Question

Suppose all possible investment opportunities in the world are limited to the four stocks list in the table​ below:

Stock	Price per Share	Number of Shares Outstanding ​(Millions)
Taggart Transcontinental	​$15.60	25
Rearden Metal	​$13.00	45
Wyatt Oil	​$29.25	10
Nielson Motors	​$26.25	26

Suppose that you are holding a market portfolio and you have invested​ $18,000 in Taggart Transcontinental. The number of shares of Rearden Metal that you hold is closest​ to:

A.

925 shares

B.

780 shares

C.

2076 shares

D.

1730 shares

Answer 1

Stock	Price	Number of shares	Market value
Taggart	$15.60	25,000,000	$390,000,000
Rearden	$13.00	45,000,000	$585,000,000
Wyatt oil	$29.25	10,000,000	$292,500,000
Nielson motors	$26.25	26,000,000	$682,500,000
Total market value			$1950,000,000

Computation of weight of each asset

Stock	Market value (M)	Weight = M / T
Taggart	$390,000,000	0.20
Rearden	$585,000,000	0.30
Wyatt oil	$292,500,000	0.15
Nielson motors	$682,500,000	0.35
Total market value (T)	$1950,000,000

If invested $18,000 in Taggart transcontinental The total value of the investment in the portfolio = $18,000 / 0.20 = $90,000

So, investment made in Rearden metal = Total investment value in portfolio * weight of rearden

= $90,000 * 0.30 = $27,000

Number of shares = $27,000 / $13 = 2,076 shares

So, Number of shares in Rearden metal = 2,076 shares