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

Given information,

Stock	Quantity	Price at t=0	Price at t=1
Harley-Davidson	100	$60	$90
Yahoo	300	$25	$15

a). Profit of a portfolio is Final value of the portfolio minus Starting value of portfolio

Starting value of portfolio = 100*60 + 300*25 = $13500

Final value of the portfolio = 100*90 + 300*15 = $13500

So profit from portfolio = $13500 - $13500 = $0

b). Return on a portfolio = Profit/Initial value

So, return on above portfolio = 0/13500 = 0%

c). For Harley-Davidson, Return = (Final price - Initial Price)/Initial price

=(90-60)/60 = 50%

d). Same for Yahoo, Return = (15-25)/25 = -40%

e). Weight of an stock in the portfolio is investment in that asset divide by total portfolio

Weight of Harley-Davidson = 6000/13500 = 44.444%

So, Weight of Yahoo = 7500/13500 = 55.556%

f). using weight, we can calculated the portfolio return by taking weighted average return of all the assets.

So for this portfolio, return = w1*r1 + w2*r2 = 44.444*0.50 + 55.556*(-0.40) = 0%

It is same as calculated earlier using the final and initial portfolio value.