Use the following portfolio information to answer questions 6 through 12 Assume you have amassed a $20 million position in Stock X. Stock X has a 26% annual volatility. Also assume you have amassed a $30 million position in Stock Q. Stock Q has a 35% annual volatility. Also assume the correlation between the rates of return for Stocks Q and X is equal to 45%. 6. What is the annual USD or $ volatility (or daily $\sigma$ = daily standard deviation) for Asset X? 7. What is the daily USD or $ volatility (or daily $\sigma$ = daily standard deviation) for Asset X? 8. What is the daily USD or $ volatility (or daily $\sigma$ = daily standard deviation) for Asset Q? 9. What is the daily portfolio covariance for the portfolio consisting of Asset X and Asset Q? 10. What is the daily portfolio standard deviation for the portfolio consisting of Asset X and Asset Q? 11. What is the 10-day 98.50% VaR in USD or $'s for the portfolio consisting of Asset X and Asset Q? 12. How do you interpret or describe the VaR value calculated in Question 11?
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Suppose that you are trying to develop a strategy for investing in a portfolio that consists of two different stocks (stock X and stock Y). The anticipated annual return for a $1000 investment in each stock under four different economic conditions has the following probability distribution: Probability | Economic condition | Stock X | Stock Y 0.1 | Recession | -$30 | $120 0.3 | Slow Growth | -$10 | $60 0.4 | Moderate Growth | $40 | -$15 0.2 | Fast Growth | $80 | -$50 (a) Compute the individual expected returns for stock X and stock Y. (b) Compute the individual standard deviations for stock X and stock Y. (c) Compute the covariance between stock X and stock Y. Explain your result. (d) If you were to invest in either stock X or stock Y, which one would you prefer? Explain. (e) Suppose that now you want to create a portfolio that consists of stock X and stock Y. In particular, you want to have 40% of your portfolio consist of stock X and the remainder of your portfolio with stock Y. Compute the expected return on the portfolio and the portfolio risk (i.e. standard deviation of the return from the portfolio). Explain how these numbers compare to (as a % of) the risk and the return obtained when ONLY invested in stock X or Y? WITHOUT making calculations, explain how the expected return on the portfolio would change if we invested in both stocks X and Y equally.
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Person interested in constructing a portfolio. Two stocks are being considered. The percent return for an investment in stock X is 40% and the expected return and variance for stock X are E(x) = 5.590 and Var(x). The expected return and variance for stock Y are E(y) = 17% and Var(y). The covariance between the returns of stock X and stock Y is unknown. What is the standard deviation (as a percent) for an investment in stock X? What is the standard deviation (as a percent) for an investment in stock Y? Using the standard deviation as a measure of risk, which of these stocks is the riskier investment? Is an investment in stock X considered to be risky compared with an investment in stock Y? What is the expected return and standard deviation (in dollars) for a person who invests $600 in stock X? What is the expected percent return and standard deviation (as a percent) for a person who constructs a portfolio by investing 50% in each stock? What is the expected percent return and standard deviation (as a percent) for a person who constructs a portfolio by investing 70% in stock X and 30% in stock Y? Compute the correlation coefficient for stock X and stock Y.
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A person is interested in constructing a portfolio. Two stocks are being considered. Let x = percent return for an investment in stock 1, and y = percent return for an investment in stock 2. The expected return and variance for stock 1 are E(x) = 8.45% and Var(x) = 25. The expected return and variance for stock 2 are E(y) = 3.40% and Var(y) = 1. The covariance between the returns is σxy = -3. (a) What is the standard deviation (as a percent) for an investment in stock 1? % What is the standard deviation (as a percent) for an investment in stock 2? % Using the standard deviation as a measure of risk, which of these stocks is the riskier investment? An investment in stock 1 would be risky compared with an investment in stock 2. (b) What is the expected return and standard deviation, in dollars, for a person who invests $400 in stock 1? expected return $ standard deviation $ (c) What is the expected percent return and standard deviation (as a percent) for a person who constructs a portfolio by investing 50% in each stock? (Round your answer for standard deviation to four decimal places.) expected return % standard deviation % (d) What is the expected percent return and standard deviation for a person who constructs a portfolio by investing 70% in stock 1 and 30% in stock 2? (Round your answer for standard deviation to four decimal places.) expected return % standard deviation % (e) Compute the correlation coefficient for x and y. Comment on the relationship between the returns for the two stocks. There is not a relationship between the variables.
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