23% Risk ( SD) 21% 25% r 0.4 Find the portfolio risk if 50% of funds is allocated for each. Determine the correlation coefficient that would be necessary to reduce the level of portfolio risk by 25%.2. Assuming the following: Average Return (Risky Portfolio) 3.86% Standard Dev (Risky Portfolio) 10.56% Average Risk Free Rate 2.18% Return on Risk Free Asset Avg 4.15% Using the formula: E(rc)=rf + y* (E(rp) - rf) Solve for: 1. % of Risky Assets (y): 2. % of Risk Free Assets (1-y): Note: You wish to generate a 7% return for your complete portfolio E(rc)