Concept explainers
a.
To discuss: If an individual would hold gold over stock and construct a graph for the same.
Introduction: An investor may invest in various stocks to reduce the risk of losses. Such a theory is called correlation theory. It is believed that an investor takes a lot of risk to achieve higher
b.
To discuss: If an individual would hold gold over stock and construct a graph for the same given that the correlation between gold and stock is + 1.
Introduction: An investor may invest in various stocks to reduce the risk of losses. Such a theory is called correlation theory. It is believed that an investor takes a lot of risk to achieve higher returns on their investment portfolio.
c.
To discuss: If the given data and assumption of correlation represent equilibrium in security market.
Introduction: An investor may invest in various stocks to reduce the risk of losses. Such a theory is called correlation theory. It is believed that an investor takes a lot of risk to achieve higher returns on their investment portfolio.
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- Consider the following information for stocks A, B, and C. The returns on the three stocks are positively correlated, but they are not perfectly correlated. (That is, each of the correlation coefficients is between 0 and 1.) Stock Expected Return Standard Deviation Beta A 11.45% 14% 0.9 B 12.55 14 1.1 C 15.30 14 1.6 Fund P has one-third of its funds invested in each of the three stocks. The risk-free rate is 6.5%, and the market is in equilibrium. (That is, required returns equal expected returns.) What is the market risk premium (rM - rRF)? Round your answer to one decimal place. % What is the beta of Fund P? Do not round intermediatearrow_forwardConsider the following information for stocks A, B, and C. The returns on the three stocks are positively correlated, but they are not perfectly correlated. (That is, each of the correlation coefficients is between 0 and 1.) Stock Expected Return Standard Deviation Beta A 9.47% 14% 0.7 B 12.44 14 1.3 C 13.92 14 1.6 Fund P has one-third of its funds invested in each of the three stocks. The risk-free rate is 6%, and the market is in equilibrium. (That is, required returns equal expected returns.) What is the market risk premium (rM - rRF)? Round your answer to two decimal places. % What is the beta of Fund P? Do not round intermediate calculations. Round your answer to two decimal places. What is the required return of Fund P? Do not round intermediate calculations. Round your answer to two decimal places. % Would you expect the standard deviation of Fund P to be less than 14%, equal to 14%, or greater than 14%? Less than 14% Greater than 14%…arrow_forwardConsider the following information for Stocks A,B, and C. The returns on the three stocks are positively correlated, but they are not perfectlycorrelated. (That is, each of the correlation coefficients is between 0 and 1.) Stock Expected Return Standard Deviation BetaA 9.55% 15% 0.9B 10.45 15 1.1C 12.70 15 1.6 Fund P has one-third of its funds invested in each of the three stocks. The risk-free rate is5.5%, and the market is in equilibrium. (That is, required returns equal expected returns.)a. What is the market risk premium (rM - rRF)?b. What is the beta of Fund P?c. What is the required return of Fund P?d. Would you expect the standard deviation of Fund P to be less than 15%, equal to 15%,or greater than 15%? Explain.arrow_forward
- Stock A has an expected return of 12%, a beta of 1.2, and a standard deviation of 20%. Stock B also has a beta of 1.2, but its expected return is 10% and its standard deviation is 15%. Portfolio AB has $300,000 invested in Stock A and $100,000 invested in Stock B. The correlation between the two stocks' returns is zero (that is, rA,B = 0). Which of the following statements is CORRECT? a. The stocks are not in equilibrium based on the CAPM; if A is valued correctly, then B is overvalued. b. The stocks are not in equilibrium based on the CAPM; if A is valued correctly, then B is undervalued. c. Portfolio AB's expected return is 11.0%. d. Portfolio AB's beta is less than 1.2. e. Portfolio AB's standard deviation is 17.5%.arrow_forwardConsider the following information for three stocks, A, B, and C. The stocks' returns are positively but not perfectly positively correlated with one another, i.e., the correlations are all between 0 and 1. Expected Standard Stock Return Deviation Beta A 10% 20% 1.0 B 10% 10% 1.0 C 12% 12% 1.4 Portfolio AB has half of its funds invested in Stock A and half in Stock B. Portfolio ABC has one third of its funds invested in each of the three stocks. The risk-free rate is 5%, and the market is in equilibrium, so required returns equal expected returns. Which of the following statements is CORRECT? a. Portfolio AB's coefficient of variation is greater than 2.0. b. Portfolio AB's required return is greater than the required return on Stock A. c. Portfolio ABC's expected return is 10.66667%. d. Portfolio ABC has a standard deviation of 20%. e. Portfolio AB has a standard deviation of 20%.arrow_forwardConsider the following information for three stocks, Stocks A, B, and C. The returns on the three stocks are positively correlated, but they are not perfectly correlated. (That is, each of the correlation coefficients is between 0 and 1.) Stock Expected Return Standard Deviation Beta A 8.30 % 15 % 0.7 B 10.30 15 1.2 C 11.50 15 1.5 Fund P has one-third of its funds invested in each of the three stocks. The risk-free rate is 5.5%, and the market is in equilibrium. (That is, required returns equal expected returns.) The data has been collected in the Microsoft Excel Online file below. Open the spreadsheet and perform the required analysis to answer the questions below. Open spreadsheet What is the market risk premium (rM - rRF)? Round your answer to two decimal places. fill in the blank 2% What is the beta of Fund P? Do not round intermediate calculations. Round your answer to two decimal places. fill in the blank 3 What is the required return of…arrow_forward
- An individual common stock has a beta of 0.9 and a correlation coefficient of 0.9. The expected return of the stock is 20%, and the standard deviation of its returns is 12%. If a risk-free asset has an expected return of 4%, then: a) the expected return on the market portfolio is 22%. b) the market returns standard deviation is 12%. c) the beta of the market returns is 0.9. d) both a) and b) are true. e) both a) and c) are true. Pls show procedure, thanksarrow_forwardAssume that stock market returns have the market index as a common factor, and that all stocks in the economy have a beta of 1.6 on the market index. Firm-specific returns all have a standard deviation of 25%. Suppose that an analyst studies 20 stocks and finds that one-half of them have an alpha of +2.5%, and the other half have an alpha of −2.5%. Suppose the analyst invests $1.0 million in an equally weighted portfolio of the positive alpha stocks, and shorts $1 million of an equally weighted portfolio of the negative alpha stocks. a. What is the expected profit (in dollars) and standard deviation of the analyst’s profit? (Do not round intermediate calculations. Round your answers to the nearest whole dollar amount.) b. How does your answer change if the analyst examines 50 stocks instead of 20 stocks? 100 stocks? (Do not round intermediate calculations. Round your answers to the nearest whole dollar amount.)arrow_forwardAssume that stock market returns have the market index as a common factor, and that all stocks in the economy have a beta of 1.7 on the market index. Firm-specific returns all have a standard deviation of 25%. Suppose that an analyst studies 20 stocks and finds that one-half of them have an alpha of +2.5%, and the other half have an alpha of -2.5%. Suppose the analyst invests $1.0 million in an equally weighted portfolio of the positive alpha stocks, and shorts $1 million of an equally weighted portfolio of the negative alpha stocks. a. What is the expected profit (in dollars) and standard deviation of the analyst's profit (round to nearest whole dollar amount)? Expected profit (in dollars) Standard deviation b. How does your answer change if the analyst examines 50 stocks instead of 20 stocks? 100 stocks (round to nearest whole dollar amount)? 50 stocks 100 stocks Standard deviatonarrow_forward
- Assume that stock market returns have the market index as a common factor, and that all stocks in the economy have a beta of 1 on the market index. Firm-specific returns all have a standard deviation of 30%.Suppose that an analyst studies 20 stocks and finds that one-half of them have an alpha of +2%, and the other half have an alpha of −2%. Suppose the analyst invests $1 million in an equally weighted portfolio of the positive alpha stocks, and shorts $1 million of an equally weighted portfolio of the negative alpha stocks.a. What is the expected profit (in dollars) and standard deviation of the analyst’s profit?b. How does your answer change if the analyst examines 50 stocks instead of 20 stocks? 100stocks?arrow_forwardStocks 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…arrow_forwardPortfolio P has equal amounts invested in each of the three stocks, A, B, and C. Stock A has a beta of 0.8, Stock B has a beta of 1.0, and Stock C has a beta of 1.2. Each of the stocks has a standard deviation of 25%. The returns on the three stocks are independent of one another (i.e., the correlation coefficients all equal zero). Assume that there is an increase in the market risk premium, but the risk-free rate remains unchanged. Which of the following statements is CORRECT? a. The required return on Stock A will increase by less than the increase in the market risk premium, while the required return on Stock C will increase by more than the increase in the market risk premium. b. The required return on the average stock will remain unchanged, but the returns of riskier stocks (such as Stock C) will increase while the returns of safer stocks (such as Stock A) will decrease. c. The required returns on all three stocks will increase by the amount of the increase in the market…arrow_forward
- EBK CONTEMPORARY FINANCIAL MANAGEMENTFinanceISBN:9781337514835Author:MOYERPublisher:CENGAGE LEARNING - CONSIGNMENT