PRINCIPLES OF CORPORATE FINANCE
13th Edition
ISBN: 9781264052059
Author: BREALEY
Publisher: MCG
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Textbook Question
Chapter 7, Problem 16PS
Portfolio risk
- a) How many variance terms and how many different covariance terms do you need to calculate the risk of a 100-share portfolio?
- b) Suppose all stocks had a standard deviation of 30% and a correlation with each other of .4. What is the standard deviation of the returns on a portfolio that has equal holdings in 50 stocks?
- c) What is the standard deviation of a fully diversified portfolio of such stocks?
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How many variance terms and how many covariance terms do you need to calculate the risk of a 100-share portfolio?
Suppose that all stocks had a standard deviation of 30% and a correlation with each other of 0.4. What is the standard deviation of the returns on a portfolio that has equal holdings in 50 stocks?
What is the standard deviation of a fully diversified portfolio of such stocks?
How many variance terms and how many covariance terms do you need to calculate therisk of a 100-share portfolio?b. Suppose that all stocks had a standard deviation of 30% and a correlation with each otherof 0.4. What is the standard deviation of the returns on a portfolio that has equal holdingsin 50 stocks?c. What is the standard deviation of a fully diversified portfolio of such stocks?
A portfolio management organization analyzes 60 stocks and constructs a mean-variance efficient portfolio using only these 60 securities.a. How many estimates of expected returns, variances, and covariances are needed to optimize this portfolio?b. If one could safely assume that stock market returns closely resemble a single-index structure, how many estimates would be needed?
Chapter 7 Solutions
PRINCIPLES OF CORPORATE FINANCE
Ch. 7 - Rate of return The level of the Syldavia market...Ch. 7 - Real versus nominal returns The Costaguana stock...Ch. 7 - Arithmetic average and compound returns Integrated...Ch. 7 - Risk premiums Here are inflation rates and U.S....Ch. 7 - Risk Premium Suppose that in year 2030, investors...Ch. 7 - Stocks vs. bonds Each of the following statements...Ch. 7 - Expected return and standard deviation A game of...Ch. 7 - Standard deviation of returns The following table...Ch. 7 - Average returns and standard deviation During the...Ch. 7 - Prob. 10PS
Ch. 7 - Prob. 11PSCh. 7 - Diversification Here are the percentage returns on...Ch. 7 - Risk and diversification In which of the following...Ch. 7 - Prob. 14PSCh. 7 - Portfolio risk To calculate the variance of a...Ch. 7 - Portfolio risk a) How many variance terms and how...Ch. 7 - Portfolio risk Table 7.8 shows standard deviations...Ch. 7 - Portfolio risk Hyacinth Macaw invests 60% of her...Ch. 7 - Stock betas What is the beta of each of the stocks...Ch. 7 - Stock betas There are few, if any, real companies...Ch. 7 - Portfolio betas A portfolio contains equal...Ch. 7 - Portfolio betas Suppose the standard deviation of...Ch. 7 - Portfolio risk Here are some historical data on...Ch. 7 - Portfolio risk Suppose that Treasury bills offer a...
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- You have observed the following returns over time: Assume that the risk-free rate is 6% and the market risk premium is 5%. What are the betas of Stocks X and Y? What are the required rates of return on Stocks X and Y? What is the required rate of return on a portfolio consisting of 80% of Stock X and 20% of Stock Y?arrow_forwardWhat is a characteristic line? How is this line used to estimate a stocks beta coefficient? Write out and explain the formula that relates total risk, market risk, and diversifiable risk.arrow_forwardIf a given stock in the portfolio had established 1.23 beta; the related expected return is at 11.7percent, and 3.5percent is the current earning of a risk-free asset; a. Determine the expected return on a portfolio that is equally invested in the two assets? b. If a portfolio of the two assets has a beta of 0.7, what are the portfolio weights? c. If a portfolio of the two assets has an expected return of 9%, what is its beta? d. If a portfolio of the two assets has a beta of 2.46, what are the portfolio weights? How do you interpret the weights for the two assets in this case? Discuss.arrow_forward
- Based on the following information, calculate the expected return and standard deviation for each of the following stocks. What are the covariance and correlation between the returns of the two stocks? Calculate the portfolio return and portfolio standard deviation if you invest equally in each asset. Returns State of Economy Prob J K Recession 0.25 -0.02 0.034 Normal 0.6 0.138 0.062 Boom 0.15 0.218 0.092arrow_forwardGiven: Calculate the expected returns and expected standard deviations of a two-stock portfolio having a correlation coefficient of 0.70 under the following conditions a. w1 = 1.00 b. w1 = 0.75 c. w1 = 0.50 d. w1 = 0.25 e. w1 = 0.05 Plot the results on a return-risk graph. Without calculations, draw in what the curve would look like first if the correlation coefficient had been 0.00 and then if it had been −0.70.arrow_forward(a) Calculate the expected rate of return, variance and standard deviation of Stock X & Stock Y. (b) Assume that the covariance between Stock X and Stock Y is -0.5%. Calculate the expected rate of return, variance and standard deviation of Jenny’s portfolio. (c) Explain why, in general, the portfolio risk is lower than the weighted average of individual stocks’ risk.arrow_forward
- Assume the risk-free rate is r = 3%. Consider the data below:Stock(stock 1, stock 2)Expected Return(15%,7%)Volatility(40%,30%)a) Find the What the minimum variance portfolio when ρ12 = 0? and then computeits expected return and volatility?b) Find the minimum variance portfolio when ρ12= =0.4? and then compute itsexpected return and volatility?c) Determine the tangent portfolios & their respective mean returns and volatilities.arrow_forwardFrom the following information, calculate covariance between stocks A and B and expected return and risk of a portfolio in which A and B are equally weighted.Which stock would be best recommend if investment in individual stock is to be made? Justify the answer using numerical calculations. Stock A Stock B Expected return 24% 35% Standard deviation 12% 18% Coefficient of correlation 0.65arrow_forwardFrom the following information, calculate covariance between stocks A and B and expected return and risk of a portfolio in which A and B are equally weighted.Which stock would be recommend if investment in individual stock is to be made? Justify answer using numerical calculations. Stock A Stock B Expected return 24% 35% Standard deviation 12% 18% Coefficient of correlation 0.65 0.65arrow_forward
- Question: Assume that using the Security Market Line (SML) the required rate of return (RA) on stock A is found to be half of the required return (RB) on stock B. The risk-free rate (Rf) is one-fourth of the required return on A. Return on market portfolio is denoted by RM. Find the ratio of beta of A to beta of B.arrow_forwardWhat are the components of the risk-free rate and What is financial risk? If the standard deviation of a stock’s return is 5% and its expected return is 8%, what it the C.V.?arrow_forwardTable attached shows the historical returns for Companies A, B and C If one investor has a portfolio consisting of 50% Company A and 50% Company B, what are the average portfolio return and standard deviation? What is Sharpe ratio if the risk-free rate is 3.8%? If another investor has a portfolio consisting of 1/3 Company A, 1/3 Company B and 1/3 Company C, what are the average portfolio return and standard deviation? What is Sharpe ratio if the risk-free rate is 3.8%?arrow_forward
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