You are considering investing $1,000 in a T-bill that pays 0.05 and a risky portfolio,P,constructed with 2 risky securities,X and Y.The weights of X and Y in P are 0.60 and 0.40,respectively.X has an expected rate of return of 0.14 and variance of 0.01,and Y has an expected rate of return of 0.10 and a variance of 0.0081.What would be the dollar values of your positions in X and Y,respectively,if you decide to hold 40% percent of your money in the risky portfolio and 60% in T-bills?
A) $240;$360
B) $360;$240
C) $100;$240
D) $240;$160
E) cannot be determined

Question

Quizplus · Accepted Answer

To determine the dollar values of the positions in securities X and Y, we will use the following formula:

Weight of X in P * Total investment in P = Dollar value of X position

Weight of Y in P * Total investment in P = Dollar value of Y position

Let's first determine the total investment in P. Since we are investing 40% of our $1000 in P and 60% in T-bills, we have:

Total investment = 0.40 * $1000 = $400 in P
Total investment = 0.60 * $1000 = $600 in T-bills

Now we can use the formula above to find the dollar values of the positions in X and Y:

Dollar value of X position = 0.60 * $400 = $240
Dollar value of Y position = 0.40 * $400 = $160

Therefore, the answer is D, $240 and $160.

You Are Considering Investing $1,000 in a T-Bill That Pays