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 (35%) 0 20 25 45 a. Calculate the expected rate of return, f, for Stock B (= 12%). A b. Calculate the standard deviation of expected returns, a, for Stock A (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.

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 (35%) 0 20 25 45 a. Calculate the expected rate of return, f, for Stock B (= 12%). A b. Calculate the standard deviation of expected returns, a, for Stock A (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.

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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Given the following excess return index model regression results Ra*= -0.059616 + 0.957478Rm* where; \sigma M = 0.80226720, the return on the market portfolio is 0.085306, and the risk-free rate is 0.018302. Note Ra* and Rm* are excess returns. Calculate the actual return for Stock A. Round to 4 decimals, and present answer as a decimal (.08, not 8%) Answer: 0.0228
Assume the CAPM holds and consider stock X, which has a return variance of 0.09 and a correlation of 0.75 with the market portfolio. The market portfolio's Sharpe ratio is 0.30 and the the risk-free rate is 5%. (a) What is Stock X's expected return? (b) What proportion of Stock X's return volatility (i.e. standard deviation) is priced by the market? Explain why this number is less than 1.
2. Suppose that the market model for stocks A and B is estimated with the following results: RA = 1% +0.9*RM+EA RB = -2% + 1.1*RM+EB The standard deviation of the markets returns is 20% and firm specific risk (standard deviation) equals 30% for A and 10% for B. a. Compute the risk (standard deviation) of each stock and the covariance between them. Suppose we form an equally weighted portfolio of stocks A and B. What will be the nonsystematic standard deviation of that portfolio? b.
Give typing answer with explanation and conclusion the expected return on stock A is 11.35%. the expected return on stock B is 8.7%. assuming CAPM holds, if the beta of stock A is higher than the beta of stock B by 0.17, what should the risk premium be?
A stock's returns have the following distribution: Demand for theCompany's Products Probability of thisDemand Occurring Rate of Return ifthis Demand Occurs Weak 0.1 (28%) Below average 0.1 (10) Average 0.4 12 Above average 0.3 22 Strong 0.1 55 1.0 Assume the risk-free rate is 3%. Calculate the stock's expected return, standard deviation, coefficient of variation, and Sharpe ratio. Do not round intermediate calculations. Round your answers to two decimal places. Stock's expected return: % Standard deviation: % Coefficient of variation: Sharpe ratio:
Suppose you inherit $100,000 at age 25 and immediately invested in a growth fund who’s annual rate of return average is 13%. Five years later, you transfer all proceeds from the scrubs fun into a long-term IRA that pays an average annual rate of 8%. Immediately you start making additional contributions of $7000 per year to the same IRA. Assuming continuous interest, steady interest rates, and a perfect record of making annualcontributions, how much is this IRA worth when you reach the age of 65? The formula that will need to be used is A = P e^r*t + D/r (e^r*t - 1). Hint: use the continuous interest formula to find the accumulated amount for the first five years, which is then the annual investment, P, into the IRA.
One of the categories of options available to investors and speculators is LEPOs. Assuming 7.00 per cent margin, what would be the percentage return and dollar profit to an investor who purchased one LEPO (for 1000 shares) for a premium of $26 220 and later closed out the position when the LEPO premium was $28 430?
Consider the following probability distribution for stocks A and B: State Probability Return on Stock A Return on Stock B 1 0.10 10% 8% 2 0.20 13% 7% 3 0.20 12% 6% 4 0.30 14% 9% 5 0.20 15% 8% The coefficient of correlation between A and B is:
We know the following expected returns for stocks A and B, given the different states of the economy: State(s) Probability E(rA,s) E(rB,s) Recession 0.1-0.06 0.04 Normal 0.5 0.09 0.07 Expansion 0.4 0.17 0.11 What is the standard deviation of returns for stock B?
A challenge we run into when forecasting future stock returns is that stock returns compound. So, when using historical averages to forecast the future, we need to average together the arithmetic and geometric average returns using Blume's Formula: R(T) = T GeoAvg + NT Arith Avg N-1 In this formula, N is the number of historical annual returns you are using to calculate your averages and T is the number of future annual returns you are forecasting. Suppose you gather the following prices for a stock in order to calculate the last 10 (N = 10) annual returns. The stock does not pay dividends. Time 0 1 Time 0 calculate the last 10 (N=10) annual returns. The stock does not pay dividends. 1 2 3 4 5 10 6 . 7 8 9 10 Price $23.16 $32.81 Price $23.16 $32.81 $33.63 $36.83 $41.95 $41.04 $33.83 $37.45 $30.56 $29.90 $47.93 Using Blume's formula, what is the expected return per year for the next 4 years (T = 4)? Enter your answer as a percentage, rounded to the nearest 0.0001. For example, for…
Stock A and B have the following probability distributions of expected future returns: Probability A B 0.1 (20%) (46%) 0.2 7 0 0.4 15 15 0.2 23 30 0.1 47 50 What is the expected rate of return for Stock A? What is the standard deviation of returns for Stock B?
Stocks A and B have the following probability distributions of expected future returns: Probability 0.1 (15%) (31%) 0.1 5 0 0.6 15 18 0.1 0.1 22 31 30 49 a. Calculate the expected rate of return, B, for Stock B (A = 13.30%.) Do not round intermediate calculations. Round your answer to two decimal places. % b. Calculate the standard deviation of expected returns, GA, for Stock A (σ = 19.42%.) 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? I. If Stock B is less highly correlated with the market than A, then it might have a higher beta than Stock A, and hence be more risky in a portfolio sense. II. If Stock B is more highly correlated with the market than A, then it might have a higher beta than Stock A, and hence be less risky in…

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