MBA 8415 — MANAGERIAL FINANCE
Assignment 5Dr. David A. Stangeland
Do not round any intermediate calculations. Final dollar answers may be rounded to two decimal places (e.g., $125.89). Final % rate, standard deviation, and portfolio weight, answers may be rounded to 8 decimal places (e.g., .12345678 or 12.345678%). Answer in the spaces provided.
1.PanCanadian Corp. stock was priced at $15 per share one year ago when you bought it. Today it just paid a dividend of $2 and its current price is $14 per share.
a)The dollar return on your investment is $______.
b)The percent return on your investment is ______%.
c)If the risk-free rate of return over this time period is 5% then PanCanadian Corp had a risk premium of
______%.
2.In the last six years, Manitoba Television Services (MTS) stock had the following returns:
Year / 1 / 2 / 3 / 4 / 5 / 6Return / 100% / -50% / 40% / -29% / 60% / -37.5%
a)The mean (or arithmetic average) annual return is ______%.
b)The 6-year holding period return is ______%.
c)The 6-year holding period return expressed as an effective rate per year is______%.
d)Which of the above returns best indicates how a 6-year investment in MTS performed? ______
e)The sample variance of the yearly returns is ______
f)The sample standard deviation of returns is ______
3.Use the data below to answer the following questions.
Security / Expected Return / Standard Deviation1 / .08 / 0
2 / .10 / .20
3 / .20 / .40
a)Assume 23 is -0.50 and your portfolio consists of securities 2 and 3.
Use calculus to determine the portfolio weights that will give you the minimum standard deviation portfolio. Hint, substitute in (1-x3) for x2, then take the derivative of the portfolio variance with respect to x3, set the derivative equal to zero and solve for x3, then solve for x2. If you cannot use calculus, use Excel and the solver tool to determine the solution; again, express x2 as (1-x3) in your formula and then use solver to solve for x2 that minimizes the result. Attach either the calculus derivation or the spreadsheet (including solver output) to the submitted assignment.
i)x2 = ______%
ii)x3 = ______%
iii)The standard deviation of this portfolio is ______.
iv)Its expected return is ______%.
v)On the graph below, carefully plot the feasible set of portfolios of securities 2 and 3 (assuming nonnegative weights for each security). Determine and plot at least five points.
b)Now assume 23 is +1.0 and your portfolio consists of securities 2 and 3.
i)On the graph below, carefully plot the feasible set of portfolios of securities 2 and 3 (assuming nonnegative weights for each security).
c)Suppose 23 is still +1.0 but now your portfolio can consist of all three securities.
i)On the graph below, carefully plot the feasible set of portfolios of securities 1, 2 and 3 (assuming nonnegative weights for each security).
ii)Indicate on the above graph which of the possible portfolios a rational risk-averse investor might consider choosing; i.e., which portfolios are efficient. Show which of the possible portfolios a rational risk-averse investor would never consider choosing; i.e., which ones are dominated. Clearly indicate your answers.
d)Now assume 23 is -1.0 and your portfolio consists of securities 2 and 3.
Determine the portfolio weights that will give you the minimum standard deviation portfolio. Hint, no calculus is necessary.
i)x2 = ______%
ii)x3 = ______%
iii)The standard deviation of this portfolio is ______.
iv)Its expected return is ______%.
v)On the graph below, carefully plot the feasible set of portfolios of securities 2 and 3 (assuming nonnegative weights for each security).
vi)Find two sets of portfolio weights that result in a portfolio with standard deviation equal to 0.10. Hint: the variance is 0.01; there are 2 square roots of 0.01 (one + and one -).
x2 = ______%
x3 = ______%
Or
x2 = ______%
x3 = ______%
vii)Which of the two portfolios with = 0.10 (from vi) would you recommend to a rational risk-averse investor? Explain very briefly.
Copyright 2002 David A. StangelandPage 1 of 4