You invest $10,000 in a complete portfolio. The complete portfolio is composed of a risky asset...

Question:

You invest $10,000 in a complete portfolio. The complete portfolio is composed of a risky asset with an expected rate of return of 15% and a standard deviation of 21% and a Treasury bill with a rate of return of 5%. How much money should be invested in the risky asset to form a portfolio with an expected return of 11%?

A) $6,000

B) $4,000

C) $7,000

D) $3,000

E) None of the above

Expected Return of a Portfolio:

The expected return of a portfolio is the gain or loss an investor anticipates to generate on an investment portfolio composed of various assets. The calculation of this measure involves identifying the weight of each asset and its rate of return.

Answer and Explanation: 1

The answer is (A) $6,000.

We will use the formula for the expected return of a portfolio with two assets:

{eq}E(R) = W_{1} \times R_{1} + W_{2} \times R_{2} {/eq}, where:

  • W = weight of an asset in the portfolio
  • R = return on the asset

Let us assume that {eq}W_{1} {/eq} is the weight of the risky asset and {eq}W_{2} {/eq} is the weight of the Treasury bill. Recall that {eq}W_{1} + W_{2} = 1 {/eq}, so {eq}W_{2} = 1 - W_{1} {/eq}. Applying this to the formula, we get:

{eq}E(R) = W_{1} \times R_{1} + (1 - W_{1}) \times R_{2} {/eq}

Thus, we have the following equation:

{eq}0.11 = W_{1} \times 0.15 + (1 - W_{1}) \times 0.05 {/eq}

Let us solve for {eq}W_{1} {/eq}.

{eq}0.11 = 0.15W_{1} + 0.05 - 0.05W_{1} {/eq}

{eq}0.15W_{1} - 0.05W_{1} = 0.11 - 0.05 {/eq}

{eq}0.1W_{1} = 0.06 {/eq}

{eq}W_{1} = \dfrac{0.06}{0.1} = 0.6 = 60\% {/eq}

60 percent of $10,000 should be invested in the risky asset giving $6,000.


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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