a.
To determine: Choosing between appropriate risk-averse person prefer to invest.
Introduction:
Arbitrage Pricing Theory (APT) is a substitute form of CAPM (
a.
Answer to Problem 8QP
The investor should prefer second market.
Explanation of Solution
In order to prefer the suitable investment it is required to calculate the variance of the portfolios formed by the various stocks from market. The diversification is effective here and it is rational that each investor prefers their own market to invest and buy from the market. We know the variables,
Suppose if we believe that the stocks in portfolio are weighted equally, the weight of each stock is
Suppose if a portfolio is formulated with many stocks with a percentage of
In our scenario,
To implement the above we need to calculate RP and E(RP). By using the supposition on equal weights and substituting the equation for Ri,
We evoke from statistics a property of expected value which is if,
Here “a” is constant and
We use the above equation to find
Now we combine and substituting both the results into a equation for variance,
The last point is since there is many stocks in each market as we require the limit is
Because
Additionally the question says that
Summary of Equations
Now we choose between appropriate risk-averse person prefer to invest,
By substituting
Since the
Therefore investor should prefer the second market
b.
To determine: Choosing between appropriate risk-averse person prefer to invest.
b.
Answer to Problem 8QP
The investor should prefer second market.
Explanation of Solution
Determine the Variance for each Portfolio
Assuming that
Since the
Therefore investor should prefer the second market
c.
To determine: Choosing between appropriate risk-averse person prefer to invest.
c.
Answer to Problem 8QP
The investor should be indifferent between the two markets.
Explanation of Solution
Determine the Variance for each Portfolio
Assuming that
Since the
Therefore investor should be indifferent between the two markets
d.
To determine: The Relationship between the Correlations of Disturbances in two markets.
d.
Explanation of Solution
It is found that the expected return are equal the indifference involves that the variance of portfolio of the two markets are identical. As a result we set the variance formula identical and calculate for the correlation of a market with the other market.
Hence for each set of correlations that have a relationship like in part c, a risk averse investor is entitled as indifferent between the two markets.
Want to see more full solutions like this?
Chapter 12 Solutions
CORPORATE FINANCE(LL)
- An analyst has modeled the stock of a company using the Fama-French three-factor model. The market return is 10%, the return on the SMB portfolio (rSMB) is 3.2%, and the return on the HML portfolio (rHML) is 4.8%. If ai = 0, bi = 1.2, ci = 20.4, and di = 1.3, what is the stock’s predicted return?arrow_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 table, which gives a security analyst’s expected return on two stocks and the market index in two scenarios: Scenario Probability Market Return Aggressive Stock Defensive Stock 1 0.5 8% 3.5% 5.3% 2 0.5 20 26 10 Required: a. What are the betas of the two stocks? (Round your answers to 2 decimal places.) b. What is the expected rate of return on each stock? (Round your answers to 2 decimal places.) c. If the T-bill rate is 8%, what are the alphas of the two stocks? (Negative values should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to 2 decimal places.)arrow_forward
- You are using the CAPM to calculate a fair return for Stardust common stock. The shares have a volatility of 28.00%, while the market has a volatility of 15.00%. The correlation between the two sets of returns is 0.3. The risk free rate is 2.60%, while the expected return on the market is 4.80%. What is the fair return for Stardust common stock?arrow_forwardConsider the following table, which gives a security analyst’s expected return on two stocks in two particular scenarios for the rate of return on the market: Market Return Aggressive Stock Defensive Stock 5% -3 4% 24 36 9 a. What are the betas of the two stocks? (Do not round intermediate calculations. Round your answers to 2 decimal places.) b. What is the expected rate of return on each stock if the two scenarios for the market return are equally likely to be 5% or 24%? (Do not round intermediate calculations. Round your answers to 1 decimal place.) c. What hurdle rate should be used by the management of the aggressive firm for a project with the risk characteristics of the defensive firm’s stock if the two scenarios for the market return are equally likely? Also, assume a T-Bill rate of 4%. (Do not round intermediate calculations. Round your answer to 2 decimal places.)arrow_forwardAn antitrust case has lead to you having to calculate a fair return (using the CAPM) for RadioEthiopea common stock. The market has a volatility of 18.00%, while the shares have a volatility of 33.00%. The correlation between the two sets of returns is -0.10. The risk free rate is 1.90%, while the expected return on the market is 4.30%. What is the fair return for RadioEthiopea common stock? 1.11% 1.77% 1.46% 1.66%arrow_forward
- Assume the return on a market index represents the common factor and all stocks in the economy have a beta of 1. Firm-specific returns all have a standard deviation of 31%. Suppose an analyst studies 20 stocks and finds that one-half have an alpha of 2.0%, and one-half have an alpha of –2.0%. The analyst then buys $1.1 million of an equally weighted portfolio of the positive-alpha stocks and sells short $1.1 million of an equally weighted portfolio of the negative-alpha stocks. Required: a. What is the expected profit (in dollars), and what is the standard deviation of the analyst’s profit? (Enter your answers in dollars not in millions. Do not round intermediate calculations. Round your answers to the nearest dollar amount. b-1. How does your answer for standard deviation change if the analyst examines 50 stocks instead of 20?arrow_forwardConsider the following table, which gives a security analyst's expected return on two stocks for two particular market returns: Market return Aggressive Stock Defensive Stock 7% 4% 2.5% 25 38 16 What is the expected rate of return on each stock if the market return is equally likely to be 7% or 25%?arrow_forward
- EBK CONTEMPORARY FINANCIAL MANAGEMENTFinanceISBN:9781337514835Author:MOYERPublisher:CENGAGE LEARNING - CONSIGNMENTIntermediate Financial Management (MindTap Course...FinanceISBN:9781337395083Author:Eugene F. Brigham, Phillip R. DavesPublisher:Cengage Learning