If the returns on a stock index can be characterized by a normal distribution with mean 12%, the probability that returns will be lower than 12% over the next period equals: 50% 25% 46% 33% 70%
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- Consider a stock portfolio consisting of two units of S' and one unit of S2. Calculate the probability of delta losses over one day, if the daily log-returns (X1, X2) of the stocks are independent with X1 are S = 100, S = 50. N(0.5, 1.1), X2 N(-0.2,0.5) and the current stocks valueAssume that the CAPM holds. One stock has an expected return of 10% and a beta of 0.6. Another stock has an expected return of 11% and a beta of 1.5. What is the expected return on the market?The next year's return on stock X is expected to be either -7% with probability 0.2 or 20% with probability 0.8. Find the stnadard deviation of the returns. a.12.37% b.11.10% c.12.88% d.11.69% e.10.80%
- 5. Given the following expectations for the next year, what is the expected return, standard deviation, and beta of Stock A? Use the excel sheet we covered to find the answer. Returns Probability Stock A Market 0.10 0.05 0.02 0.25 0.09 0.08 0.30 0.13 0.12 0.25 0.19 0.15 0.10 0.21 0.16If a stock has an expected rate of return of 12%. And the standard deviation is 11% then it's annual return will be never negative. True or False? °True °falseYou have estimated the following probability distributions of expected future returns for Stocks X and Y: Stock X Stock Y Probability Return Probability Return 0.1 -12 % 0.2 4 % 0.1 11 0.2 7 0.3 14 0.3 11 0.3 30 0.2 17 0.2 40 0.1 30 What is the expected rate of return for Stock X? Stock Y? Round your answers to one decimal place.Stock X: % Stock Y: % What is the standard deviation of expected returns for Stock X? For Stock Y? Round your answers to two decimal places.Stock X: % Stock Y: % Which stock would you consider to be riskier? is riskier because it has a standard deviation of returns.
- Stocks A and B have the following probability distributions of expected future returns: profitability A B 0.1 11% 27% 0.2 3 0 0.4 12 20 0.2 24 28 0.1 36 43 Calculate the expected rate of return, , for Stock B ( = 12.70%.) Do not round intermediate calculations. Round your answer to two decimal places. % Calculate the standard deviation of expected returns, σA, for Stock A (σB = 18.54%.) Do not round intermediate calculations. Round your answer to two decimal places. % Now calculate the coefficient of variation for Stock B. Do not round intermediate calculations. Round your answer to two decimal places. Is it possible that most investors might regard Stock B as being less risky than Stock A? If Stock B is more highly correlated with the market than A, then it might have the same beta as Stock A, and hence be just as risky in a portfolio sense. If Stock B is less highly correlated with the market than A, then it might have a lower beta than Stock A, and hence be…A stock has the following projected rates of return (outcomes): 10%, 15%, and 30%. The probabilities of their outcomes are 15%, 50%, and 35% respectively. What are the expected return and standard deviation of this stock?XYZ stock's returns will have the following probability distribution during the possible states of the economy.a. Calculate the expected return on XYZ stock.b. Calculate the standard devivation of XYZ stock returns.c. Calculate the coefficient of variation of XYZ stock.State of Economy Probability Return Boom 30% 32.50% Normal 40% 10.25% Recession 30% -15.75%
- EXPECTED RETURNS Stocks X and Y have the following probability distributions ofexpected future returns:Probability X Y0.1 (10%) (35%)0.2 2 00.4 12 200.2 20 2S0.1 38 45a. Calculate the expected rate of return, rˆY, for Stock Y ( rˆX= 12%).b. Calculate the standard deviation of expected returns, σX, for Stock X (σY =20.35%). Now calculate the coefficient of variation for Stock Y. Is it possible thatmost investors will regard Stock Y as being less risky than Stock X? Explain.EXPECTED RETURNS Stocks A and B have the following probability distributions of expected future returns: Probability 0.1 0.2 0.4 0.2 0.1 A (10%) 2 12 20 38 B (35%) 0 20 25 45 a. Calculate the expected rate of return, f, for Stock B (₁ = 12%). b. Calculate the standard deviation of expected returns, σ, for Stock A ( = 20.35%). Now calculate the coefficient of variation for Stock B. Is it possible that most investors will regard Stock B as being less risky than Stock A? Explain. c. Assume the risk-free rate is 2.5%. What are the Sharpe ratios for Stocks A and B? Are these calculations consistent with the information obtained from the coefficient of variation calculations in part b? Explain.Suppose that the index model for stocks A and B is estimated from excess returns with the following results:RA = 3% + .7RM + eARB = −2% + 1.2RM + eBσM = 20%; R-squareA = .20; R-squareB = .12What is the standard deviation of each stock?