Question

Suppose you invest in 100 shares of Harley-Davidson at $60 per share and 300 shares of Yahoo at $25 per share. Over the next year, the price of Harley-Davidson increases to $90 and the price of Yahoo decreases to $15 per share.
(a)What is your profit (in $) from the portfolio?

$

(b)Using your answer in part (a), calculate the return on your portfolio (as a percent).

%

(c)What is the return on your investment in Harley-Davidson stock (as a percent)?

%

(d)What is the return on your investment in Yahoo stock (as a percent)?

%

(e)What are the weights (in decimals) of Harley-Davidson and Yahoo in the portfolio at the beginning of the year? (Round your answers to three decimal places.)

Harley-Davidson

Yahoo

(f)

A portfolio is a collection of assets. Therefore, the return of a portfolio can also be expressed in terms of the realized returns of each asset in the portfolio and the weight of each asset. Using this idea, compute the realized returns (as a decimal) of the portfolio (this is the approach used by investors and one that we will use for the remainder of the problems). (Round your answer to two decimal places.)

Answer 1

Answer:

(a) $0 (b) 0% (c) 50% (d) -40% (e) 0.444 and 0.556 (f) -0.05

Explanation:

(a) Profit (in $) = (increase in price per share of Harley-Davidson * number of Harley-Davidson shares held) - (decrease in price per share of Yahoo * number of Yahoo shares held)

= $90 - $60 = $30 increase in Harley Davidson and $25 - $15 =$10 decrease in Yahoo

= ($30*100) - ($10*300) = $0

(b) return on portfolio = return/capital invested * 100 = $0/($60 * 100 + $25 * 300) = $0/$13500 = 0%

(c) return on investment in Harley = return/capital invested in Harley * 100 = $30*100/$60*1000 = $3000/$6000 = 50%

(d) return on investment in Yahoo = return/capital invested in Yahoo * 100 = -$10*300/$25*300 = -$3000/$7500 = - 40% (negative rate of return)

(e) Weighting at the beginning of year (in decimals)

Harley Davidson = $60 * 100 units/ total invested ($60 * 100 + $25 * 300)

                            = $6000/$13500 = 0.444

Yahoo = $25 * 300 units/ total invested

           = $7500/$13500 = 0.556

(f) realized returns (as a decimal) of the portfolio = 0.444*50% + 0.556*-40%

                                                                                 = -0.0493728

                                                                                 = - 0.05 (to decimal places)