( :). ( 26 + a За + 2b Consider two assets with returns: rı = b r2 = in two states. - a a + 26 Calculate the values of a and b so that the portfolio consisting of 2 units of r1 and 4 -1 unit of r2, has a return ) and answer: find the s um a + b.
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- Consider two assets, A and B. A earns +4%, -5%, or +3%, in scenarios 1, 2, and 3. B earns -5%, +3%, or +4%, in scenarios 1, 2, and 3. Each scenario is equally likely. Compute the expected rates of return and SD for each asset, A and B. Now, consider a portfolio of assets A and B called AB, where the investor holds fraction 59% of his portfolio in A and fraction (1-59%) in B. Compute the standard deviation of AB. Compare the new standard deviation to that of each asset's individual standard deviation. What was the change in standard deviation between asset A and portfolio AB? StDev(AB) - StDev(A). Report answer to the four decimal place.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.)We have three assets A1, A2, A3 and the following information: E(r1)=15%, σ1=12%,; E(r2)=19% and risk σ2=30%; E(r3)=25% and Risk σ3=35% a) Calculate the effective diversification between A1, A2, A3, and assume ρ12=ρ13=ρ23=0, the expected returns are i.17%, ii.11%
- Q11. n is the number of periods of an investment, PV is the starting value, FVn is the future value n periods ahead, and ^ means 'to the power of'. What is the correct formula for calculating return? Group of answer choices 1. (FVn/PV)^n - 1 2. (FVn/PV)^n 3. (PV/FVn)^n - 1 4. 1 - (FVn/PV)^nQuestion 2 You must choose between two investments, X and Y . The profitability index (PI), net present value (NPV) and internal rate of return (IRR) of the two investments are as follows: Criteria Investment X Investment Y NPV R44 000 −R22 000 PI 1,945 0,071 IRR 16,00% 8,04% Which investment(s) should you choose, taking all the above criteria into consideration, if the cost of capital is equal to 12% per year? [1] X [2] Y [3] Both X and Y [4] Neither X nor Y [5] Too little information to make a decision 17 DSC1630QUESTION 2 Exhibit 6.2 USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) Asset (A) Asset (B) E(RA) = 25% E(RB) = 15% (σA) = 18% (σB) = 11% WA = 0.75 WB = 0.25 COVA,B = −0.0009 Refer to Exhibit 6.2. What is the expected return of a portfolio of two risky assets if the expected return E(Ri), standard deviation ( σ i ), covariance (COVi,j), and asset weight (Wi) are as shown above? a. 18.64% b. 22.5% c. 11% d. 13.65% e. 20.0%
- Asset 1 has a standard deviation of returns of 0.15 while Asset 2 has a standard deviation of returns of 0.20. The correlation coefficient between the returns of the two assets is 0.34. Which of the following is closest to the covariance of the returns of the two assets if they are combined into an equally weighted portfolio? Group of answer choices 0.0129 0.0207 0.0102 0.1440As 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%?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 ratio
- Consider a single-index model economy. The index portfolio M has E(RM ) = 6%, σM = 18%.An individual asset i has an estimate of βi = 1.1 and σ2ei = 0.0225 using the single index modelRi = αi + βiRM + ei. The forecast of asset i’s return is E(ri) = 12%. rf = 4%. a) According to asset i’s return forecast, calculate αi. (b) Calculate the optimal weight of combining asset i and the index portfolio M . (c) Calculate the Sharpe ratio of the index portfolio M and the portfolio optimally combiningasset i and the index portfolio M .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%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%.