Assume Abebe has bought 100 shares of Awash bank at the beginning of 2020 for 1,000 birr each Year End of 2020 End of 2021 End of 2021 End of 2022 Dividend received 20,000 0 10,000 30,000 Share price 1,100// share 1,200// share 900// share 1200// share Year End of 2020 End of 2021 End of 2021 End of 2022 Dividend received 20,000 0 10,000 30,000 Share price 1,100// share 1,200// share 900// share 1200// share Compute total return(dividend and capital gain) of each year in birr and in percentage 2. Kate recently invested in real estate with the intention of selling the property one year from today. She has modeled the returns on that investment based on three economic scenarios. She believes that if the economy stays healthy, then her investment will generate a 30 percent return. However, if the economy softens, as predicted, the return will be 10 percent, while the return will be -25 percent if the economy slips into a recession. If the probabilities of the healthy, soft, and recessionary states are 0.4,0.5 , and 0.1 , respectively, then what are the expected return, risk(standard deviation) and coefficient of variation for Kate's investment? 3. The beta of an asset is equal to 0 . what will the expected return be? 4. The expected return on the market portfolio is 15 percent, and the return on the risk-free security is 5 percent. What is the expected return on a portfolio with a beta equal to 0.5 ? 5. You know that the CAPM predicts that the market return of a stock is 23.6 percent. If the risk-free rate of return is 8 percent and the expected return on the market is 20 percent, then what is beta? 6. Elaine has narrowed her investment alternatives to two stocks: Stock M, which has a 23 percent expected return, and Stock Y, which has an 8 percent expected return. If Elaine requires a 16 percent return on her total investment, what proportion of her portfolio will she invest in each stock? 7. Barbara is considering investing in a stock, and is aware that the return on that investment is particularly sensitive to how the economy is performing. Her analysis suggests that four states of the economy can affect the return on the investment. Using the table of returns and probabilities below, find the expected return, the standard deviation and coefficient of variation of the return on Barbara's investment. Probability Return Boom 0.1 25.00% Good 0.4 15.00% Level 0.3 10.00% Slump 0.2 -5.00% Probability Return Boom 0.1 25.00% Good 0.4 15.00% Level 0.3 10.00% Slump 0.2 -5.00% Portfolios with more than one asset: Emmy is analyzing a two-stock portfolio that consists of a Utility stock and a Commodity stock. She knows that the return on the Utility has a standard deviation of 40 percent, and the return on the Commodity has a standard deviation of 30 percent. However, she does not know the exact covariance in the returns of the two stocks. If she invests 50% in each stock, Compute : a) expected risk of the portfolio b) Compute the risk( SD) of the portfolio if covariance of the two stock? i. 0.12 , ii. 0 , and iii. -0.12 c) Which covariance results in to better pertfolio, why? Given the returns and probabilities for the three possible states listed here, calculate the covariance, coefficient of correlation between the returns of Stock A and Stock B. Probability Return(A) Return(B) Good 0.35 0.30 0.50 OK 0.50 0.10 0.10 Poor 0.15 -0.25 -0.30 Probability Return(A) Return(B) Good 0.35 0.30 0.50 OK 0.50 0.10 0.10 Poor 0.15 -0.25 -0.30

Question

Assume Abebe has bought 100 shares of Awash bank at the beginning of 2020 for 1,000 birr each Year End of 2020 End of 2021 End of 2021 End of 2022 Dividend received 20,000 0 10,000 30,000 Share price 1,100// share 1,200// share 900// share 1200// share Year End of 2020 End of 2021 End of 2021 End of 2022 Dividend received 20,000 0 10,000 30,000 Share price 1,100// share 1,200// share 900// share 1200// share Compute total return(dividend and capital gain) of each year in birr and in percentage 2. Kate recently invested in real estate with the intention of selling the property one year from today. She has modeled the returns on that investment based on three economic scenarios. She believes that if the economy stays healthy, then her investment will generate a 30 percent return. However, if the economy softens, as predicted, the return will be 10 percent, while the return will be -25 percent if the economy slips into a recession. If the probabilities of the healthy, soft, and recessionary states are 0.4,0.5 , and 0.1 , respectively, then what are the expected return, risk(standard deviation) and coefficient of variation for Kate's investment? 3. The beta of an asset is equal to 0 . what will the expected return be? 4. The expected return on the market portfolio is 15 percent, and the return on the risk-free security is 5 percent. What is the expected return on a portfolio with a beta equal to 0.5 ? 5. You know that the CAPM predicts that the market return of a stock is 23.6 percent. If the risk-free rate of return is 8 percent and the expected return on the market is 20 percent, then what is beta? 6. Elaine has narrowed her investment alternatives to two stocks: Stock M, which has a 23 percent expected return, and Stock Y, which has an 8 percent expected return. If Elaine requires a 16 percent return on her total investment, what proportion of her portfolio will she invest in each stock? 7. Barbara is considering investing in a stock, and is aware that the return on that investment is particularly sensitive to how the economy is performing. Her analysis suggests that four states of the economy can affect the return on the investment. Using the table of returns and probabilities below, find the expected return, the standard deviation and coefficient of variation of the return on Barbara's investment. Probability Return Boom 0.1 25.00% Good 0.4 15.00% Level 0.3 10.00% Slump 0.2 -5.00% Probability Return Boom 0.1 25.00% Good 0.4 15.00% Level 0.3 10.00% Slump 0.2 -5.00% Portfolios with more than one asset: Emmy is analyzing a two-stock portfolio that consists of a Utility stock and a Commodity stock. She knows that the return on the Utility has a standard deviation of 40 percent, and the return on the Commodity has a standard deviation of 30 percent. However, she does not know the exact covariance in the returns of the two stocks. If she invests 50% in each stock, Compute : a) expected risk of the portfolio b) Compute the risk( SD) of the portfolio if covariance of the two stock? i. 0.12 , ii. 0 , and iii. -0.12 c) Which covariance results in to better pertfolio, why? Given the returns and probabilities for the three possible states listed here, calculate the covariance, coefficient of correlation between the returns of Stock A and Stock B. Probability Return(A) Return(B) Good 0.35 0.30 0.50 OK 0.50 0.10 0.10 Poor 0.15 -0.25 -0.30 Probability Return(A) Return(B) Good 0.35 0.30 0.50 OK 0.50 0.10 0.10 Poor 0.15 -0.25 -0.30

Answer 1

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Answer 2

Question 1 asks for computation of total return which requires adding dividends and capital gains for each year then dividing by initial investment for percentage total return. For instance, at the end of 2020, the dividend received is 20,000 birr and the capital gain (or loss) is computed by multiplying the number of shares by the difference in share price with the purchase price (100 * (1100 - 1000) = 10,000 birr). Total return in birr would then be 30,000 birr and as a percentage, the total return would be 30,000/ (1000*100) * 100%.Question 2 employs the concept of expected return. To find the expected return, multiply each possible outcome with its probability and then sum these up. The standard deviation (risk) can be computed as the square root of the summation of the probability of each state times the square of the return in each state subtracted by the squredaneswer of the expected return. The coefficient of variatino is derived by dividing the standard deviation by the expected return.Question 3 talks about beta which measures an inherent risk linked with an investment and the correlation between an investment and the market. According to the CAPM or the Capital Asset Pricing Model, an asset with a beta of 0 has an expected return equal to the risk-free return. There is no risk premium associated it.Question 4 brings in the concept of beta and CAPM. The expected return on a portfolio comprising one risky and one risk-free asset in respects to this risk can be derived using the formula of expected return = rf + β(rm - rf) where rf = return on risk-free security, β = beta of portfolio and rm = return on market portfolio.Question 5's context is also CAPM. In which, beta happens to be a measure of market risk. Formula to compute beta = (rm - rf)/rm, here the values of risk-free rate, market return are all figures spoken of.Question 6 applies Expected Portfolio Return formula wirther quantifying individual proportions of investment in stock equals their weighted average.Question 7 has a find similar objectives as question 2 regarding expected values, standard deviation and coefficient of variation, but in this case probabilities of each measurement are no longer equal.Question 8 comprises components of portfolio variance and pertfolio standard deviation, combined based on the weights (amount of money you pour in into investments), standard deviations and their covariance.Question 9 comes down to calculation of the covariance and constant of correlation between the returns designed for both stocks, - giving importance to instances of stock B along with A, in 3 circumstances.

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