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You have $16,000 to invest in a stock portfolio. Your choices are Stock X with an expected return...

Question:

You have $16,000 to invest in a stock portfolio. Your choices are Stock X with an expected return of 15 percent and Stock Y with an expected return of 10 percent. If your goal is to create a portfolio with an expected return of 12.85 percent, how much money will you invest in Stock X and Stock Y? (Do not round intermediate calculations. Round your answer to the nearest dollar, e.g. 32).

Amount Invested
Stock X $                     
Stock Y $                    

Weighted average returns of a portfolio:

Weighted average returns on a portfolio can be calculated as sum of products of Weights and return of each individual asset present in the portfolio. The portfolio weights can also be calculated using the same formula if the portfolio returns are provided.

Answer and Explanation: 1

The basic formula for expected return from portfolio is:

{eq}Return =\sum_{w_{i}*r}^{i} {/eq}

Here 'w' is the weight on individual asset and 'r' is the return.

For two asset the formula can be shortened to:

{eq}Return= (w_{X}*r_{X})+(w_{Y}*r_{Y}) {/eq}

Here we have:

Return=12.85

rX=15

rY=10

Now wX+wY=1, since these are the only assets present.

wX=1-wY

Hence we substitute wX with 1-wY in the equation.

12.85=((1-wY)*15)+(wY*10)

12.85=15-15wY+10wY

wY=0.43 or 43%

wX=1-0.43=0.57 or 57%

Hence the amounts invested are:

X=$16,000*0.57=$9,120

Y=$16,000*0.43=$6,880


Learn more about this topic:

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Portfolio Weight, Return & Variance: Definition & Examples

from

Chapter 12 / Lesson 1
20K

A portfolio can be designed in several different ways. It is important to understand the basics of a portfolio before building and managing one. In this lesson, we will go over the weight, return, and variance of a portfolio.


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