Question

In: Finance

Problem 1. Stocks offer an expected rate of return of 18%, with a standard deviation of...

Problem 1. Stocks offer an expected rate of return of 18%, with a standard deviation of 22%. Gold offers an expected return of 10% with a standard deviation of 30%.

a) In light of the apparent inferiority of gold with respect to both mean return and volatility, would anyone hold gold? If so, demonstrate graphically why one would do so.

b) Given the data above, reanswer a) with the additional assumption that the correlation coefficient between gold and stocks equals 1. Draw a graph illustrating why one would or would not hold gold in one’s portfolio. Could this set of assumptions for expected returns, standard deviations, and correlation represent an equilibrium for the security market?

Problem 2. Consider the following properties of the returns of stock 1, the returns of stock 2 and the returns of the market portfolio (m):

Standard deviation of stock 1                                                                         σ1 = 0.30

Standard deviation of stock 2                                                                         σ2 = 0.30

Correlation between stock 1 and the market portfolio                                   ρ1, m = 0.2

Correlation between stock 2 and the market portfolio                                   ρ2, m = 0.5

Standard deviation of the market portfolio                                                     σm = 0.2

Expected return of stock 1                                                                  E (r1) = 0.08

Suppose further that the risk-free rate is 5%.

a) According to the Capital Asset Pricing Model, what should be the expected return on the market portfolio and the expected return of stock 2?

b) Suppose that the correlation between the return of stock 1 and the return of stock 2 is 0.5. What is the expected return, the beta, and the standard deviation of the return of a portfolio that has a 50% investment in stock 1 and a 50% investment in stock 2?

c) Is the portfolio you constructed in part b) an efficient portfolio? Assuming the CAPM is true, could you build a combination of the market portfolio and the portfolio of part b) to increase the expected return of the market portfolio without changing the variance of the combined portfolio.

Solutions

Expert Solution

Problem 1:

a) Gold might seem dominated by stocks but it is still an attractive asset to hold as a part of the portfolio if not alone. If the correlation between gold and stocks is very low, it can be hold as a part in portfolio. In the above graph it can be seen that the graph for the portfolio of stocks and gold touch the optimal allocation line at the optimal tangency portfolio P

b) if the correlation between gold and stocks equal one, then hold should not be held. the set of risk and return combination of stock and gold would plot as a straight line with a negative slope/refer to the graph above. It shows that in this case any portfolio that contains any gold is dominated by only stock portfolio and this holding gold is not an option. If explained in a different manner the CAL for only stock portfolio is steeper than any other CAL passing through all other possible portfolio.

Problem 2:

(a) Computation of the expected return on the market portfolio and the expected return of stock 2 using capital asset pricing model.We have,

Step1: Computation of the beta.We have,

Beta = Correlation between stock 2 and the market portfolio x standard deviation of stock 2 / standard deviation of market

Beta = 0.5 x 0.3/0.2 = 0.75

Hence,the beta of stock 2 is 0.75

Beta of Stock1:

Beta =  Correlation between stock 1 and the market portfolio x standard deviation of stock 1 / standard deviation of market

Beta = 0.2 x 0.3/0.2 = 0.30

Hence,the beta of stock 1 is 0.30

Step2: Computation of the expected return of stock 2.We have,

Expected return = Risk-free return + Beta ( Market return - Risk-free return)

For Stock1:

0.08 = 0.05 + 0.3( Market return - 0.05)

0.3( Market return - 0.05) = 0.03

Market return = 0.1 + 0.05 = 0.15*100 = 15 %

Hence, the expected market return is 15%.

For stock2:

Expected return = 0.05 + 0.75( 0.15 - 0.05)

Expected return = 0.05 + 0.075 = 0.125*100 = 12.50 %

Hence,the expected return of stock 2 is 12.50 %

(b-1) Computation of the expected return of portfolio of stock A & B.We have,

Expected return = (Weight of Stock 1 x Expected return of stock 1) + (Weight of stock 2 x Expected return of stock 2)

Expected return = ( 0.50 x 0.08) + (0.50 x 0.1250)

Expected return = 0.04 + 0.0625 = 0.1025*100 = 10.25 %

Hence,the expected return of the portfolio is 10.25 %.

(b-2) Computation of the standard deviation of the portfolio.We have,

Standard deviation = [ ] 1/2

Standard deviation = [ (0.5)2 (0.3)2 + (0.5)2 (0.3)2 + 2x 0.3 x 0.3 x 0.5x0.5]1/2

Standard deviation = [ 0.0225 + 0.0225 + 0.045 ]1/2

Standard deviation = 0.30*100 = 30 %

Hence,the standard deviation of the portfolio of stock 1 and stock 2 shall be 30%.

(c) Computation of the weight of stock 1 & 2 using minimum variance portfolio.We have,

W1 =

W1 = (0.3)2 - 0.3 x 0.3 x 0.5 / (0.3)2 + (0.3)2 - 2 x 0.3 x 0.3 x 0.5

W1 = 0.09 - 0.045 / ( 0.09 + 0.09 - 0.09)

W1 = 0.045 / 0.09 = 0.5

W1 = 0.50

W2 = 1 - W1 = 1 - 0.50 = 0.50

Hence, the weight of stock 1 & 2 shall be 0.5 and 0.5 by using minimum variance portfolio. Therefore, the portfolio constructed in part(b) is the efficient portfolio and expected return of the market portfolio without changing the variances of the combined portfolio are 10.25 % and there is no change from part(b)


Related Solutions

Stocks offer an expected return of 18%, with a standard deviation 22%. Gold offers an expected...
Stocks offer an expected return of 18%, with a standard deviation 22%. Gold offers an expected return of 10% with a standard deviation of 30%. a) In the light of the apparent inferiority of gold with respect to both mean and return volatility, would anyone hold gold? b) Re-answer (a) with the additional assumption that the correlation coefficient between gold and stocks equals 1. Explain why one would or would not hold gold in one’s portfolio. Could this set of...
The market expected return is 14% with a standard deviation of 18%. The risk-free rate is...
The market expected return is 14% with a standard deviation of 18%. The risk-free rate is 6%. Security XYZ has just paid a dividend of $1 and has a current price of $13.95. What is the beta of Security XYZ if its dividend is expected to grow at 6% per year indefinitely? 1.05 0.85 0.90 0.95
RISK AND RETURN – (A) Consider the expected return and standard deviation of these four stocks...
RISK AND RETURN – (A) Consider the expected return and standard deviation of these four stocks (chart below). If investors are buying only one stock, which one of these stocks would no investor buy? Why? (PLEASE INCLUDE FORMULAS USED TO SOLVE PROBLEM FOR EXCEL). STOCK EXPECTED RETURN STANDARD DEVIATION A 6% 1% B 7% 1.5% C 7% 2% D 8% 2% ADDING AN ASSET TO A PORTFOLIO - (B) Your current portfolio's cash returns over the past three years look...
You manage a risky mutual fund with expected rate of return of 18% and standard deviation...
You manage a risky mutual fund with expected rate of return of 18% and standard deviation of 28%. The T-bill rate is 8%. What is the slope of the CAL of your risky mutual fund? Show the position of your client on your fund’s CAL. Suppose that your client decides to invest in your portfolio a proportion ‘y’ of the total investment budget so that the overall portfolio will have an expected rate of return of 16%. What is the...
Fund A offer an expected return of 8% with a standard deviation of 15%, and Fund...
Fund A offer an expected return of 8% with a standard deviation of 15%, and Fund B offers an expected return of 5% with a standard deviation of 25%. a. Would Fund B be held by investors?Explainwith the aid of a diagram using Markowitz Portfoliotheory.(8marks) b. How would you answer part a. if the correlation coefficient between Funds A and B were 1? Could these expected returnsand standard deviationsrepresent an equilibrium in the market?(12marks)
1 - What is the range, expected rate of return, variance, and standard deviation of the...
1 - What is the range, expected rate of return, variance, and standard deviation of the information below? Economic Condition Probability Expected Return Better than expected 0.15 0.65 Good 0.25 0.3 Average 0.45 0.15 Poor 0.1 -0.15 Terrible 0.05 -0.35 2 - A stock has a beta of 1.65, risk-free rate of return of 0.04, and a market risk premium of 0.15. What is the required rate of return?
What is the expected return, standard deviation, and CV for each of these stocks? Which offers...
What is the expected return, standard deviation, and CV for each of these stocks? Which offers you the best risk/reward ratio? Prob. Alpha Beta 0.2 Great 22% 31% 0.4 Average 12% 15% 0.2 Poor -5% -10% 0.2 Catastrophic -15% -20%
Stocks A and B each have an expected return of 15%, a standard deviation of 20%,...
Stocks A and B each have an expected return of 15%, a standard deviation of 20%, and a beta of 1.2. The returns on the two stocks have a correlation coefficient of -1.0. You have a portfolio that consists of 50% A and 50% B. Which of the following statements is CORRECT? The portfolio's standard deviation is zero (i.e., a riskless portfolio). The portfolio's standard deviation is greater than 20%. The portfolio's expected return is less than 15%. The portfolio's...
What is the Standard deviation ? Consider two stocks, Stock D, with an expected return of...
What is the Standard deviation ? Consider two stocks, Stock D, with an expected return of 13 percent and a standard deviation of 31 percent, and Stock I, an international company, with an expected return of 16 percent and a standard deviation of 42 percent. The correlation between the two stocks is –0.10. What are the expected return and standard deviation of the minimum variance portfolio? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2...
The expected rate of return for Stock A is? The​ investment's standard deviation for stock A?...
The expected rate of return for Stock A is? The​ investment's standard deviation for stock A? COMMON STOCK A       COMMON STOCK B   PROBABILITY   RETURN   PROBABILITY   RETURN 0.20   11%   0.10   -4% 0.60   16%   0.40   7% 0.20   19%   0.40   14%        0.10   22%
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT