Consider historical data showing that the average annual rate of return on the S&P 500 portfolio over the past 85 years has a oughly 8% more than the Treasury bill return and that the S&P 500 standard deviation has been about 27% per year. Assume alues are representative of investors' expectations for future performance and that the current T-bill rate is 3%. alculate the expected return and variance of portfolios invested in T-bills and the S&P 500 index with weights as shown bel lote: Round your "Expected Return" answers to 2 decimal places and "Variance" answers to 4 decimal places. WBills 0.0 0.2 0.4 0.6 0.8 1.0 WIndex 1.0 0.8 0.6 0.4 0.2 0.0 Expected Return 11.00 % % % % % % Variance 0.0729 Example

Consider historical data showing that the average annual rate of return on the S&P 500 portfolio over the past 85 years has a oughly 8% more than the Treasury bill return and that the S&P 500 standard deviation has been about 27% per year. Assume alues are representative of investors' expectations for future performance and that the current T-bill rate is 3%. alculate the expected return and variance of portfolios invested in T-bills and the S&P 500 index with weights as shown bel lote: Round your "Expected Return" answers to 2 decimal places and "Variance" answers to 4 decimal places. WBills 0.0 0.2 0.4 0.6 0.8 1.0 WIndex 1.0 0.8 0.6 0.4 0.2 0.0 Expected Return 11.00 % % % % % % Variance 0.0729 Example

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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Using single-period arithmetic returns, calculate the value after two periods for the realized returns of these two portfolios: (Portfolio A) $100 invested, realizing a period with a 10% gain, followed by another period with a 10% gain ("average" 10% per period gain) (Portfolio B) $100 invested, realizing a period with a 50% gain, but followed by a period with a 25% loss ("average" 12.5% per period gain) What is the difference in dollars after these two periods (Portfolio A value minus Portfolio B value)?
Consider the following information: State of Economy Probability of State of Economy 0.60 0.40 Boom Bust Rate of Return if State Occurs Stock B Stock C 0.23 0.42 0.08 -0.09 Stock A 0.15 0.16 a. What is the expected return on an equally weighted portfolio of these three stocks? (Do not round Round the final answer to 2 decimal places.) Expected return b. What is the variance of a portfolio invested 20% each in A and B and 60% in C? (Do not round interm the final answer to 6 decimal places.) Variance
Based on current dividend yields and expected capital gains, the expected rates of return on portfolios A and B are 11% and 14%, respectively. The beta of A is .8, while that of B is 1.5. The T-bill rate is currently 6%, while the expected rate of return of the S&P 500 index is 12%. The standard deviation of portfolio A is 10% annually, while that of B is 31%, and that of the index is 20%. a. If you currently hold a market index portfolio, what would be the alpha for Portfolios A and B?
I. Consider the following information about K oll and Nell for one-time period: Suppose that the correlation coefficient between the returns for Koll and Nell is -0.40'. If you invest 30% in Koll and 70% in Nell, what are the expected return and standard deviation of the portfolio? Interpret your results. II. The investor achieved the following annual rate of returns over the last four-year period: 25% in Y1, 15% in Y2, 20% in Y3, 10% in Y4. (a) Calculate the geometric average rate of return for the whole 4 year period. (b) Calculate the logarithmic average rate of return for the whole 4 year period. III. Suppose you have a portfolio of IBM and Dell with a beta of 0.4 and 1.1, respectively. If you put 40% of your money in IBM, 55% in Dell and 5% in the risk-free asset, calculate and interpret the beta of your portfolio. IV. Suppose that the beta value for Kei is 1.5, and the risk-free rate of interest is 4%. The investor wishes to (i) have a shareholding in only one company, Kei, and…
Indicate whether the following statements are true or false (circle one). Use 1 or 2 sentences to discuss why it is so. (a) If R, is simple 1-month return, then the annualized return is 12 x R, after assuming all R = R. True False Why? (b) Let and r GSA be continuously compounded 1 - month returns for Goldman Sachs Group (GS) and American International Group (AIG). If we construct a portfolio using the share ain[0, 1] for GS, the portfolio cc return is ľ AIG = 0x*y +(1-x)*r True False Why? (c) In 5. (b)., if 5% quantile of the portfolio cc return is given as AIG, GS, r 40.05 = -0.5, then 5% monthly Value-at-Risk for the $10,000 investment in this portfolio is $10,000 × (-0.5) = -$ 5,000. True False r
Consider historical data showing that the average annual rate of return on the S&P 500 portfolio over the past 85 years has averaged roughly 8% more than the Treasury bill return and that the S&P 500 standard deviation has been about 26% per year. Assume these values are representative of investors' expectations for future performance and that the current T-bill rate is 5%. Calculate the expected return and variance of portfolios invested in T-bills and the S&P 500 index with weights as shown below. (Enter your answers as decimals rounded to 4 places. Leave no cells blank - be certain to enter "O" wherever required.) Wills Windex Expected Return Variance 0.0 1.0 0.1300 0.0676 Example 0.2 0.8 0.4 0.6 0.6 0.4 0.8 0.2 1.0 0.0
Consider a treasury bill with a rate of return of 5% and the following risky securities:Security A: E(r) = .15; variance = .0400Security B: E(r) = .10; variance = .0225Security C: E(r) = .12; variance = .1000Security D: E(r) = .13; variance = .0625The investor must develop a complete portfolio by combining the risk-free asset with one of the securities mentioned above. The security the investor should choose as part of his complete portfolio to achieve the best Sharpe ratio would be?
Your portfolio allocates equal funds to the DW Co. and Woodpecker, Inc. DW Co. stock has an annual return mean and standard deviation of 15 percent and 44 percent, respectively. Woodpecker, Inc., stock has an annual return mean and standard deviation of 11.4 percent and 58 percent, respectively. The return correlation between DW Co. and Woodpecker, Inc., is zero. What is the smallest expected loss for your portfolio in the coming month with a probability of 16 percent? (Negative value should be indicated by a minus sign. Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Omit the "%" sign in your response.) Smallest expected loss %
Suppose that the S&P 500, with a beta of 1.0, has an expected return of 14% and T-bills provide a risk-free return of 5%. a. What would be the expected return and beta of portfolios constructed from these two assets with weights in the S&P 500 of (i) 0; (ii) 0.25; (iii) 0.50; (iv) 0.75; (v) 1.0? (Leave no cells blank - be certain to enter "0" wherever required. Do not round intermediate calculations. Enter the value of Expected return as a percentage rounded to 2 decimal places and value of Beta rounded to 2 decimal places.) b. How does expected return vary with beta? (Do not round intermediate calculations.)
Your portfolio allocates equal funds to DW Co. and Woodpecker, Inc., DW Co. stock has an annual return mean and standard deviation of 9 percent and 30 percent, respectively. Woodpecker, Inc., stock has an annual return mean and standard deviation of 20 percent and 46 percent, respectively. The return correlation between DW Co. and Woodpecker, Inc., is zero. What is the smallest expected loss for your portfolio in the coming month with a probability of 16 percent? (Negative amounts should be indicated by a minus sign. Round your answer to 2 decimal places. Omit the "%" signs in your response.) Smallest expected loss. -12.81
Your portfolio allocates equal funds to DW Co. and Woodpecker, Inc. DW Co. stock has an annual return mean and standard deviation of 10 percent and 33 percent, respectively. Woodpecker, Inc., stock has an annual return mean and standard deviation of 21 percent and 47 percent, respectively. The return correlation between DW Co. and Woodpecker, Inc., is zero. What is the smallest expected loss for your portfolio in the coming month with a probability of 2.5 percent? (A negative value should be indicated by a minus sign. Do not round intermediate calculations. Round the z-score value to 3 decimal places when calculating your answer. Enter your answer as a percent rounded to 2 decimal places.) Smallest expected loss %
Consider the following table, which gives a security analyst's expectations for return on the market and two well diversified portfolios of cyclical and defensive over the next year, assuming the risk-free rate is 5%: Bust Boom Probability .25 .75 Market Return Cyclical (C) -10% 32% -4% 20% Defensive (D) 2% 14% At least one of the two portfolios is mispriced. Construct an arbitrage strategy with an initial position of $1 (either long or short) in the risk-free asset, to give an arbitrage profit at the end of the year. The arbitrage strategy must not have any position in the market portfolio - you can only hold positions in the risk-free asset, and the cyclical and defensive portfolios. What is the profit per $1 long (or short) the risk-free asset?

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