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Salsk061 [2.6K]
3 years ago
5

Given the following information, what is the standard deviation of the returns on a portfolio that is invested 40 percent in Sto

ck A, 35 percent in Stock B, and the remainder in Stock C?
Rate of Return is State Occurs

State of Economy Probability of State of economy Stock A Stock B Stock C

Normal .65 14.3% 16.7% 18.2%
Recession .35 -9.8% 5.4% -26.9%

a. 12.72 percent
b. 14.07 percent
c. 1.41 percent
d. 7.41 percent
e. 11.86 percent
Business
1 answer:
olasank [31]3 years ago
3 0

Answer:

The correct option is e. 11.86 percent.

Explanation:

Note: The data in this question are merged together and they are therefore sorted before answering the question. See the attached pdf for the full question with the sorted data.

The standard deviation of the returns on a portfolio can now be calculated using the following steps:

Step 1: Calculation of expected returns under each state of the economy

This can be calculated using the following formula:

Expected return under a state of the economy = (Percentage invested in Stock A * Return of Stock A under the state of the economy) + (Percentage invested in Stock B * Return of Stock B under the state of the economy) + (Percentage invested in Stock C * Return of Stock C under the state of the economy) …………… (1)

Substituting the relevant values into equation (1), we have:

Expected return under Normal = (40% * 14.3%) + (35% * 16.7%) + (25% * 18.2%) = 0.16115

Expected return under Recession = (40% * (-9.8%)) + (35% * 5.4%) + (25% * (-26.9%)) = -0.08755

Step 2: Calculation of expected return of the portfolio

This can be calculated using the following formula:

Portfolio expected return = (Probability of Normal Occurring * Expected Return under Normal) + (Probability of Recession Occurring * Expected Return under Recession) …………………. (2)

Substituting the relevant values into equation (2), we have:

Portfolio expected return = (0.65 * 0.16115) + (0.35 * (-0.08755)) = 0.074105

Step 3: Calculation of the variance of the returns on the portfolio

This can be calculated using the following formula:

Variance of the portfolio = (Probability of Normal Occurring * (Expected Return under Normal - Portfolio expected return)^2) + (Probability of Recession Occurring * (Expected Return under Recession - Portfolio expected return)^2) …………………….. (3)

Substituting the relevant values into equation (3), we have:

Variance of the portfolio = (0.65 * (0.16115 - 0.074105)^2) + (0.35 * (-0.08755 - 0.074105)^2) = 0.014071259475

Step 4: Calculation of the standard deviation of the returns on the portfolio

This can be calculated using the following formula:

Standard deviation of the portfolio = Variance of the portfolio^0.5 ............. (4)

Substituting the variance of the portfolio obtained in step 3 into equation (4), we have:

Standard deviation of the portfolio = 0.014071259475^0.5 = 0.118622339696197, or 11.8622339696197%

Rounding to 2 decimal places, we have:

Standard deviation of the portfolio = 11.86%

This implies the standard deviation of the returns on the portfolio is 11.86%.

Therefore, the correct option is e. 11.86 percent.

Download pdf
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Answer:

$15,000

Explanation:

Complete question <em>"Rhett purchased a 12% zero-coupon bond with a 15-year maturity and a $15,000 par value 15 years ago. The bond matures tomorrow. How much will Rhett receive in total from this investment, assuming all payments are made on these bonds as expected?"</em>

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A - Answer:

To answer the question, we must consider two key terms:

1. Outsourcing; and

2. Internal Controls

1. In business, Outsourcing refers to the practice of engaging a party outside a company to perform services and create goods that were previously performed internally by the company's employees and staff.

This business move is usually undertaken by organisations who are looking to reduce costs. One of its side effects is that it affects a lot of jobs, ranging from customer support to manufacturing to the back office.

2. Internal Controls refer to systematic measures (such as reviews, checks and balances, methods and procedures) created by a business entity to conduct its operations in an orderly and efficient manner, safeguard its assets and resources, deter and detect errors, fraud, and theft, ensure accuracy and completeness of its accounting data, produce reliable and timely financial and management information, and ensure adherence to its policies and objectives.

In business, the outsourcing service provider will usually report to the Internal Control Unit of the company outsourcing its service.

The problems that arise include but are not limited to the following:

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A - Explanation:

i) <em>Vicarious Liability:</em> There are liabilities associated with Spotless, Inc.,'s activities. Ifs such a liability engage, it can be vicariously transferred to Time Treasures Company.

Vicarious Liability is a concept which holds that there can be a person responsible for the actions of another because of a special relationship the parties maintain, like employee/employer and parent/child. Outsourcing is one of such relationships.

Even though there is a legal agreement backed up by consideration between Time Treasures Company and Spotless Inc., should a visitor slip and fall within the premises from a wet or slippery ground that was just cleaned, they most likely would hold Time Treasure Liable.

<em>ii) Quality of Service Delivery</em>

Internal control, because of the reason stated above, will still bear the responsibility of supervising the Janitorial company to ensure that their work lines up with its standards, policies, goals and objectives. The challenge, therefore, is how does Time Treasures' internal control interact with Spotless Inc.?

How will it ensure accountability?

It is often said that one can outsource an activity but not the responsibility that comes with executing the activity or getting the work done to specification.

So how does one ensure responsibility and accountability with a third party?

<em>iii) Security Threats   </em>

With new entities accessing Time Treasures' system, there is a new level of security threat.

This is because cleaners usually are given access to every part of the company. Given that the recruitment process of Time Treasures' most likely will be different from those of Spotless Inc. There might have been loopholes in their recruitment process (for instance, overlooking background checks) which could lead to the existence of a bad hire with a potential to commit fraud or theft.

B - Answer:

Some of the recommendations to control risk after reading the contract include but are not limited to:

1. Understand and Monitor Point of Interaction with the system

2. Clarify expectations using Service-level agreements containing protocols, standards, and expectations

3. Monitoring of Spotless Inc. to ensure that her (that is Time Treasure) controls are working

B - Explanation

<em>1. Understand and Monitor Point of Interaction with the system</em>

Monitoring the performance or activities Spotless Inc. staff would be a necessary function of Internal Control. Time Treasure would have to determine if the interactions are at the control activity or enterprise level. This helps to highlight high risky security point in the system.

<em>2. Clarifying expectation using Service Level Agreements</em>

Getting the Spotless Inc. to sign a service level agreement itemizing expectations concerning protocols, standards, about how those third parties are going to perform relative to the control environment is a great way to mitigate the risks of irresponsibility.

<em>3. </em>Companies monitor how the third parties are performing and verify the activities that third parties are undertaking to make sure controls are operating effectively.

Performance monitoring can be executed through a right-to-audit clause in the Service Level AGreement that gives either the company or auditor permission to perform testing.

Cheers!

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